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requirejs.config({
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paths: {
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'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
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'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.5/lunr.min',
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'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.min',
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\documentclass[12pt,a4paper]{article}
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\usepackage[a4paper,text={16.5cm,25.2cm},centering]{geometry}
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\usepackage{lmodern}
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\setlength{\parskip}{1.2ex}
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\hypersetup
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{ pdfauthor = { Matti Pastell },
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pdftitle={ FIR filter design with Julia },
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colorlinks=TRUE,
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linkcolor=black,
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citecolor=blue,
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urlcolor=blue
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}
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\title{ FIR filter design with Julia }
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\author{ Matti Pastell }
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\date{ 21th April 2016 }
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\begin{document}
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\maketitle
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\section{Introduction}
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This an example of a julia script that can be published using \href{http://mpastell.github.io/Weave.jl/latest/usage/}{Weave}. The script can be executed normally using Julia or published to HTML or pdf with Weave. Text is written in markdown in lines starting with "\texttt{\#'} " and code is executed and results are included in the published document.
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Notice that you don't need to define chunk options, but you can using \texttt{\#+}. just before code e.g. \texttt{\#+ term=True, caption='Fancy plots.'}. If you're viewing the published version have a look at the \href{FIR_design_plots.jl}{source} to see the markup.
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\section{FIR Filter Design}
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We'll implement lowpass, highpass and ' bandpass FIR filters. If you want to read more about DSP I highly recommend \href{http://www.dspguide.com/}{The Scientist and Engineer's Guide to Digital Signal Processing} which is freely available online.
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\subsection{Calculating frequency response}
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DSP.jl package doesn't (yet) have a method to calculate the the frequency response of a FIR filter so we define it:
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\begin{lstlisting}
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(*@\HLJLk{using}@*) (*@\HLJLn{Plots}@*)(*@\HLJLp{,}@*) (*@\HLJLn{DSP}@*)
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(*@\HLJLnf{gr}@*)(*@\HLJLp{()}@*)
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(*@\HLJLk{function}@*) (*@\HLJLnf{FIRfreqz}@*)(*@\HLJLp{(}@*)(*@\HLJLn{b}@*)(*@\HLJLoB{::}@*)(*@\HLJLn{Array}@*)(*@\HLJLp{,}@*) (*@\HLJLn{w}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{range}@*)(*@\HLJLp{(}@*)(*@\HLJLni{0}@*)(*@\HLJLp{,}@*) (*@\HLJLn{stop}@*)(*@\HLJLoB{=}@*)(*@\HLJLn{\ensuremath{\pi}}@*)(*@\HLJLp{,}@*) (*@\HLJLn{length}@*)(*@\HLJLoB{=}@*)(*@\HLJLni{1024}@*)(*@\HLJLp{))}@*)
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(*@\HLJLn{n}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{length}@*)(*@\HLJLp{(}@*)(*@\HLJLn{w}@*)(*@\HLJLp{)}@*)
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(*@\HLJLn{h}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{Array}@*)(*@\HLJLp{{\{}}@*)(*@\HLJLn{ComplexF32}@*)(*@\HLJLp{{\}}(}@*)(*@\HLJLn{undef}@*)(*@\HLJLp{,}@*) (*@\HLJLn{n}@*)(*@\HLJLp{)}@*)
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(*@\HLJLn{sw}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{0}@*)
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(*@\HLJLk{for}@*) (*@\HLJLn{i}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{1}@*)(*@\HLJLoB{:}@*)(*@\HLJLn{n}@*)
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(*@\HLJLk{for}@*) (*@\HLJLn{j}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{1}@*)(*@\HLJLoB{:}@*)(*@\HLJLnf{length}@*)(*@\HLJLp{(}@*)(*@\HLJLn{b}@*)(*@\HLJLp{)}@*)
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(*@\HLJLn{sw}@*) (*@\HLJLoB{+=}@*) (*@\HLJLn{b}@*)(*@\HLJLp{[}@*)(*@\HLJLn{j}@*)(*@\HLJLp{]}@*)(*@\HLJLoB{*}@*)(*@\HLJLnf{exp}@*)(*@\HLJLp{(}@*)(*@\HLJLoB{-}@*)(*@\HLJLn{im}@*)(*@\HLJLoB{*}@*)(*@\HLJLn{w}@*)(*@\HLJLp{[}@*)(*@\HLJLn{i}@*)(*@\HLJLp{])}@*)(*@\HLJLoB{{\textasciicircum}-}@*)(*@\HLJLn{j}@*)
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(*@\HLJLk{end}@*)
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(*@\HLJLn{h}@*)(*@\HLJLp{[}@*)(*@\HLJLn{i}@*)(*@\HLJLp{]}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{sw}@*)
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(*@\HLJLn{sw}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{0}@*)
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(*@\HLJLk{end}@*)
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(*@\HLJLk{return}@*) (*@\HLJLn{h}@*)
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(*@\HLJLk{end}@*)
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\end{lstlisting}
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\begin{lstlisting}
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FIRfreqz (generic function with 2 methods)
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\end{lstlisting}
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\subsection{Design Lowpass FIR filter}
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Designing a lowpass FIR filter is very simple to do with DSP.jl, all you need to do is to define the window length, cut off frequency and the window. We will define a lowpass filter with cut off frequency at 5Hz for a signal sampled at 20 Hz. We will use the Hamming window, which is defined as: $w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$
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\begin{lstlisting}
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(*@\HLJLn{fs}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{20}@*)
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(*@\HLJLn{f}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{digitalfilter}@*)(*@\HLJLp{(}@*)(*@\HLJLnf{Lowpass}@*)(*@\HLJLp{(}@*)(*@\HLJLni{5}@*)(*@\HLJLp{,}@*) (*@\HLJLn{fs}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{fs}@*)(*@\HLJLp{),}@*) (*@\HLJLnf{FIRWindow}@*)(*@\HLJLp{(}@*)(*@\HLJLnf{hamming}@*)(*@\HLJLp{(}@*)(*@\HLJLni{61}@*)(*@\HLJLp{)))}@*)
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(*@\HLJLn{w}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{range}@*)(*@\HLJLp{(}@*)(*@\HLJLni{0}@*)(*@\HLJLp{,}@*) (*@\HLJLn{stop}@*)(*@\HLJLoB{=}@*)(*@\HLJLn{pi}@*)(*@\HLJLp{,}@*) (*@\HLJLn{length}@*)(*@\HLJLoB{=}@*)(*@\HLJLni{1024}@*)(*@\HLJLp{)}@*)
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(*@\HLJLn{h}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{FIRfreqz}@*)(*@\HLJLp{(}@*)(*@\HLJLn{f}@*)(*@\HLJLp{,}@*) (*@\HLJLn{w}@*)(*@\HLJLp{)}@*)
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\end{lstlisting}
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\begin{lstlisting}
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1024-element Array{Complex{Float32},1}:
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1.0f0 + 0.0f0im
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0.99546844f0 + 0.095055714f0im
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0.98191506f0 + 0.1892486f0im
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0.95946306f0 + 0.28172377f0im
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0.9283168f0 + 0.37164196f0im
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0.8887594f0 + 0.45818728f0im
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0.84115064f0 + 0.54057467f0im
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0.7859234f0 + 0.618057f0im
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0.72357976f0 + 0.6899319f0im
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0.65468615f0 + 0.7555481f0im
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(*@\ensuremath{\vdots}@*)
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0.00043952762f0 - 0.00041908873f0im
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0.0005152718f0 - 0.00040521423f0im
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0.0005873293f0 - 0.00037745363f0im
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0.0006531789f0 - 0.0003367371f0im
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0.0007105166f0 - 0.00028444792f0im
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0.0007573364f0 - 0.00022237403f0im
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0.0007920005f0 - 0.00015264557f0im
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0.0008132961f0 - 7.766036f-5im
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0.0008204784f0 - 3.1148685f-18im
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\end{lstlisting}
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\subsection{Plot the frequency and impulse response}
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The next code chunk is executed in term mode, see the \href{FIR_design.jl}{script} for syntax.
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\begin{lstlisting}
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(*@\HLJLnB{julia> }@*)(*@\HLJLn{h{\_}db}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{log10}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{abs}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{h}@*)(*@\HLJLp{));}@*)
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(*@\HLJLnB{julia> }@*)(*@\HLJLn{ws}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{w}@*)(*@\HLJLoB{/}@*)(*@\HLJLn{pi}@*)(*@\HLJLoB{*}@*)(*@\HLJLp{(}@*)(*@\HLJLn{fs}@*)(*@\HLJLoB{/}@*)(*@\HLJLni{2}@*)(*@\HLJLp{)}@*)
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0.0:0.009775171065493646:10.0
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\end{lstlisting}
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\begin{lstlisting}
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(*@\HLJLnf{plot}@*)(*@\HLJLp{(}@*)(*@\HLJLn{ws}@*)(*@\HLJLp{,}@*) (*@\HLJLn{h{\_}db}@*)(*@\HLJLp{,}@*)
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(*@\HLJLn{xlabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Frequency (Hz)"}@*)(*@\HLJLp{,}@*) (*@\HLJLn{ylabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Magnitude (db)"}@*)(*@\HLJLp{)}@*)
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\end{lstlisting}
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\includegraphics[width=\linewidth]{/home/travis/build/mpastell/Weave.jl/doc/build/examples/tmpbkvEK8/FIR_design_4_1.pdf}
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And again with default options
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\begin{lstlisting}
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(*@\HLJLn{h{\_}phase}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{unwrap}@*)(*@\HLJLp{(}@*)(*@\HLJLoB{-}@*)(*@\HLJLn{atan}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{imag}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{h}@*)(*@\HLJLp{),}@*)(*@\HLJLn{real}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{h}@*)(*@\HLJLp{)))}@*)
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(*@\HLJLnf{plot}@*)(*@\HLJLp{(}@*)(*@\HLJLn{ws}@*)(*@\HLJLp{,}@*) (*@\HLJLn{h{\_}phase}@*)(*@\HLJLp{,}@*)
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(*@\HLJLn{xlabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Frequency (Hz)"}@*)(*@\HLJLp{,}@*) (*@\HLJLn{ylabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Phase (radians)"}@*)(*@\HLJLp{)}@*)
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\end{lstlisting}
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\includegraphics[width=\linewidth]{/home/travis/build/mpastell/Weave.jl/doc/build/examples/tmpbkvEK8/FIR_design_5_1.pdf}
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\end{document}
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\documentclass[12pt,a4paper]{article}
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\usepackage[a4paper,text={16.5cm,25.2cm},centering]{geometry}
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\usepackage{lmodern}
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\usepackage{amssymb,amsmath}
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\usepackage{bm}
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\usepackage{graphicx}
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\usepackage{microtype}
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\usepackage{hyperref}
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\setlength{\parindent}{0pt}
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\setlength{\parskip}{1.2ex}
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\hypersetup
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{ pdfauthor = { Matti Pastell },
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pdftitle={ FIR filter design with Julia },
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colorlinks=TRUE,
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linkcolor=black,
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citecolor=blue,
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urlcolor=blue
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}
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\title{ FIR filter design with Julia }
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\author{ Matti Pastell }
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|
||||
\date{ 21th April 2016 }
|
||||
|
||||
\usepackage[T1]{fontenc}
|
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\lstset{
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basicstyle=\ttfamily\footnotesize,
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upquote=true,
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breaklines=true,
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\newcommand{\HLJLgt}[1]{#1}
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||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
|
||||
|
||||
\section{Introduction}
|
||||
|
||||
This an example of a julia script that can be published using \href{http://mpastell.github.io/Weave.jl/latest/usage/}{Weave}. The script can be executed normally using Julia or published to HTML or pdf with Weave. Text is written in markdown in lines starting with "\texttt{\#'} " and code is executed and results are included in the published document.
