60 lines
1.3 KiB
Mathematica
60 lines
1.3 KiB
Mathematica
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clear;
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close all;
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Fe = 24000;
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Te = 1/Fe;
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Rb = 6000;
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M = 2^1;
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Ts = log2(M)/Rb;
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Ns = floor(Ts/Te);
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N = 20;
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bits = randi([0, 1], 1, N);
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T = (0:N*Ns/log2(M)-1) * Te;
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X_m = 2 * bits - 1; % mapping
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X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
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h = rcosdesign(0.5, 8, Ns); % réponse impulsionnelle en racine de cosinus surélevé.
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X_f = filter(h, 1, X_k); % produit de convolution (filtrage)
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figure;
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plot(T, X_f);
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title("Signal transmis via le modulateur 4");
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xlabel("Secondes (s)");
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ylabel("Amplitude");
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%ylim([ -1.1 1.1 ]);
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F = linspace(0, Fe/2, N);
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alpha = 0.5;
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sigma = 1;
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indices = abs(F) < (1-alpha)/2/Ts;
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DSP_theorique = indices(indices);
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indices = (1-alpha)/2/Ts < abs(F) & abs(F) < (1+alpha)/2/Ts;
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DSP_theorique = [ DSP_theorique, indices(indices) .* (1 + cos( pi*Ts/alpha .* ( abs(F(indices)) - (1-alpha)/2/Ts ) ))/2 ];
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DSP_theorique = [ DSP_theorique, zeros(1, N-length(DSP_theorique)) ];
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DSP_theorique = DSP_theorique*sigma;
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DSP_numerique = pwelch(X_f);
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F_num = linspace(0, Fe/2, length(DSP_numerique));
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figure;
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plot(F_num, DSP_numerique/max(smoothdata(DSP_numerique)));
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hold;
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plot(F, DSP_theorique);
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title("DSP du signal transmis via le modulateur 4 et son équivalent théorique");
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xlabel("Fréquence (Hz)");
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ylabel("Amplitude");
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%ylim([ 0 1 ]);
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legend("DSP numérique", "DSP théorique");
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