Getting Started with Digital Signal Processing (DSP) in Engee

Working with functions

Loading and visualisation of the signal

The using function makes the listed modules available to the user, similar to the import function in other languages:

Multiple outputs do not have to be bracketed as in MATLAB.

using DSP, WAV, Plots
plotly()

s, fs = wavread("/user/test.wav")

plot(0:1/fs:(length(s)-1)/fs, s)

Output

getting started dsp 1

The function below takes a spectrogram with standard parameters for speech (Hanning windows 25 ms, overlap 10 ms), constructs and returns a spectrogram:

S = spectrogram(s[:,1], convert(Int, 25e-3*fs), convert(Int, 10e-3*fs); window=hanning)
Plots.heatmap(S.time.*1000, S.freq, pow2db.(S.power), xguide = "Время, мс", yguide = "Частота, Гц")

Output

getting started dsp 2

Signal processing

Now let’s pass the signal through a filter to simulate the phone’s bandwidth, and plot its spectrogram again:

responsetype = Bandpass(300, 3400; fs=fs)
prototype = Butterworth(8)
telephone_filter = digitalfilter(responsetype, prototype)

Let’s look at the filter characteristic:

Variables can have Unicode names. This is typed as \omega + tab.

ω = 0:0.01:pi
H = freqz(telephone_filter, ω)

Filter our signal:

sf = filt(telephone_filter, s)

Sf = spectrogram(s[:,1], convert(Int, 25e-3*fs), convert(Int, 10e-3*fs); window=hanning)
Plots.heatmap(Sf.time.*1000, Sf.freq, pow2db.(Sf.power), xguide = "Время, мс", yguide = "Частота, Гц")

Output

getting started dsp 3

Reproduction of results

using Base64

function audioplayer(filepath)
  markup = """<audio controls="controls" {autoplay}>
        <source src="$filepath" />
        Your browser does not support the audio element.
        </audio>"""

  display(MIME("text/html") ,markup)
 end

 function audioplayer(s, fs)
  buf = IOBuffer()
  wavwrite(s, buf; Fs=fs)
  data = base64encode(unsafe_string(pointer(buf.data), buf.size))
  markup = """<audio controls="controls" {autoplay}>
        <source src="data:audio/wav;base64,$data" type="audio/wav" />
        Your browser does not support the audio element.
        </audio>"""
  display(MIME("text/html") ,markup)
end

audioplayer(s, fs)
audioplayer(sf, fs)

Output

Signal oversampling

In this example we will look at resampling an audio signal from 48kHz to 44.1kHz using a low pass filter design followed by resampling of the signal.

Let’s find the interpolation and decimation coefficients.

using Plots
using DSP

Fdat = 48e3;
Fcd = 44.1e3;
LM = Rational{Int32}(Fcd/Fdat);
L = LM.num;
M = LM.den;
(L,M)

Output

(147, 160)

Visualise the original audio signal:

t = 0:1/Fdat:0.25-1/Fdat;
x = sin.(2*pi*1.5e3*t);
gr()
plot(t, x, line=:stem, marker=:circle)
xlims!((0,0.001))

Output

getting started dsp 4

Let’s resample and overlay the obtained signal on the original one

f = (Fdat/2)*min(1/L,1/M)
win = DSP.Windows.kaiser(3579,3);
fir = DSP.Filters.digitalfilter(DSP.Filters.Lowpass(f/48e3),FIRWindow(win)).

xup = DSP.Filters.resample(x,Int64(L),fir);
y = L.*xup[1:M:end].

t_res = (0:(length(y)-1))/Fcd;
plot!(t_res, y, line=:stem, marker=:circle)

Output

getting started dsp 5