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Tone generator

DTMF is a two-tone multi-frequency analogue signal, in other words, each symbol corresponds to a set of two frequencies.

Scope of application of DTMF tones: automatic telephone signalling between devices. In particular, such tones are used to control the connection between analogue equipment.

DTMF implementation

Connecting libraries.

In [ ]:
Pkg.add(["WAV", "DSP"])
   Resolving package versions...
  No Changes to `~/.project/Project.toml`
  No Changes to `~/.project/Manifest.toml`
In [ ]:
using Plots
using FFTW
using DSP
using WAV

Declaring system parameters

In [ ]:
# symbols = ["1", "5", "0", "8", "6", "4", "7", "7", "0", "0", "0"]; # Набор символов
symbols = ["5", "0", "8"]; # Набор символов
lfg = [697 770 852 941]; # Группа нижних частот
hfg = [1209 1336 1477];  # Группа верхних частот
f = [reshape(ones(3, 1) * lfg, 1, 12); repeat(hfg, 1, 4)];
Fs = 8000;       # Частота дискретизации 8 кГц
N = 800;        # Длительность тональности 100 мс
t = [0:N-1;] ./ Fs; # 800 дискретов на Fs
pit = t * 2 * pi;
tones = zeros(N, length(symbols));

Filling in tonalities

In [ ]:
for i = 1:length(symbols)
    if symbols[i] == "1"
        tones[:, i] = sum(sin.(f[:, 1] * pit'), dims=1)'
    elseif symbols[i] == "2"
        tones[:, i] = sum(sin.(f[:, 2] * pit'), dims=1)'
    elseif symbols[i] == "3"
        tones[:, i] = sum(sin.(f[:, 3] * pit'), dims=1)'
    elseif symbols[i] == "4"
        tones[:, i] = sum(sin.(f[:, 4] * pit'), dims=1)'
    elseif symbols[i] == "5"
        tones[:, i] = sum(sin.(f[:, 5] * pit'), dims=1)'
    elseif symbols[i] == "6"
        tones[:, i] = sum(sin.(f[:, 6] * pit'), dims=1)'
    elseif symbols[i] == "7"
        tones[:, i] = sum(sin.(f[:, 7] * pit'), dims=1)'
    elseif symbols[i] == "8"
        tones[:, i] = sum(sin.(f[:, 8] * pit'), dims=1)'
    elseif symbols[i] == "9"
        tones[:, i] = sum(sin.(f[:, 9] * pit'), dims=1)'
    elseif symbols[i] == "*"
        tones[:, i] = sum(sin.(f[:, 10] * pit'), dims=1)'
    elseif symbols[i] == "0"
        tones[:, i] = sum(sin.(f[:, 11] * pit'), dims=1)'
    elseif symbols[i] == "#"
        tones[:, i] = sum(sin.(f[:, 12] * pit'), dims=1)'
    end
end

Specifies pauses between tones.

In [ ]:
    N8::Int64 = N / 8
    tones = [tones; 0.05 * randn(N8, length(symbols))];
    tones = [0.05 * randn(N8, 1); tones[:]];

Analysing the results

Let's plot the graph of the signal.

In [ ]:
N = length(tones);
t = [0:N-1;] / Fs;
plot(1e3 * t, tones, xlabel="Время, мс", ylabel="Амплитуда", title="DTMF сигнал")
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Plotting a graph of the spectrum.

The spectrum is plotted using the fast Fourier transform.

In [ ]:
Spec = 10 * log10.(abs.(fftshift(fft(tones)) ./ 1000) .^ 2);
freqs = fftshift(fftfreq(length(t), Fs))
plot(freqs, Spec, xlim=(650, 1500), xticks=650:100:1500, xlabel="Частота, Гц", ylabel="Мощьность, дБ", title="Спектр DTMF сигнала")
Out[0]:

From the presented graphs it is difficult to clearly understand what was the original set of symbols. For more convenient representation, let's build a spectrogram of the original signal.

In [ ]:
spgr = DSP.spectrogram(tones[:,1], 255, 128; fs = Fs); # Создание спектрограммы исходного DTMF сигнала
Plots.heatmap(spgr.time.*1000, spgr.freq, pow2db.(spgr.power), xguide = "Время, мс", yguide = "Частота, Гц",ylim =(500, 1500), yticks=650:100:1500)
Out[0]:

From the spectrogram it follows that the set of symbols was: 5,0,8.

Conclusion

By the end of the development of this example you have been shown the possibilities of implementing a tone generator in Engee, as well as the possibilities of visualising modulated signals to perform a convenient analysis of these signals.