2016-04-22 13:44:30 +02:00
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% FIR filter design with Julia
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% Matti Pastell
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% 21th April 2016
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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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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.jl) to see the markup.
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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 Gadfly, DSP
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function FIRfreqz(b::Array, w = linspace(0, π, 1024))
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n = length(w)
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h = Array{Complex64}(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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## 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 = linspace(0, pi, 1024)
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h = FIRfreqz(f, w)
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~~~~~~~~~~~~~
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## Plot the frequency and impulse response
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~~~~{.julia}
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h_db = log10(abs(h))
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2016-04-27 20:24:44 +02:00
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ws = w/pi*(fs/2)
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~~~~~~~~~~~~~
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2016-04-22 13:44:30 +02:00
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2016-04-27 20:24:44 +02:00
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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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2016-12-16 19:18:37 +01:00
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julia> plot(y = h_db, x = ws, Geom.line,
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2016-04-22 13:44:30 +02:00
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Guide.xlabel("Frequency (Hz)"), Guide.ylabel("Magnitude (db)"))
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2017-05-15 16:28:10 +02:00
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Plot(...)
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2017-03-13 15:12:57 +01:00
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2016-04-22 13:44:30 +02:00
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~~~~~~~~~~~~~
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2016-04-27 20:24:44 +02:00
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![](figures/FIR_design_4_1.png)\
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2016-04-22 13:44:30 +02:00
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And again with default options
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~~~~{.julia}
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h_phase = unwrap(-atan2(imag(h),real(h)))
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plot(y = h_phase, x = ws, Geom.line,
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Guide.xlabel("Frequency (Hz)"), Guide.ylabel("Phase (radians)"))
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~~~~~~~~~~~~~
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2016-04-27 20:24:44 +02:00
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![](figures/FIR_design_5_1.png)\
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2016-04-22 13:44:30 +02:00
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