|
||||
|
||||
|
||||
Notice that you don't need to define chunk options, but you can using \texttt{\#+}. just before code e.g. \texttt{\#+ term=True, caption='Fancy plots.'}. If you're viewing the published version have a look at the \href{FIR_design_plots.jl}{source} to see the markup.
|
||||
|
||||
|
||||
\section{FIR Filter Design}
|
||||
|
||||
We'll implement lowpass, highpass and ' bandpass FIR filters. If you want to read more about DSP I highly recommend \href{http://www.dspguide.com/}{The Scientist and Engineer's Guide to Digital Signal Processing} which is freely available online.
|
||||
|
||||
|
||||
\subsection{Calculating frequency response}
|
||||
|
||||
DSP.jl package doesn't (yet) have a method to calculate the the frequency response of a FIR filter so we define it:
|
||||
|
||||
|
||||
\begin{lstlisting}
|
||||
(*@\HLJLk{using}@*) (*@\HLJLn{Plots}@*)(*@\HLJLp{,}@*) (*@\HLJLn{DSP}@*)
|
||||
(*@\HLJLnf{gr}@*)(*@\HLJLp{()}@*)
|
||||
|
||||
(*@\HLJLk{function}@*) (*@\HLJLnf{FIRfreqz}@*)(*@\HLJLp{(}@*)(*@\HLJLn{b}@*)(*@\HLJLoB{::}@*)(*@\HLJLn{Array}@*)(*@\HLJLp{,}@*) (*@\HLJLn{w}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{range}@*)(*@\HLJLp{(}@*)(*@\HLJLni{0}@*)(*@\HLJLp{,}@*) (*@\HLJLn{stop}@*)(*@\HLJLoB{=}@*)(*@\HLJLn{\ensuremath{\pi}}@*)(*@\HLJLp{,}@*) (*@\HLJLn{length}@*)(*@\HLJLoB{=}@*)(*@\HLJLni{1024}@*)(*@\HLJLp{))}@*)
|
||||
(*@\HLJLn{n}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{length}@*)(*@\HLJLp{(}@*)(*@\HLJLn{w}@*)(*@\HLJLp{)}@*)
|
||||
(*@\HLJLn{h}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{Array}@*)(*@\HLJLp{{\{}}@*)(*@\HLJLn{ComplexF32}@*)(*@\HLJLp{{\}}(}@*)(*@\HLJLn{undef}@*)(*@\HLJLp{,}@*) (*@\HLJLn{n}@*)(*@\HLJLp{)}@*)
|
||||
(*@\HLJLn{sw}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{0}@*)
|
||||
(*@\HLJLk{for}@*) (*@\HLJLn{i}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{1}@*)(*@\HLJLoB{:}@*)(*@\HLJLn{n}@*)
|
||||
(*@\HLJLk{for}@*) (*@\HLJLn{j}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{1}@*)(*@\HLJLoB{:}@*)(*@\HLJLnf{length}@*)(*@\HLJLp{(}@*)(*@\HLJLn{b}@*)(*@\HLJLp{)}@*)
|
||||
(*@\HLJLn{sw}@*) (*@\HLJLoB{+=}@*) (*@\HLJLn{b}@*)(*@\HLJLp{[}@*)(*@\HLJLn{j}@*)(*@\HLJLp{]}@*)(*@\HLJLoB{*}@*)(*@\HLJLnf{exp}@*)(*@\HLJLp{(}@*)(*@\HLJLoB{-}@*)(*@\HLJLn{im}@*)(*@\HLJLoB{*}@*)(*@\HLJLn{w}@*)(*@\HLJLp{[}@*)(*@\HLJLn{i}@*)(*@\HLJLp{])}@*)(*@\HLJLoB{{\textasciicircum}-}@*)(*@\HLJLn{j}@*)
|
||||
(*@\HLJLk{end}@*)
|
||||
(*@\HLJLn{h}@*)(*@\HLJLp{[}@*)(*@\HLJLn{i}@*)(*@\HLJLp{]}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{sw}@*)
|
||||
(*@\HLJLn{sw}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{0}@*)
|
||||
(*@\HLJLk{end}@*)
|
||||
(*@\HLJLk{return}@*) (*@\HLJLn{h}@*)
|
||||
(*@\HLJLk{end}@*)
|
||||
\end{lstlisting}
|
||||
|
||||
\begin{lstlisting}
|
||||
FIRfreqz (generic function with 2 methods)
|
||||
\end{lstlisting}
|
||||
|
||||
|
||||
\subsection{Design Lowpass FIR filter}
|
||||
|
||||
Designing a lowpass FIR filter is very simple to do with DSP.jl, all you need to do is to define the window length, cut off frequency and the window. We will define a lowpass filter with cut off frequency at 5Hz for a signal sampled at 20 Hz. We will use the Hamming window, which is defined as: $w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$
|
||||
|
||||
|
||||
\begin{lstlisting}
|
||||
(*@\HLJLn{fs}@*) (*@\HLJLoB{=}@*) (*@\HLJLni{20}@*)
|
||||
(*@\HLJLn{f}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{digitalfilter}@*)(*@\HLJLp{(}@*)(*@\HLJLnf{Lowpass}@*)(*@\HLJLp{(}@*)(*@\HLJLni{5}@*)(*@\HLJLp{,}@*) (*@\HLJLn{fs}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{fs}@*)(*@\HLJLp{),}@*) (*@\HLJLnf{FIRWindow}@*)(*@\HLJLp{(}@*)(*@\HLJLnf{hamming}@*)(*@\HLJLp{(}@*)(*@\HLJLni{61}@*)(*@\HLJLp{)))}@*)
|
||||
(*@\HLJLn{w}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{range}@*)(*@\HLJLp{(}@*)(*@\HLJLni{0}@*)(*@\HLJLp{,}@*) (*@\HLJLn{stop}@*)(*@\HLJLoB{=}@*)(*@\HLJLn{pi}@*)(*@\HLJLp{,}@*) (*@\HLJLn{length}@*)(*@\HLJLoB{=}@*)(*@\HLJLni{1024}@*)(*@\HLJLp{)}@*)
|
||||
(*@\HLJLn{h}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{FIRfreqz}@*)(*@\HLJLp{(}@*)(*@\HLJLn{f}@*)(*@\HLJLp{,}@*) (*@\HLJLn{w}@*)(*@\HLJLp{)}@*)
|
||||
\end{lstlisting}
|
||||
|
||||
\begin{lstlisting}
|
||||
1024-element Array{Complex{Float32},1}:
|
||||
1.0f0 + 0.0f0im
|
||||
0.99546844f0 + 0.095055714f0im
|
||||
0.98191506f0 + 0.1892486f0im
|
||||
0.95946306f0 + 0.28172377f0im
|
||||
0.9283168f0 + 0.37164196f0im
|
||||
0.8887594f0 + 0.45818728f0im
|
||||
0.84115064f0 + 0.54057467f0im
|
||||
0.7859234f0 + 0.618057f0im
|
||||
0.72357976f0 + 0.6899319f0im
|
||||
0.65468615f0 + 0.7555481f0im
|
||||
(*@\ensuremath{\vdots}@*)
|
||||
0.00043952762f0 - 0.00041908873f0im
|
||||
0.0005152718f0 - 0.00040521423f0im
|
||||
0.0005873293f0 - 0.00037745363f0im
|
||||
0.0006531789f0 - 0.0003367371f0im
|
||||
0.0007105166f0 - 0.00028444792f0im
|
||||
0.0007573364f0 - 0.00022237403f0im
|
||||
0.0007920005f0 - 0.00015264557f0im
|
||||
0.0008132961f0 - 7.766036f-5im
|
||||
0.0008204784f0 - 3.1148685f-18im
|
||||
\end{lstlisting}
|
||||
|
||||
|
||||
\subsection{Plot the frequency and impulse response}
|
||||
|
||||
The next code chunk is executed in term mode, see the \href{FIR_design.jl}{script} for syntax.
