mirror of https://github.com/mpastell/Weave.jl
113 lines
2.5 KiB
Markdown
113 lines
2.5 KiB
Markdown
% FIR filter design with Julia
|
|
% Matti Pastell
|
|
% 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.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 Gadfly, DSP
|
|
|
|
function FIRfreqz(b::Array, w = linspace(0, π, 1024))
|
|
n = length(w)
|
|
h = Array{Complex64}(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 = linspace(0, pi, 1024)
|
|
h = FIRfreqz(f, w)
|
|
~~~~~~~~~~~~~
|
|
|
|
|
|
|
|
|
|
## Plot the frequency and impulse response
|
|
|
|
|
|
~~~~{.julia}
|
|
h_db = log10(abs(h))
|
|
ws = w/pi*(fs/2)
|
|
~~~~~~~~~~~~~
|
|
|
|
|
|
|
|
|
|
The next code chunk is executed in term mode, see the [script](FIR_design.jl) for syntax.
|
|
|
|
~~~~{.julia}
|
|
julia> plot(y = h_db, x = ws, Geom.line,
|
|
Guide.xlabel("Frequency (Hz)"), Guide.ylabel("Magnitude (db)"))
|
|
Plot(...)
|
|
|
|
~~~~~~~~~~~~~
|
|
|
|
|
|
\
|
|
|
|
|
|
|
|
And again with default options
|
|
|
|
|
|
~~~~{.julia}
|
|
h_phase = unwrap(-atan2(imag(h),real(h)))
|
|
plot(y = h_phase, x = ws, Geom.line,
|
|
Guide.xlabel("Frequency (Hz)"), Guide.ylabel("Phase (radians)"))
|
|
~~~~~~~~~~~~~
|
|
|
|
|
|
\
|
|
|