mirror of https://github.com/mpastell/Weave.jl
151 lines
3.4 KiB
Plaintext
151 lines
3.4 KiB
Plaintext
---
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author: "Matti Pastell"
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title: "FIR filter design with Julia"
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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://weavejl.mpastell.com/dev/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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Notice that you don't need to define chunk options, but you can using
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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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<!-- this setup dependencies, but doesn't appear in the generated document -->
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# FIR Filter Design
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We'll implement lowpass, highpass and ' bandpass FIR filters. If
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you want to read more about DSP I highly recommend [The Scientist
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and Engineer's Guide to Digital Signal
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Processing](http://www.dspguide.com/) which is freely available
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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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~~~~{.julia}
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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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~~~~~~~~~~~~~
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~~~~
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FIRfreqz (generic function with 2 methods)
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~~~~
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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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~~~~{.julia}
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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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~~~~~~~~~~~~~
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~~~~
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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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⋮
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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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~~~~
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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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~~~~{.julia}
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julia> h_db = log10.(abs.(h));
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julia> ws = w/pi*(fs/2)
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0.0:0.009775171065493646:10.0
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~~~~~~~~~~~~~
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~~~~{.julia}
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plot(ws, h_db,
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xlabel = "Frequency (Hz)", ylabel = "Magnitude (db)")
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~~~~~~~~~~~~~
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\
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And again with default options
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~~~~{.julia}
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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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~~~~~~~~~~~~~
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\
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