|
||||
|
||||
|
||||
\begin{lstlisting}
|
||||
(*@\HLJLnB{julia> }@*)(*@\HLJLn{h{\_}db}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{log10}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{abs}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{h}@*)(*@\HLJLp{));}@*)
|
||||
|
||||
(*@\HLJLnB{julia> }@*)(*@\HLJLn{ws}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{w}@*)(*@\HLJLoB{/}@*)(*@\HLJLn{pi}@*)(*@\HLJLoB{*}@*)(*@\HLJLp{(}@*)(*@\HLJLn{fs}@*)(*@\HLJLoB{/}@*)(*@\HLJLni{2}@*)(*@\HLJLp{)}@*)
|
||||
0.0:0.009775171065493646:10.0
|
||||
\end{lstlisting}
|
||||
|
||||
\begin{lstlisting}
|
||||
(*@\HLJLnf{plot}@*)(*@\HLJLp{(}@*)(*@\HLJLn{ws}@*)(*@\HLJLp{,}@*) (*@\HLJLn{h{\_}db}@*)(*@\HLJLp{,}@*)
|
||||
(*@\HLJLn{xlabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Frequency (Hz)"}@*)(*@\HLJLp{,}@*) (*@\HLJLn{ylabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Magnitude (db)"}@*)(*@\HLJLp{)}@*)
|
||||
\end{lstlisting}
|
||||
|
||||
\includegraphics[width=\linewidth]{/home/travis/build/mpastell/Weave.jl/doc/build/examples/tmpnofuLR/FIR_design_plots_4_1.pdf}
|
||||
|
||||
And again with default options
|
||||
|
||||
|
||||
\begin{lstlisting}
|
||||
(*@\HLJLn{h{\_}phase}@*) (*@\HLJLoB{=}@*) (*@\HLJLnf{unwrap}@*)(*@\HLJLp{(}@*)(*@\HLJLoB{-}@*)(*@\HLJLn{atan}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{imag}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{h}@*)(*@\HLJLp{),}@*)(*@\HLJLn{real}@*)(*@\HLJLoB{.}@*)(*@\HLJLp{(}@*)(*@\HLJLn{h}@*)(*@\HLJLp{)))}@*)
|
||||
(*@\HLJLnf{plot}@*)(*@\HLJLp{(}@*)(*@\HLJLn{ws}@*)(*@\HLJLp{,}@*) (*@\HLJLn{h{\_}phase}@*)(*@\HLJLp{,}@*)
|
||||
(*@\HLJLn{xlabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Frequency (Hz)"}@*)(*@\HLJLp{,}@*) (*@\HLJLn{ylabel}@*) (*@\HLJLoB{=}@*) (*@\HLJLs{"Phase (radians)"}@*)(*@\HLJLp{)}@*)
|
||||
\end{lstlisting}
|
||||
|
||||
\includegraphics[width=\linewidth]{/home/travis/build/mpastell/Weave.jl/doc/build/examples/tmpnofuLR/FIR_design_plots_5_1.pdf}
|
||||
|
||||
|
||||
\end{document}
|
||||
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|
@ -0,0 +1 @@
|
|||
var DOCUMENTER_CURRENT_VERSION = "dev";
|
||||
|
|
@ -9,7 +9,7 @@ weave(joinpath(dirname(pathof(Weave)), "../examples", "FIR_design
|
|||
cache_path = "cache", cache=:off,
|
||||
template = nothing, highlight_theme = nothing, css = nothing,
|
||||
pandoc_options = "",
|
||||
latex_cmd = "xelatex")</code></pre><p>Weave an input document to output file.</p><ul><li><code>doctype</code>: :auto = set based on file extension or specify one of the supported formats. See <code>list_out_formats()</code></li><li><code>informat</code>: :auto = set based on file extension or set to <code>"noweb"</code>, <code>"markdown"</code> or <code>script</code></li><li><code>out_path</code>: Path where the output is generated. Can be: <code>:doc</code>: Path of the source document, <code>:pwd</code>: Julia working directory, <code>"somepath"</code>: output directory as a String e.g <code>"/home/mpastell/weaveout"</code> or filename as string e.g. ~/outpath/outfile.tex.</li><li><code>args</code>: dictionary of arguments to pass to document. Available as WEAVE_ARGS</li><li><code>mod</code>: Module where Weave <code>eval</code>s code. Defaults to <code>:sandbox</code> to create new sandbox module, you can also pass a module e.g. <code>Main</code>.</li><li><code>fig_path</code>: where figures will be generated, relative to out_path</li><li><code>fig_ext</code>: Extension for saved figures e.g. <code>".pdf"</code>, <code>".png"</code>. Default setting depends on <code>doctype</code>.</li><li><code>cache_path</code>: where of cached output will be saved.</li><li><code>cache</code>: controls caching of code: <code>:off</code> = no caching, <code>:all</code> = cache everything, <code>:user</code> = cache based on chunk options, <code>:refresh</code>, run all code chunks and save new cache.</li><li><code>throw_errors</code> if <code>false</code> errors are included in output document and the whole document is executed. if <code>true</code> errors are thrown when they occur.</li><li><code>template</code> : Template (file path) for md2html or md2tex formats.</li><li><code>highlight_theme</code> : Theme (Highlights.AbstractTheme) for used syntax highlighting</li><li><code>css</code> : CSS (file path) used for md2html format</li><li><code>pandoc_options</code> = String array of options to pass to pandoc for <code>pandoc2html</code> and <code>pandoc2pdf</code> formats e.g. ["–toc", "-N"]</li><li><code>latex_cmd</code> the command used to make pdf from .tex</li></ul><p><strong>Note:</strong> Run Weave from terminal and not using IJulia, Juno or ESS, they tend to mess with capturing output.</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/efec59cdbf096a1aa15ba4e5a7d9d4bc21fef2c9/src/Weave.jl#L53-L89">source</a></section><h2><a class="nav-anchor" id="Tangle-1" href="#Tangle-1">Tangle</a></h2><p>Tangling extracts the code from document:</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Weave.tangle-Tuple{Any}" href="#Weave.tangle-Tuple{Any}"><code>Weave.tangle</code></a> — <span class="docstring-category">Method</span>.</div><div><div><p><code>tangle(source ; out_path=:doc, informat="noweb")</code></p><p>Tangle source code from input document to .jl file.</p><ul><li><code>informat</code>: <code>"noweb"</code> of <code>"markdown"</code></li><li><code>out_path</code>: Path where the output is generated. Can be: <code>:doc</code>: Path of the source document, <code>:pwd</code>: Julia working directory, <code>"somepath"</code>, directory name as a string e.g <code>"/home/mpastell/weaveout"</code></li></ul><p>or filename as string e.g. ~/outpath/outfile.jl.</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/efec59cdbf096a1aa15ba4e5a7d9d4bc21fef2c9/src/Weave.jl#L23-L31">source</a></section><h2><a class="nav-anchor" id="Supported-formats-1" href="#Supported-formats-1">Supported formats</a></h2><p>Weave sets the output format based on the file extension, but you can also set it using <code>doctype</code> option. The rules for detecting the format are:</p><pre><code class="language-julia">ext == ".jl" && return "md2html"
|
||||
latex_cmd = "xelatex")</code></pre><p>Weave an input document to output file.</p><ul><li><code>doctype</code>: :auto = set based on file extension or specify one of the supported formats. See <code>list_out_formats()</code></li><li><code>informat</code>: :auto = set based on file extension or set to <code>"noweb"</code>, <code>"markdown"</code> or <code>script</code></li><li><code>out_path</code>: Path where the output is generated. Can be: <code>:doc</code>: Path of the source document, <code>:pwd</code>: Julia working directory, <code>"somepath"</code>: output directory as a String e.g <code>"/home/mpastell/weaveout"</code> or filename as string e.g. ~/outpath/outfile.tex.</li><li><code>args</code>: dictionary of arguments to pass to document. Available as WEAVE_ARGS</li><li><code>mod</code>: Module where Weave <code>eval</code>s code. Defaults to <code>:sandbox</code> to create new sandbox module, you can also pass a module e.g. <code>Main</code>.</li><li><code>fig_path</code>: where figures will be generated, relative to out_path</li><li><code>fig_ext</code>: Extension for saved figures e.g. <code>".pdf"</code>, <code>".png"</code>. Default setting depends on <code>doctype</code>.</li><li><code>cache_path</code>: where of cached output will be saved.</li><li><code>cache</code>: controls caching of code: <code>:off</code> = no caching, <code>:all</code> = cache everything, <code>:user</code> = cache based on chunk options, <code>:refresh</code>, run all code chunks and save new cache.</li><li><code>throw_errors</code> if <code>false</code> errors are included in output document and the whole document is executed. if <code>true</code> errors are thrown when they occur.</li><li><code>template</code> : Template (file path) for md2html or md2tex formats.</li><li><code>highlight_theme</code> : Theme (Highlights.AbstractTheme) for used syntax highlighting</li><li><code>css</code> : CSS (file path) used for md2html format</li><li><code>pandoc_options</code> = String array of options to pass to pandoc for <code>pandoc2html</code> and <code>pandoc2pdf</code> formats e.g. ["–toc", "-N"]</li><li><code>latex_cmd</code> the command used to make pdf from .tex</li></ul><p><strong>Note:</strong> Run Weave from terminal and not using IJulia, Juno or ESS, they tend to mess with capturing output.</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/6510ea0556809fa5c523ff79e8d28f074963246d/src/Weave.jl#L53-L89">source</a></section><h2><a class="nav-anchor" id="Tangle-1" href="#Tangle-1">Tangle</a></h2><p>Tangling extracts the code from document:</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Weave.tangle-Tuple{Any}" href="#Weave.tangle-Tuple{Any}"><code>Weave.tangle</code></a> — <span class="docstring-category">Method</span>.</div><div><div><p><code>tangle(source ; out_path=:doc, informat="noweb")</code></p><p>Tangle source code from input document to .jl file.</p><ul><li><code>informat</code>: <code>"noweb"</code> of <code>"markdown"</code></li><li><code>out_path</code>: Path where the output is generated. Can be: <code>:doc</code>: Path of the source document, <code>:pwd</code>: Julia working directory, <code>"somepath"</code>, directory name as a string e.g <code>"/home/mpastell/weaveout"</code></li></ul><p>or filename as string e.g. ~/outpath/outfile.jl.</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/6510ea0556809fa5c523ff79e8d28f074963246d/src/Weave.jl#L23-L31">source</a></section><h2><a class="nav-anchor" id="Supported-formats-1" href="#Supported-formats-1">Supported formats</a></h2><p>Weave sets the output format based on the file extension, but you can also set it using <code>doctype</code> option. The rules for detecting the format are:</p><pre><code class="language-julia">ext == ".jl" && return "md2html"
|
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contains(ext, ".md") && return "md2html"
|
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contains(ext, ".rst") && return "rst"
|
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contains(ext, ".tex") && return "texminted"
|
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|
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multimarkdown: MultiMarkdown
|
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md2pdf: Julia markdown to latex
|
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asciidoc: AsciiDoc
|
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hugo: Hugo markdown (using shortcodes)</code></pre></div><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Weave.list_out_formats-Tuple{}" href="#Weave.list_out_formats-Tuple{}"><code>Weave.list_out_formats</code></a> — <span class="docstring-category">Method</span>.</div><div><div><p><code>list_out_formats()</code></p><p>List supported output formats</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/efec59cdbf096a1aa15ba4e5a7d9d4bc21fef2c9/src/Weave.jl#L11-L15">source</a></section><h2><a class="nav-anchor" id="Document-syntax-1" href="#Document-syntax-1">Document syntax</a></h2><p>Weave uses noweb, markdown or script syntax for defining the code chunks and documentation chunks. You can also weave Jupyter notebooks. The format is detected based on the file extension, but you can also set it manually using the <code>informat</code> parameter.</p><p>The rules for autodetection are:</p><pre><code class="language-julia">ext == ".jl" && return "script"
|
||||
hugo: Hugo markdown (using shortcodes)</code></pre></div><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Weave.list_out_formats-Tuple{}" href="#Weave.list_out_formats-Tuple{}"><code>Weave.list_out_formats</code></a> — <span class="docstring-category">Method</span>.</div><div><div><p><code>list_out_formats()</code></p><p>List supported output formats</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/6510ea0556809fa5c523ff79e8d28f074963246d/src/Weave.jl#L11-L15">source</a></section><h2><a class="nav-anchor" id="Document-syntax-1" href="#Document-syntax-1">Document syntax</a></h2><p>Weave uses noweb, markdown or script syntax for defining the code chunks and documentation chunks. You can also weave Jupyter notebooks. The format is detected based on the file extension, but you can also set it manually using the <code>informat</code> parameter.</p><p>The rules for autodetection are:</p><pre><code class="language-julia">ext == ".jl" && return "script"
|
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ext == ".jmd" && return "markdown"
|
||||
ext == ".ipynb" && return "notebook"
|
||||
return "noweb"</code></pre><h2><a class="nav-anchor" id="Noweb-format-1" href="#Noweb-format-1">Noweb format</a></h2><h3><a class="nav-anchor" id="Code-chunks-1" href="#Code-chunks-1">Code chunks</a></h3><p>start with a line marked with <code><<>>=</code> or <code><<options>>=</code> and end with line marked with <code>@</code>. The code between the start and end markers is executed and the output is captured to the output document. See <a href="../chunk_options/">chunk options</a>.</p><h3><a class="nav-anchor" id="Documentation-chunks-1" href="#Documentation-chunks-1">Documentation chunks</a></h3><p>Are the rest of the document (between <code>@</code> and <code><<>>=</code> lines and the first chunk be default) and can be written with several different markup languages.</p><p><a href=" https://github.com/mpastell/Weave.jl/blob/master/examples/julia_sample.mdw">Sample document</a></p><h2><a class="nav-anchor" id="Markdown-format-1" href="#Markdown-format-1">Markdown format</a></h2><p>Markdown code chunks are defined using fenced code blocks with options following on the same line. e.g. to hide code from output you can use:</p><p><code></code>`<code>julia; echo=false</code></p><p><a href="https://github.com/mpastell/Weave.jl/blob/master/examples/gadfly_md_sample.jmd">See sample document:</a></p><h2><a class="nav-anchor" id="Script-format-1" href="#Script-format-1">Script format</a></h2><p>Weave also support script input format with a markup in comments. These scripts can be executed normally using Julia or published with Weave. Documentation is in lines starting with <code>#'</code>, <code>#%%</code> or <code># %%</code>, and code is executed and results are included in the weaved document.</p><p>All lines that are not documentation are treated as code. You can set chunk options using lines starting with <code>#+</code> just before code e.g. <code>#+ term=true</code>.</p><p>The format is identical to <a href="http://mpastell.com/pweave/pypublish.html">Pweave</a> and the concept is similar to publishing documents with MATLAB or using Knitr's <a href="http://yihui.name/knitr/demo/stitch/">spin</a>. Weave will remove the first empty space from each line of documentation.</p><p><a href="https://github.com/mpastell/Weave.jl/blob/master/examples/FIR_design.jl">See sample document:</a></p><h2><a class="nav-anchor" id="Inline-code-1" href="#Inline-code-1">Inline code</a></h2><p>You can also add inline code to your documents using</p><pre><code class="language-none">`j juliacode`</code></pre><p>syntax. The code will be replaced with the output of running the code. If the code produces figures the filename or base64 encoded string will be added to output e.g. to include a Plots figure in markdown you can use:</p><pre><code class="language-none">`)</code></pre><h2><a class="nav-anchor" id="Setting-document-options-in-header-1" href="#Setting-document-options-in-header-1">Setting document options in header</a></h2><p>You can use a YAML header in the beginning of the input document delimited with "–-" to set the document title, author and date e.g. and default document options. Each of Weave command line arguments can be set in header using <code>options</code> field. Below is an example that sets document <code>out_path</code> and <code>doctype</code> using the header.</p><pre><code class="language-none">---
|
||||
return "noweb"</code></pre><h2><a class="nav-anchor" id="Noweb-format-1" href="#Noweb-format-1">Noweb format</a></h2><h3><a class="nav-anchor" id="Code-chunks-1" href="#Code-chunks-1">Code chunks</a></h3><p>start with a line marked with <code><<>>=</code> or <code><<options>>=</code> and end with line marked with <code>@</code>. The code between the start and end markers is executed and the output is captured to the output document. See <a href="../chunk_options/">chunk options</a>.</p><h3><a class="nav-anchor" id="Documentation-chunks-1" href="#Documentation-chunks-1">Documentation chunks</a></h3><p>Are the rest of the document (between <code>@</code> and <code><<>>=</code> lines and the first chunk be default) and can be written with several different markup languages.</p><p><a href=" https:/github.com/mpastell/Weave.jl/blob/master/examples/julia_sample.mdw">Sample document</a></p><h2><a class="nav-anchor" id="Markdown-format-1" href="#Markdown-format-1">Markdown format</a></h2><p>Markdown code chunks are defined using fenced code blocks with options following on the same line. e.g. to hide code from output you can use:</p><p><code></code>`<code>julia; echo=false</code></p><p><a href="https://github.com/mpastell/Weave.jl/blob/master/examples/gadfly_md_sample.jmd">See sample document:</a></p><h2><a class="nav-anchor" id="Script-format-1" href="#Script-format-1">Script format</a></h2><p>Weave also support script input format with a markup in comments. These scripts can be executed normally using Julia or published with Weave. Documentation is in lines starting with <code>#'</code>, <code>#%%</code> or <code># %%</code>, and code is executed and results are included in the weaved document.</p><p>All lines that are not documentation are treated as code. You can set chunk options using lines starting with <code>#+</code> just before code e.g. <code>#+ term=true</code>.</p><p>The format is identical to <a href="http://mpastell.com/pweave/pypublish.html">Pweave</a> and the concept is similar to publishing documents with MATLAB or using Knitr's <a href="http://yihui.name/knitr/demo/stitch/">spin</a>. Weave will remove the first empty space from each line of documentation.</p><p><a href="https://github.com/mpastell/Weave.jl/blob/master/examples/FIR_design.jl">See sample document:</a></p><h2><a class="nav-anchor" id="Inline-code-1" href="#Inline-code-1">Inline code</a></h2><p>You can also add inline code to your documents using</p><pre><code class="language-none">`j juliacode`</code></pre><p>syntax. The code will be replaced with the output of running the code. If the code produces figures the filename or base64 encoded string will be added to output e.g. to include a Plots figure in markdown you can use:</p><pre><code class="language-none">`)</code></pre><h2><a class="nav-anchor" id="Setting-document-options-in-header-1" href="#Setting-document-options-in-header-1">Setting document options in header</a></h2><p>You can use a YAML header in the beginning of the input document delimited with "–-" to set the document title, author and date e.g. and default document options. Each of Weave command line arguments can be set in header using <code>options</code> field. Below is an example that sets document <code>out_path</code> and <code>doctype</code> using the header.</p><pre><code class="language-none">---
|
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title : Weave example
|
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author : Matti Pastell
|
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date: 15th December 2016
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doctype : github
|
||||
---</code></pre><h2><a class="nav-anchor" id="Passing-arguments-to-documents-1" href="#Passing-arguments-to-documents-1">Passing arguments to documents</a></h2><p>You can pass arguments as dictionary to the weaved document using the <code>args</code> argument to <code>weave</code>. The dictionary will be available as <code>WEAVE_ARGS</code> variable in the document.</p><p>This makes it possible to create the same report easily for e.g. different date ranges of input data from a database or from files with similar format giving the filename as input.</p><p>In order to pass a filename to a document you need call <code>weave</code> using:</p><pre><code class="language-julia">weave("mydoc.jmd", args = Dict("filename" => "somedata.h5"))</code></pre><p>and you can access the filename from document as follows:</p><pre><code class="language-none"> ```julia
|
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print(WEAVE_ARGS["filename"])
|
||||
```</code></pre><p>You can use the <code>out_path</code> argument to control the name of the output document.</p><h2><a class="nav-anchor" id="Include-Weave-document-in-Julia-1" href="#Include-Weave-document-in-Julia-1">Include Weave document in Julia</a></h2><p>You can call <code>include_weave</code> on a Weave document to run the contents of all code chunks in Julia.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Weave.include_weave" href="#Weave.include_weave"><code>Weave.include_weave</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">include_weave(doc, informat=:auto)</code></pre><p>Include code from Weave document calling <code>include_string</code> on all code from doc. Code is run in the path of the include document.</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/efec59cdbf096a1aa15ba4e5a7d9d4bc21fef2c9/src/Weave.jl#L195-L200">source</a></section><footer><hr/><a class="previous" href="../getting_started/"><span class="direction">Previous</span><span class="title">Getting started</span></a><a class="next" href="../publish/"><span class="direction">Next</span><span class="title">Publishing to html and pdf</span></a></footer></article></body></html>
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```</code></pre><p>You can use the <code>out_path</code> argument to control the name of the output document.</p><h2><a class="nav-anchor" id="Include-Weave-document-in-Julia-1" href="#Include-Weave-document-in-Julia-1">Include Weave document in Julia</a></h2><p>You can call <code>include_weave</code> on a Weave document to run the contents of all code chunks in Julia.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Weave.include_weave" href="#Weave.include_weave"><code>Weave.include_weave</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">include_weave(doc, informat=:auto)</code></pre><p>Include code from Weave document calling <code>include_string</code> on all code from doc. Code is run in the path of the include document.</p></div></div><a class="source-link" target="_blank" href="https://github.com/mpastell/Weave.jl/blob/6510ea0556809fa5c523ff79e8d28f074963246d/src/Weave.jl#L195-L200">source</a></section><footer><hr/><a class="previous" href="../getting_started/"><span class="direction">Previous</span><span class="title">Getting started</span></a><a class="next" href="../publish/"><span class="direction">Next</span><span class="title">Publishing to html and pdf</span></a></footer></article></body></html>
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!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");var r="2"==e.version[0];e.jp=function(){this.pipeline.reset(),this.pipeline.add(e.jp.stopWordFilter,e.jp.stemmer),r?this.tokenizer=e.jp.tokenizer:(e.tokenizer&&(e.tokenizer=e.jp.tokenizer),this.tokenizerFn&&(this.tokenizerFn=e.jp.tokenizer))};var t=new e.TinySegmenter;e.jp.tokenizer=function(n){if(!arguments.length||null==n||null==n)return[];if(Array.isArray(n))return n.map(function(t){return r?new e.Token(t.toLowerCase()):t.toLowerCase()});for(var i=n.toString().toLowerCase().replace(/^\s+/,""),o=i.length-1;o>=0;o--)if(/\S/.test(i.charAt(o))){i=i.substring(0,o+1);break}return t.segment(i).filter(function(e){return!!e}).map(function(t){return r?new e.Token(t):t})},e.jp.stemmer=function(e){return e},e.Pipeline.registerFunction(e.jp.stemmer,"stemmer-jp"),e.jp.wordCharacters="一二三四五六七八九十百千万億兆一-龠々〆ヵヶぁ-んァ-ヴーｱ-ﾝﾞa-zA-Zａ-ｚＡ-Ｚ0-9０-９",e.jp.stopWordFilter=function(t){if(-1===e.jp.stopWordFilter.stopWords.indexOf(r?t.toString():t))return t},e.jp.stopWordFilter=e.generateStopWordFilter("これ それ あれ この その あの ここ そこ あそこ こちら どこ だれ なに なん 何 私 貴方 貴方方 我々 私達 あの人 あのかた 彼女 彼 です あります おります います は が の に を で え から まで より も どの と し それで しかし".split(" ")),e.Pipeline.registerFunction(e.jp.stopWordFilter,"stopWordFilter-jp")}});
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</div>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="md-sidebar md-sidebar--secondary" data-md-component="toc">
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<div class="md-sidebar__scrollwrap">
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<div class="md-sidebar__inner">
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<nav class="md-nav md-nav--secondary">
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<label class="md-nav__title" for="__toc">Table of contents</label>
|
||||
<ul class="md-nav__list" data-md-scrollfix>
|
||||
|
||||
<li class="md-nav__item">
|
||||
<a href="#options-for-code" title="Options for code" class="md-nav__link">
|
||||
Options for code
|
||||
</a>
|
||||
|
||||
</li>
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||||
|
||||
<li class="md-nav__item">
|
||||
<a href="#options-for-figures" title="Options for figures" class="md-nav__link">
|
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Options for figures
|
||||
</a>
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||||
|
||||
</li>
|
||||
|
||||
<li class="md-nav__item">
|
||||
<a href="#set-default-chunk-options" title="Set default chunk options" class="md-nav__link">
|
||||
Set default chunk options
|
||||
</a>
|
||||
|
||||
</li>
|
||||
|
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|
||||
|
||||
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||||
</ul>
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||||
</nav>
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</div>
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||||
<div class="md-content">
|
||||
<article class="md-content__inner md-typeset">
|
||||
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||||
|
||||
<a href="https://github.com/mpastell/Weave.jl/edit/master/docs/chunk_options.md" title="Edit this page" class="md-icon md-content__icon"></a>
|
||||
|
||||
|
||||
<p><a id='Chunk-options-1'></a></p>
|
||||
<h1 id="chunk-options">Chunk options</h1>
|
||||
<p>I've mostly followed <a href="http://yihui.name/knitr/options">Knitr</a>'s naming for chunk options, but not all options are implemented.</p>
|
||||
<p>Options are separated using ";" and need to be valid Julia expressions. Example: A code chunk that saves and displays a 12 cm wide image and hides the source code:</p>
|
||||
<div class="code"><pre><span></span><span class="o"><<</span><span class="n">out_width</span><span class="o">=</span><span class="s">"12cm"</span><span class="p">;</span> <span class="n">echo</span><span class="o">=</span><span class="kc">false</span> <span class="o">>>=</span>
|
||||
<span class="k">using</span> <span class="n">Gadfly</span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="nb">π</span><span class="p">,</span> <span class="mi">200</span><span class="p">)</span>
|
||||
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">Geom</span><span class="o">.</span><span class="n">line</span><span class="p">)</span>
|
||||
<span class="err">@</span>
|
||||
</pre></div>
|
||||
|
||||
|
||||
<p>Weave currently supports the following chunk options with the following defaults:</p>
|
||||
<p><a id='Options-for-code-1'></a></p>
|
||||
<h2 id="options-for-code">Options for code</h2>
|
||||
<ul>
|
||||
<li><code>echo = true</code>. Echo the code in the output document. If <code>false</code> the source code will be hidden.</li>
|
||||
<li><code>results = "markup"</code>. The output format of the printed results. "markup" for literal block, "hidden" for hidden results or anything else for raw output (I tend to use ‘tex’ for Latex and ‘rst’ for rest. Raw output is useful if you wan’t to e.g. create tables from code chunks.</li>
|
||||
<li><code>eval = true</code>. Evaluate the code chunk. If false the chunk won’t be executed.</li>
|
||||
<li><code>term=false</code>. If true the output emulates a REPL session. Otherwise only stdout and figures will be included in output.</li>
|
||||
<li><code>label</code>. Chunk label, will be used for figure labels in Latex as fig:label</li>
|
||||
<li><code>wrap = true</code>. Wrap long lines from output.</li>
|
||||
<li><code>line_width = 75</code>. Line width for wrapped lines.</li>
|
||||
<li><code>cache = false</code>. Cache results, depends on <code>cache</code> parameter on <code>weave</code> function.</li>
|
||||
<li><code>hold = false</code>. Hold all results until the end of the chunk.</li>
|
||||
<li><code>tangle = true</code>. Set tangle to false to exclude chunk from tangled code.</li>
|
||||
</ul>
|
||||
<p><a id='Options-for-figures-1'></a></p>
|
||||
<h2 id="options-for-figures">Options for figures</h2>
|
||||
<ul>
|
||||
<li><code>fig_width</code>. Figure width passed to plotting library e.g. <code>800</code></li>
|
||||
<li><code>fig_height</code> Figure height passed to plotting library</li>
|
||||
<li><code>out_width</code>. Width of saved figure in output markup e.g. "50%", "12cm", <code>\\0.5linewidth</code></li>
|
||||
<li><code>out_height</code>. Height of saved figure in output markup</li>
|
||||
<li><code>dpi</code>=96. Resolution of saved figures.</li>
|
||||
<li><code>fig_cap</code>. Figure caption.</li>
|
||||
<li><code>label</code>. Chunk label, will be used for figure labels in Latex as fig:label</li>
|
||||
<li><code>fig_ext</code>. File extension (format) of saved figures.</li>
|
||||
<li><code>fig_pos="htpb"</code>. Figure position in Latex.</li>
|
||||
<li><code>fig_env="figure"</code>. Figure environment in Latex.</li>
|
||||
</ul>
|
||||
<p><a id='Set-default-chunk-options-1'></a></p>
|
||||
<h2 id="set-default-chunk-options">Set default chunk options</h2>
|
||||
<p>You can set or change the default chunk options for a document either before running weave or inside the weaved document. You can e.g. use a hidden chunk in the beginning of the source document to set the options:</p>
|
||||
<div class="code"><pre><span></span><span class="o"><<</span><span class="n">echo</span> <span class="o">=</span> <span class="kc">false</span><span class="o">>>=</span>
|
||||
<span class="k">import</span> <span class="n">Weave</span>
|
||||
<span class="n">Weave</span><span class="o">.</span><span class="n">set_chunk_defaults</span><span class="p">(</span><span class="kt">Dict</span><span class="p">{</span><span class="kt">Symbol</span><span class="p">,</span> <span class="kt">Any</span><span class="p">}(</span>
|
||||
<span class="o">:</span><span class="n">out_width</span> <span class="o">=></span> <span class="s">"</span><span class="se">\\</span><span class="s">0.5linewidth"</span><span class="p">,</span>
|
||||
<span class="o">:</span><span class="n">results</span> <span class="o">=></span> <span class="s">"tex"</span>
|
||||
<span class="p">))</span>
|
||||
<span class="err">@</span>
|
||||
</pre></div>
|
||||
|
||||
|
||||
<div class="code"><pre><span></span>set_chunk_defaults(opts)
|
||||
get_chunk_defaults()
|
||||
restore_chunk_defaults()
|
||||
</pre></div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
</article>
|
||||
</div>
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||||
</div>
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</main>
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<a href="../notebooks/" title="Working with Jupyter notebooks" class="md-flex md-footer-nav__link md-footer-nav__link--next" rel="next">
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<div class="md-footer-copyright">
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<div class="md-footer-copyright__highlight">
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Matti Pastell 2016-2018
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</div>
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powered by
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and
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<a href="https://squidfunk.github.io/mkdocs-material/">
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Material for MkDocs</a>
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<link rel="stylesheet" href="../assets/fonts/font-awesome.css">
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</footer>
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</div>
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<script src="../assets/javascripts/application.583bbe55.js"></script>
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<script>app.initialize({version:"1.0",url:{base:".."}})</script>
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<script>!function(e,a,t,n,o,c,i){e.GoogleAnalyticsObject=o,e.ga=e.ga||function(){(e.ga.q=e.ga.q||[]).push(arguments)},e.ga.l=1*new Date,c=a.createElement(t),i=a.getElementsByTagName(t)[0],c.async=1,c.src="https://www.google-analytics.com/analytics.js",i.parentNode.insertBefore(c,i)}(window,document,"script",0,"ga"),ga("create","UA-6474352-10","auto"),ga("set","anonymizeIp",!0),ga("send","pageview");var links=document.getElementsByTagName("a");if(Array.prototype.map.call(links,function(e){e.host!=document.location.host&&e.addEventListener("click",function(){var a=e.getAttribute("data-md-action")||"follow";ga("send","event","outbound",a,e.href)})}),document.forms.search){var query=document.forms.search.query;query.addEventListener("blur",function(){if(this.value){var e=document.location.pathname;ga("send","pageview",e+"?q="+this.value)}})}</script>
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</body>
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</html>
|
||||
|
|
@ -1,23 +0,0 @@
|
|||
\relax
|
||||
\providecommand\hyper@newdestlabel[2]{}
|
||||
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
|
||||
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
|
||||
\global\let\oldcontentsline\contentsline
|
||||
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
|
||||
\global\let\oldnewlabel\newlabel
|
||||
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
|
||||
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
|
||||
\AtEndDocument{\ifx\hyper@anchor\@undefined
|
||||
\let\contentsline\oldcontentsline
|
||||
\let\newlabel\oldnewlabel
|
||||
\fi}
|
||||
\fi}
|
||||
\global\let\hyper@last\relax
|
||||
\gdef\HyperFirstAtBeginDocument#1{#1}
|
||||
\providecommand*\HyPL@Entry[1]{}
|
||||
\HyPL@Entry{0<</S/D>>}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {2}FIR Filter Design}{1}{section.2}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Calculating frequency response}{1}{subsection.2.1}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Design Lowpass FIR filter}{2}{subsection.2.2}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Plot the frequency and impulse response}{2}{subsection.2.3}}
|
||||
File diff suppressed because one or more lines are too long
|
|
@ -1,99 +0,0 @@
|
|||
---
|
||||
title: FIR filter design with Julia
|
||||
author: Matti Pastell
|
||||
date: 21th April 2016
|
||||
---
|
||||
|
||||
|
||||
# Introduction
|
||||
|
||||
|
||||
This an example of a julia script that can be published using
|
||||
[Weave](http://mpastell.github.io/Weave.jl/latest/usage/).
|
||||
The script can be executed normally using Julia
|
||||
or published to HTML or pdf with Weave.
|
||||
Text is written in markdown in lines starting with "`#'` " and code
|
||||
is executed and results are included in the published document.
|
||||
|
||||
|
||||
Notice that you don't need to define chunk options, but you can using
|
||||
`#+`. just before code e.g. `#+ term=True, caption='Fancy plots.'`.
|
||||
If you're viewing the published version have a look at the
|
||||
[source](FIR_design_plots.jl) to see the markup.
|
||||
|
||||
|
||||
|
||||
# FIR Filter Design
|
||||
|
||||
|
||||
We'll implement lowpass, highpass and ' bandpass FIR filters. If
|
||||
you want to read more about DSP I highly recommend [The Scientist
|
||||
and Engineer's Guide to Digital Signal
|
||||
Processing](http://www.dspguide.com/) which is freely available
|
||||
online.
|
||||
|
||||
|
||||
## Calculating frequency response
|
||||
|
||||
|
||||
DSP.jl package doesn't (yet) have a method to calculate the
|
||||
the frequency response of a FIR filter so we define it:
|
||||
|
||||
```julia
|
||||
using Plots, DSP
|
||||
gr()
|
||||
|
||||
function FIRfreqz(b::Array, w = range(0, stop=π, length=1024))
|
||||
n = length(w)
|
||||
h = Array{ComplexF32}(undef, n)
|
||||
sw = 0
|
||||
for i = 1:n
|
||||
for j = 1:length(b)
|
||||
sw += b[j]*exp(-im*w[i])^-j
|
||||
end
|
||||
h[i] = sw
|
||||
sw = 0
|
||||
end
|
||||
return h
|
||||
end
|
||||
```
|
||||
|
||||
## Design Lowpass FIR filter
|
||||
|
||||
|
||||
Designing a lowpass FIR filter is very simple to do with DSP.jl, all you
|
||||
need to do is to define the window length, cut off frequency and the
|
||||
window. We will define a lowpass filter with cut off frequency at 5Hz for a signal
|
||||
sampled at 20 Hz.
|
||||
We will use the Hamming window, which is defined as:
|
||||
$w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$
|
||||
|
||||
```julia
|
||||
fs = 20
|
||||
f = digitalfilter(Lowpass(5, fs = fs), FIRWindow(hamming(61)))
|
||||
w = range(0, stop=pi, length=1024)
|
||||
h = FIRfreqz(f, w)
|
||||
```
|
||||
|
||||
## Plot the frequency and impulse response
|
||||
|
||||
|
||||
The next code chunk is executed in term mode, see the [script](FIR_design.jl) for syntax.
|
||||
|
||||
```julia; term=true
|
||||
h_db = log10.(abs.(h));
|
||||
ws = w/pi*(fs/2)
|
||||
```
|
||||
|
||||
```julia
|
||||
plot(ws, h_db,
|
||||
xlabel = "Frequency (Hz)", ylabel = "Magnitude (db)")
|
||||
```
|
||||
|
||||
And again with default options
|
||||
|
||||
```julia
|
||||
h_phase = unwrap(-atan.(imag.(h),real.(h)))
|
||||
plot(ws, h_phase,
|
||||
xlabel = "Frequency (Hz)", ylabel = "Phase (radians)")
|
||||
```
|
||||
|
|
@ -1,667 +0,0 @@
|
|||
This is XeTeX, Version 3.14159265-2.6-0.99998 (TeX Live 2017/Debian) (preloaded format=xelatex 2018.4.30) 13 AUG 2018 14:49
|
||||
entering extended mode
|
||||
\write18 enabled.
|
||||
%&-line parsing enabled.
|
||||
**FIR_design.tex
|
||||
(./FIR_design.tex
|
||||
LaTeX2e <2017-04-15>
|
||||
Babel <3.18> and hyphenation patterns for 3 language(s) loaded.
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
|
||||
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo
|
||||
File: size12.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
|
||||
)
|
||||
\c@part=\count79
|
||||
\c@section=\count80
|
||||
\c@subsection=\count81
|
||||
\c@subsubsection=\count82
|
||||
\c@paragraph=\count83
|
||||
\c@subparagraph=\count84
|
||||
\c@figure=\count85
|
||||
\c@table=\count86
|
||||
\abovecaptionskip=\skip41
|
||||
\belowcaptionskip=\skip42
|
||||
\bibindent=\dimen102
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty
|
||||
Package: geometry 2010/09/12 v5.6 Page Geometry
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
|
||||
Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
|
||||
\KV@toks@=\toks14
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty
|
||||
Package: ifpdf 2017/03/15 v3.2 Provides the ifpdf switch
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty
|
||||
Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO)
|
||||
Package ifvtex Info: VTeX not detected.
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty
|
||||
Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional
|
||||
)
|
||||
\Gm@cnth=\count87
|
||||
\Gm@cntv=\count88
|
||||
\c@Gm@tempcnt=\count89
|
||||
\Gm@bindingoffset=\dimen103
|
||||
\Gm@wd@mp=\dimen104
|
||||
\Gm@odd@mp=\dimen105
|
||||
\Gm@even@mp=\dimen106
|
||||
\Gm@layoutwidth=\dimen107
|
||||
\Gm@layoutheight=\dimen108
|
||||
\Gm@layouthoffset=\dimen109
|
||||
\Gm@layoutvoffset=\dimen110
|
||||
\Gm@dimlist=\toks15
|
||||
)
|
||||
(/usr/share/texmf/tex/latex/lm/lmodern.sty
|
||||
Package: lmodern 2009/10/30 v1.6 Latin Modern Fonts
|
||||
LaTeX Font Info: Overwriting symbol font `operators' in version `normal'
|
||||
(Font) OT1/cmr/m/n --> OT1/lmr/m/n on input line 22.
|
||||
LaTeX Font Info: Overwriting symbol font `letters' in version `normal'
|
||||
(Font) OML/cmm/m/it --> OML/lmm/m/it on input line 23.
|
||||
LaTeX Font Info: Overwriting symbol font `symbols' in version `normal'
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\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
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\BOOKMARK [1][-]{section.2}{FIR\040Filter\040Design}{}% 2
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\BOOKMARK [2][-]{subsection.2.1}{Calculating\040frequency\040response}{section.2}% 3
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\BOOKMARK [2][-]{subsection.2.2}{Design\040Lowpass\040FIR\040filter}{section.2}% 4
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---
|
||||
title: FIR filter design with Julia
|
||||
author: Matti Pastell
|
||||
date: 21th April 2016
|
||||
---
|
||||
|
||||
|
||||
# Introduction
|
||||
|
||||
|
||||
This an example of a julia script that can be published using
|
||||
[Weave](http://mpastell.github.io/Weave.jl/latest/usage/).
|
||||
The script can be executed normally using Julia
|
||||
or published to HTML or pdf with Weave.
|
||||
Text is written in markdown in lines starting with "`#'` " and code
|
||||
is executed and results are included in the published document.
|
||||
|
||||
|
||||
Notice that you don't need to define chunk options, but you can using
|
||||
`#+`. just before code e.g. `#+ term=True, caption='Fancy plots.'`.
|
||||
If you're viewing the published version have a look at the
|
||||
[source](FIR_design_plots.jl) to see the markup.
|
||||
|
||||
|
||||
|
||||
# FIR Filter Design
|
||||
|
||||
|
||||
We'll implement lowpass, highpass and ' bandpass FIR filters. If
|
||||
you want to read more about DSP I highly recommend [The Scientist
|
||||
and Engineer's Guide to Digital Signal
|
||||
Processing](http://www.dspguide.com/) which is freely available
|
||||
online.
|
||||
|
||||
|
||||
## Calculating frequency response
|
||||
|
||||
|
||||
DSP.jl package doesn't (yet) have a method to calculate the
|
||||
the frequency response of a FIR filter so we define it:
|
||||
|
||||
~~~~{.julia}
|
||||
using Plots, DSP
|
||||
gr()
|
||||
|
||||
function FIRfreqz(b::Array, w = range(0, stop=π, length=1024))
|
||||
n = length(w)
|
||||
h = Array{ComplexF32}(undef, n)
|
||||
sw = 0
|
||||
for i = 1:n
|
||||
for j = 1:length(b)
|
||||
sw += b[j]*exp(-im*w[i])^-j
|
||||
end
|
||||
h[i] = sw
|
||||
sw = 0
|
||||
end
|
||||
return h
|
||||
end
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
|
||||
~~~~
|
||||
FIRfreqz (generic function with 2 methods)
|
||||
~~~~
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
## Design Lowpass FIR filter
|
||||
|
||||
|
||||
Designing a lowpass FIR filter is very simple to do with DSP.jl, all you
|
||||
need to do is to define the window length, cut off frequency and the
|
||||
window. We will define a lowpass filter with cut off frequency at 5Hz for a signal
|
||||
sampled at 20 Hz.
|
||||
We will use the Hamming window, which is defined as:
|
||||
$w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$
|
||||
|
||||
~~~~{.julia}
|
||||
fs = 20
|
||||
f = digitalfilter(Lowpass(5, fs = fs), FIRWindow(hamming(61)))
|
||||
w = range(0, stop=pi, length=1024)
|
||||
h = FIRfreqz(f, w)
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
## Plot the frequency and impulse response
|
||||
|
||||
|
||||
The next code chunk is executed in term mode, see the [script](FIR_design.jl) for syntax.
|
||||
|
||||
~~~~{.julia}
|
||||
julia> h_db = log10.(abs.(h));
|
||||
|
||||
julia> ws = w/pi*(fs/2)
|
||||
0.0:0.009775171065493646:10.0
|
||||
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
|
||||
|
||||
~~~~{.julia}
|
||||
plot(ws, h_db,
|
||||
xlabel = "Frequency (Hz)", ylabel = "Magnitude (db)")
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
|
||||
\
|
||||
|
||||
|
||||
|
||||
|
||||
And again with default options
|
||||
|
||||
~~~~{.julia}
|
||||
h_phase = unwrap(-atan.(imag.(h),real.(h)))
|
||||
plot(ws, h_phase,
|
||||
xlabel = "Frequency (Hz)", ylabel = "Phase (radians)")
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
|
||||
\
|
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|
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|
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<html lang="en" class="no-js">
|
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<head>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width,initial-scale=1">
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|
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<meta name="author" content="M">
|
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<meta name="lang:clipboard.copy" content="Copy to clipboard">
|
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<meta name="lang:clipboard.copied" content="Copied to clipboard">
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<a href="https://github.com/mpastell/Weave.jl/edit/master/docs/examples/FIR_design.md" title="Edit this page" class="md-icon md-content__icon"></a>
|
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<h1 id="introduction">Introduction</h1>
|
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|
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<a href="http://mpastell.github.io/Weave.jl/latest/usage/">Weave</a>.
|
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|
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Text is written in markdown in lines starting with "<code>#'</code> " and code
|
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is executed and results are included in the published document.</p>
|
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|
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|
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If you're viewing the published version have a look at the
|
||||
<a href="../FIR_design_plots.jl">source</a> to see the markup.</p>
|
||||
<h1 id="fir-filter-design">FIR Filter Design</h1>
|
||||
<p>We'll implement lowpass, highpass and ' bandpass FIR filters. If
|
||||
you want to read more about DSP I highly recommend <a href="http://www.dspguide.com/">The Scientist
|
||||
and Engineer's Guide to Digital Signal
|
||||
Processing</a> which is freely available
|
||||
online.</p>
|
||||
<h2 id="calculating-frequency-response">Calculating frequency response</h2>
|
||||
<p>DSP.jl package doesn't (yet) have a method to calculate the
|
||||
the frequency response of a FIR filter so we define it:</p>
|
||||
<div class="code"><pre><span></span><span class="k">using</span> <span class="n">Plots</span><span class="p">,</span> <span class="n">DSP</span>
|
||||
<span class="n">gr</span><span class="p">()</span>
|
||||
|
||||
<span class="k">function</span> <span class="n">FIRfreqz</span><span class="p">(</span><span class="n">b</span><span class="o">::</span><span class="kt">Array</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="nb">π</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">1024</span><span class="p">))</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">length</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
|
||||
<span class="n">h</span> <span class="o">=</span> <span class="kt">Array</span><span class="p">{</span><span class="n">ComplexF32</span><span class="p">}(</span><span class="n">undef</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
|
||||
<span class="n">sw</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span><span class="o">:</span><span class="n">n</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">1</span><span class="o">:</span><span class="n">length</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
|
||||
<span class="n">sw</span> <span class="o">+=</span> <span class="n">b</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="nb">im</span><span class="o">*</span><span class="n">w</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="o">^-</span><span class="n">j</span>
|
||||
<span class="k">end</span>
|
||||
<span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">sw</span>
|
||||
<span class="n">sw</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<span class="k">end</span>
|
||||
<span class="k">return</span> <span class="n">h</span>
|
||||
<span class="k">end</span>
|
||||
<span class="o">~~~~~~~~~~~~~</span>
|
||||
</pre></div>
|
||||
|
||||
|
||||
<p>FIRfreqz (generic function with 2 methods)
|
||||
~~~~</p>
|
||||
<h2 id="design-lowpass-fir-filter">Design Lowpass FIR filter</h2>
|
||||
<p>Designing a lowpass FIR filter is very simple to do with DSP.jl, all you
|
||||
need to do is to define the window length, cut off frequency and the
|
||||
window. We will define a lowpass filter with cut off frequency at 5Hz for a signal
|
||||
sampled at 20 Hz.
|
||||
We will use the Hamming window, which is defined as:
|
||||
$w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$</p>
|
||||
<p>~~~~{.julia}
|
||||
fs = 20
|
||||
f = digitalfilter(Lowpass(5, fs = fs), FIRWindow(hamming(61)))
|
||||
w = range(0, stop=pi, length=1024)
|
||||
h = FIRfreqz(f, w)</p>
|
||||
<div class="code"><pre><span></span>## Plot the frequency and impulse response
|
||||
|
||||
|
||||
The next code chunk is executed in term mode, see the [script](FIR_design.jl) for syntax.
|
||||
|
||||
~~~~{.julia}
|
||||
julia> h_db = log10.(abs.(h));
|
||||
|
||||
julia> ws = w/pi*(fs/2)
|
||||
0.0:0.009775171065493646:10.0
|
||||
</pre></div>
|
||||
|
||||
|
||||
<p>~~~~{.julia}
|
||||
plot(ws, h_db,
|
||||
xlabel = "Frequency (Hz)", ylabel = "Magnitude (db)")</p>
|
||||
<div class="code"><pre><span></span>\
|
||||
|
||||
|
||||
|
||||
|
||||
And again with default options
|
||||
|
||||
~~~~{.julia}
|
||||
h_phase = unwrap(-atan.(imag.(h),real.(h)))
|
||||
plot(ws, h_phase,
|
||||
xlabel = "Frequency (Hz)", ylabel = "Phase (radians)")
|
||||
</pre></div>
|
||||
|
||||
|
||||
<p><img alt="" src="../figures/FIR_design_5_1.png" />\ </p>
|
||||
|
||||
|
||||
|
||||
|
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#' ---
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#' title: FIR filter design with Julia
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#' author: Matti Pastell
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#' date: 21th April 2016
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#' ---
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#' # Introduction
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||||
#' This an example of a julia script that can be published using
|
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#' [Weave](http://mpastell.github.io/Weave.jl/latest/usage/).
|
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#' The script can be executed normally using Julia
|
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#' or published to HTML or pdf with Weave.
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#' Text is written in markdown in lines starting with "`#'` " and code
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#' is executed and results are included in the published document.
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|
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#' `#+`. just before code e.g. `#+ term=True, caption='Fancy plots.'`.
|
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#' If you're viewing the published version have a look at the
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#' [source](FIR_design_plots.jl) to see the markup.
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#' # FIR Filter Design
|
||||
|
||||
#' We'll implement lowpass, highpass and ' bandpass FIR filters. If
|
||||
#' you want to read more about DSP I highly recommend [The Scientist
|
||||
#' and Engineer's Guide to Digital Signal
|
||||
#' Processing](http://www.dspguide.com/) which is freely available
|
||||
#' online.
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#' ## Calculating frequency response
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#' DSP.jl package doesn't (yet) have a method to calculate the
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#' the frequency response of a FIR filter so we define it:
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using Plots, DSP
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gr()
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function FIRfreqz(b::Array, w = range(0, stop=π, length=1024))
|
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n = length(w)
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h = Array{ComplexF32}(undef, n)
|
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sw = 0
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for i = 1:n
|
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for j = 1:length(b)
|
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sw += b[j]*exp(-im*w[i])^-j
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end
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h[i] = sw
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sw = 0
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end
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return h
|
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end
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#' ## Design Lowpass FIR filter
|
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#' Designing a lowpass FIR filter is very simple to do with DSP.jl, all you
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#' need to do is to define the window length, cut off frequency and the
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#' window. We will define a lowpass filter with cut off frequency at 5Hz for a signal
|
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#' sampled at 20 Hz.
|
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#' We will use the Hamming window, which is defined as:
|
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#' $w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$
|
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fs = 20
|
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f = digitalfilter(Lowpass(5, fs = fs), FIRWindow(hamming(61)))
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w = range(0, stop=pi, length=1024)
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h = FIRfreqz(f, w)
|
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#' ## Plot the frequency and impulse response
|
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#' The next code chunk is executed in term mode, see the [script](FIR_design.jl) for syntax.
|
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#+ term=true
|
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h_db = log10.(abs.(h));
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ws = w/pi*(fs/2)
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#+
|
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plot(ws, h_db,
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xlabel = "Frequency (Hz)", ylabel = "Magnitude (db)")
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#' And again with default options
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h_phase = unwrap(-atan.(imag.(h),real.(h)))
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plot(ws, h_phase,
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xlabel = "Frequency (Hz)", ylabel = "Phase (radians)")
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<h1 id="getting-started">Getting started</h1>
|
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<p>The best way to get started using Weave.jl is to look at the example input and output documents. Examples for different formats are included in the packages <code>examples</code> directory.</p>
|
||||
<p>First have a look at source document using markdown code chunks and Plots.jl for figures: <a href="../examples/FIR_design.jmd">FIR_design.jmd</a> and then see the output in different formats:</p>
|
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|
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<li>Pandoc markdown: <a href="../examples/FIR_design.txt">FIR_design.txt</a></li>
|
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<p><em>Producing pdf output requires that you have pdflatex installed.</em></p>
|
||||
<p>Add dependencies for the example if needed:</p>
|
||||
<div class="code"><pre><span></span><span class="k">using</span> <span class="n">Pkg</span><span class="p">;</span> <span class="n">Pkg</span><span class="o">.</span><span class="n">add</span><span class="o">.</span><span class="p">([</span><span class="s">"Plots"</span><span class="p">,</span> <span class="s">"DSP"</span><span class="p">])</span>
|
||||
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|
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|
||||
|
||||
<p>Weave the files to your working directory using:</p>
|
||||
<div class="code"><pre><span></span><span class="k">using</span> <span class="n">Weave</span>
|
||||
<span class="c">#Markdown</span>
|
||||
<span class="n">weave</span><span class="p">(</span><span class="n">joinpath</span><span class="p">(</span><span class="n">dirname</span><span class="p">(</span><span class="n">pathof</span><span class="p">(</span><span class="n">Weave</span><span class="p">)),</span> <span class="s">"../examples"</span><span class="p">,</span> <span class="s">"FIR_design.jmd"</span><span class="p">),</span>
|
||||
<span class="n">doctype</span><span class="o">=</span><span class="s">"pandoc"</span>
|
||||
<span class="n">out_path</span><span class="o">=:</span><span class="n">pwd</span><span class="p">)</span>
|
||||
<span class="c">#HTML</span>
|
||||
<span class="n">weave</span><span class="p">(</span><span class="n">joinpath</span><span class="p">(</span><span class="n">dirname</span><span class="p">(</span><span class="n">pathof</span><span class="p">(</span><span class="n">Weave</span><span class="p">)),</span> <span class="s">"../examples"</span><span class="p">,</span> <span class="s">"FIR_design.jmd"</span><span class="p">),</span>
|
||||
<span class="n">out_path</span><span class="o">=:</span><span class="n">pwd</span><span class="p">,</span>
|
||||
<span class="n">doctype</span> <span class="o">=</span> <span class="s">"md2html"</span><span class="p">)</span>
|
||||
<span class="c">#pdf</span>
|
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|
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<p><a id='Weave.jl-Scientific-Reports-Using-Julia-1'></a></p>
|
||||
<h1 id="weavejl-scientific-reports-using-julia">Weave.jl - Scientific Reports Using Julia</h1>
|
||||
<p>This is the documentation of <a href="http://github.com/mpastell/weave.jl">Weave.jl</a>. Weave is a scientific report generator/literate programming tool for Julia. It resembles <a href="http://mpastell.com/pweave">Pweave</a>, Knitr, rmarkdown and Sweave.</p>
|
||||
<p><strong>Current features</strong></p>
|
||||
<ul>
|
||||
<li>Noweb, markdown or script syntax for input documents.</li>
|
||||
<li>Execute code as terminal or "script" chunks.</li>
|
||||
<li>Capture Plots <em>(or Gadfly and PyPlot figures on 0.6)</em>.</li>
|
||||
<li>Supports LaTex, Pandoc, Github markdown, MultiMarkdown, Asciidoc and reStructuredText output</li>
|
||||
<li>Publish markdown directly to html and pdf using julia or Pandoc markdown.</li>
|
||||
<li>Simple caching of results</li>
|
||||
<li>Convert to and from IJulia notebooks</li>
|
||||
</ul>
|
||||
<p><img alt="Weave code and output" src="http://mpastell.com/images/weave_demo.png" /></p>
|
||||
<p><a id='Contents-1'></a></p>
|
||||
<h2 id="contents">Contents</h2>
|
||||
<ul>
|
||||
<li><a href="getting_started/#Getting-started-1">Getting started</a></li>
|
||||
<li><a href="usage/#Using-Weave-1">Using Weave</a><ul>
|
||||
<li><a href="usage/#Weave-1">Weave</a></li>
|
||||
<li><a href="usage/#Tangle-1">Tangle</a></li>
|
||||
<li><a href="usage/#Supported-formats-1">Supported formats</a></li>
|
||||
<li><a href="usage/#Document-syntax-1">Document syntax</a></li>
|
||||
<li><a href="usage/#Noweb-format-1">Noweb format</a></li>
|
||||
<li><a href="usage/#Markdown-format-1">Markdown format</a></li>
|
||||
<li><a href="usage/#Script-format-1">Script format</a></li>
|
||||
<li><a href="usage/#Inline-code-1">Inline code</a></li>
|
||||
<li><a href="usage/#Passing-arguments-to-documents-1">Passing arguments to documents</a></li>
|
||||
<li><a href="usage/#Include-Weave-document-in-Julia-1">Include Weave document in Julia</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="publish/#Publishing-to-html-and-pdf-1">Publishing to html and pdf</a><ul>
|
||||
<li><a href="publish/#Templates-1">Templates</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="chunk_options/#Chunk-options-1">Chunk options</a><ul>
|
||||
<li><a href="chunk_options/#Options-for-code-1">Options for code</a></li>
|
||||
<li><a href="chunk_options/#Options-for-figures-1">Options for figures</a></li>
|
||||
<li><a href="chunk_options/#Set-default-chunk-options-1">Set default chunk options</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="notebooks/#Working-with-Jupyter-notebooks-1">Working with Jupyter notebooks</a><ul>
|
||||
<li><a href="notebooks/#Weaving-from-Jupyter-notebooks-1">Weaving from Jupyter notebooks</a></li>
|
||||
<li><a href="notebooks/#Output-to-Jupyter-notebooks-1">Output to Jupyter notebooks</a></li>
|
||||
<li><a href="notebooks/#Converting-between-formats-1">Converting between formats</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="function_index/#Function-index-1">Function index</a></li>
|
||||
</ul>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
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|
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<a href="getting_started/" title="Getting started" class="md-flex md-footer-nav__link md-footer-nav__link--next" rel="next">
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<div class="md-flex__cell md-flex__cell--stretch md-footer-nav__title">
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Next
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Getting started
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<div class="md-footer-copyright__highlight">
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Matti Pastell 2016-2018
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</div>
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</footer>
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<script src="assets/javascripts/application.583bbe55.js"></script>
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@ -1,36 +0,0 @@
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|
||||
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|
||||
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||||
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||||
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e=b.lastIndexOf("."),k=b.split("/")[0];if(-1!==e&&(!("."===k||".."===k)||1<e))d=b.substring(e,b.length),b=b.substring(0,e);return i.nameToUrl(c(b,a&&a.id,!0),d,!0)},defined:function(b){return t(r,p(b,a,!1,!0).id)},specified:function(b){b=p(b,a,!1,!0).id;return t(r,b)||t(h,b)}});a||(j.undef=function(b){x();var c=p(b,a,!0),e=m(h,b);d(b);delete r[b];delete S[c.url];delete $[b];T(A,function(a,c){a[0]===b&&A.splice(c,1)});e&&(e.events.defined&&($[b]=e.events),y(b))});return j},enable:function(a){m(h,a.id)&&
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s(a).enable()},completeLoad:function(a){var b,c,d=m(j.shim,a)||{},g=d.exports;for(x();A.length;){c=A.shift();if(null===c[0]){c[0]=a;if(b)break;b=!0}else c[0]===a&&(b=!0);E(c)}c=m(h,a);if(!b&&!t(r,a)&&c&&!c.inited){if(j.enforceDefine&&(!g||!da(g)))return e(a)?void 0:w(C("nodefine","No define call for "+a,null,[a]));E([a,d.deps||[],d.exportsFn])}D()},nameToUrl:function(a,b,c){var d,e,h;(d=m(j.pkgs,a))&&(a=d);if(d=m(aa,a))return i.nameToUrl(d,b,c);if(g.jsExtRegExp.test(a))d=a+(b||"");else{d=j.paths;
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a=a.split("/");for(e=a.length;0<e;e-=1)if(h=a.slice(0,e).join("/"),h=m(d,h)){H(h)&&(h=h[0]);a.splice(0,e,h);break}d=a.join("/");d+=b||(/^data\:|\?/.test(d)||c?"":".js");d=("/"===d.charAt(0)||d.match(/^[\w\+\.\-]+:/)?"":j.baseUrl)+d}return j.urlArgs?d+((-1===d.indexOf("?")?"?":"&")+j.urlArgs):d},load:function(a,b){g.load(i,a,b)},execCb:function(a,b,c,d){return b.apply(d,c)},onScriptLoad:function(a){if("load"===a.type||ja.test((a.currentTarget||a.srcElement).readyState))N=null,a=I(a),i.completeLoad(a.id)},
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onScriptError:function(a){var b=I(a);if(!e(b.id))return w(C("scripterror","Script error for: "+b.id,a,[b.id]))}};i.require=i.makeRequire();return i}var g,x,y,D,I,E,N,J,s,O,ka=/(\/\*([\s\S]*?)\*\/|([^:]|^)\/\/(.*)$)/mg,la=/[^.]\s*require\s*\(\s*["']([^'"\s]+)["']\s*\)/g,Q=/\.js$/,ia=/^\.\//;x=Object.prototype;var K=x.toString,fa=x.hasOwnProperty,ha=Array.prototype.splice,z=!!("undefined"!==typeof window&&"undefined"!==typeof navigator&&window.document),ea=!z&&"undefined"!==typeof importScripts,ja=
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z&&"PLAYSTATION 3"===navigator.platform?/^complete$/:/^(complete|loaded)$/,Y="undefined"!==typeof opera&&"[object Opera]"===opera.toString(),F={},q={},R=[],M=!1;if("undefined"===typeof define){if("undefined"!==typeof requirejs){if(G(requirejs))return;q=requirejs;requirejs=void 0}"undefined"!==typeof require&&!G(require)&&(q=require,require=void 0);g=requirejs=function(b,c,d,e){var n,p="_";!H(b)&&"string"!==typeof b&&(n=b,H(c)?(b=c,c=d,d=e):b=[]);n&&n.context&&(p=n.context);(e=m(F,p))||(e=F[p]=g.s.newContext(p));
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n&&e.configure(n);return e.require(b,c,d)};g.config=function(b){return g(b)};g.nextTick="undefined"!==typeof setTimeout?function(b){setTimeout(b,4)}:function(b){b()};require||(require=g);g.version="2.1.16";g.jsExtRegExp=/^\/|:|\?|\.js$/;g.isBrowser=z;x=g.s={contexts:F,newContext:ga};g({});v(["toUrl","undef","defined","specified"],function(b){g[b]=function(){var c=F._;return c.require[b].apply(c,arguments)}});if(z&&(y=x.head=document.getElementsByTagName("head")[0],D=document.getElementsByTagName("base")[0]))y=
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x.head=D.parentNode;g.onError=ca;g.createNode=function(b){var c=b.xhtml?document.createElementNS("http://www.w3.org/1999/xhtml","html:script"):document.createElement("script");c.type=b.scriptType||"text/javascript";c.charset="utf-8";c.async=!0;return c};g.load=function(b,c,d){var e=b&&b.config||{};if(z)return e=g.createNode(e,c,d),e.setAttribute("data-requirecontext",b.contextName),e.setAttribute("data-requiremodule",c),e.attachEvent&&!(e.attachEvent.toString&&0>e.attachEvent.toString().indexOf("[native code"))&&
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!Y?(M=!0,e.attachEvent("onreadystatechange",b.onScriptLoad)):(e.addEventListener("load",b.onScriptLoad,!1),e.addEventListener("error",b.onScriptError,!1)),e.src=d,J=e,D?y.insertBefore(e,D):y.appendChild(e),J=null,e;if(ea)try{importScripts(d),b.completeLoad(c)}catch(m){b.onError(C("importscripts","importScripts failed for "+c+" at "+d,m,[c]))}};z&&!q.skipDataMain&&T(document.getElementsByTagName("script"),function(b){y||(y=b.parentNode);if(I=b.getAttribute("data-main"))return s=I,q.baseUrl||(E=s.split("/"),
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s=E.pop(),O=E.length?E.join("/")+"/":"./",q.baseUrl=O),s=s.replace(Q,""),g.jsExtRegExp.test(s)&&(s=I),q.deps=q.deps?q.deps.concat(s):[s],!0});define=function(b,c,d){var e,g;"string"!==typeof b&&(d=c,c=b,b=null);H(c)||(d=c,c=null);!c&&G(d)&&(c=[],d.length&&(d.toString().replace(ka,"").replace(la,function(b,d){c.push(d)}),c=(1===d.length?["require"]:["require","exports","module"]).concat(c)));if(M){if(!(e=J))N&&"interactive"===N.readyState||T(document.getElementsByTagName("script"),function(b){if("interactive"===
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b.readyState)return N=b}),e=N;e&&(b||(b=e.getAttribute("data-requiremodule")),g=F[e.getAttribute("data-requirecontext")])}(g?g.defQueue:R).push([b,c,d])};define.amd={jQuery:!0};g.exec=function(b){return eval(b)};g(q)}})(this);
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||||
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