cenas cenadas cenas

TP3a/DiogoEliseu_TP3_2.m

@@ -14,18 +14,21 @@ EEG = EEG';
 Ls = length(sintetico);
 Ts = 0.125;
 Fs = 1/Ts;
-Fs_vector = (0:Ls/2-1)/(Ls/2) * Fs;
+Fs_vector = linspace(0, 2*pi*Fs, Ls)/(pi*Fs);
+Fs_vector_pi = Fs_vector(1:(length(Fs_vector)/2));
 
 % sinal cello
 Lc = length(cello.x);
 Tc = cello.dt;
 Fc = 1/Tc;
-Fc_vector = (0:Lc/2-1)/(Lc/2) * Fc;
+Fc_vector = linspace(0, 2*pi*Fc, Lc)/(pi*Fc);
+Fc_vector_pi = Fc_vector(1:(length(Fc_vector)/2));
 
 % sinal EEG
 Le = length(EEG);
 Fe = 100;
-Fe_vector = (1:Le/2-1)/(Le/2) * Fe/2;
+Fe_vector = linspace(0, 2*pi*Fe, Le)/(pi*Fe);
+Fe_vector_pi = Fe_vector(1:(length(Fe_vector)/2));
 
 figure(1)
 
@@ -36,7 +39,7 @@ xlabel('t'), ylabel('sintetico[t]'), title('sinal sintetico');
 subplot(2,1,2)
 DFT_synth = fft(sintetico, Ls);
 DFT_synth_pi = DFT_synth(1 : (Ls)/2);
-plot(Fs_vector, abs(DFT_synth_pi))
+plot(Fs_vector_pi, abs(DFT_synth_pi))
 xlabel('\omega/\pi'), ylabel('|X(\omega)|'), title('DFT sintetico em [0, \pi]')
 
 figure(2)
@@ -48,7 +51,7 @@ xlabel('t'), ylabel('cello[t]'), title('sinal cello');
 subplot(2,1,2)
 DFT_cello = fft(cello.x, Lc);
 DFT_cello_pi = DFT_cello(1 : (Lc)/2);
-plot(Fc_vector, abs(DFT_cello_pi))
+plot(Fc_vector_pi, abs(DFT_cello_pi))
 xlabel('\omega/\pi'), ylabel('|X(\omega)|'), title('DFT cello em [0, \pi]')
 
 figure(3)
@@ -58,9 +61,9 @@ plot(EEG);
 xlabel('t'), ylabel('eeg[t]'), title('sinal EEG');
 
 subplot(2,1,2)
-DFT_EEG = fft(EEG, Le-1);
-DFT_EEG_pi = DFT_EEG(1 : (Le-1)/2);
-plot(Fe_vector, abs(DFT_EEG_pi))
+DFT_EEG = fft(EEG, Le);
+DFT_EEG_pi = DFT_EEG(1 : (Le)/2);
+plot(Fe_vector_pi, abs(DFT_EEG_pi))
 xlabel('\omega/\pi'), ylabel('|X(\omega)|'), title('DFT EEG em [0, \pi]')
 
 

TP3b/DiogoEliseu_TP3_5.m

@@ -0,0 +1,49 @@
+%% Inicialização do ambiente
+clear; close all; clc
+
+%% Exercício 5
+load("DiogoEliseu_TP3_5filt.mat");
+
+figure(1)
+plotinhos(passa_baixa_SOS, passa_baixa_G)
+sgtitle('Low-pass')
+
+figure(2)
+plotinhos(passa_alta_SOS, passa_alta_G)
+sgtitle('High-pass')
+
+figure(3)
+plotinhos(passa_banda_SOS, passa_banda_G)
+sgtitle('Band-pass')
+
+figure(4)
+plotinhos(corta_banda_SOS, corta_banda_G)
+sgtitle('Band-Cut')
+
+function plotinhos(SOS, G)
+[num, den] = sos2tf(SOS, G);
+[z, p, ~] = tf2zp(num, den);
+[h, w] = freqz(num, den);
+w_pi = w/pi;
+gain = 20.*log10(abs(h));
+
+subplot(2,2,1)
+% Módulo
+plot(w_pi, gain);
+ylabel("Gain (dB)"); xlabel("\omega/\pi"); title('Filter Gain');
+
+subplot(2,2,2)
+% Fase
+%freqz(p,1);
+plot(w_pi, unwrap(angle(h)));
+ylabel("Phase (degrees)"); xlabel("Normalized Frequency (x\pi rad/sample)"); title('Phase');
+
+subplot(2,2,3)
+% Resposta Impulsional
+impulseplot(tf(num, den));
+
+subplot(2,2,4)
+% Zeros e Polos
+zplane(z, p);
+title("Pole-Zero plot");
+end

TP3b/DiogoEliseu_TP3_6.m

@@ -0,0 +1,65 @@
+%% Inicialização do ambiente
+clear ; close all; clc
+
+%% Exercício 6
+sintetico_data = fopen('sintetico.csv');
+sintetico = textscan(sintetico_data, '%f', 'Delimiter', ',');
+sintetico = sintetico{1,1};
+fclose(sintetico_data);
+
+fn = [0.91, 0.85, 0.91, 0.95];
+
+xf = DiogoEliseu_TP3_6f(sintetico, fn(1), 0);
+for i=2:(length(fn)-1)
+    %figure(i)
+    xf = DiogoEliseu_TP3_6f(xf, fn(i), 0);
+end
+figure(1)
+DiogoEliseu_TP3_6f(xf, fn(length(fn)), 1);
+
+
+function filtrado = DiogoEliseu_TP3_6f(xo,fn,graf)
+    Ls = length(xo);
+    d = fdesign.notch('N,F0,Q', 8, fn, 10);
+    Hd = design(d);
+    SOS = Hd.SOS;
+    G = Hd.ScaleValues;
+    [num, den] = sos2tf(SOS, G);
+    w_2pi = linspace(0, 2*pi, length(xo))/pi;
+    w_pi = w_2pi(1:(length(w_2pi)/2));
+    h = freqz(num, den, w_2pi);
+    gain = 20.*log10(abs(h));
+    [z, p, ~] = tf2zp(num, den);
+    filtrado = filter(num, den, xo);
+    if (graf == 1)
+        subplot(2,3,1)
+        plot(xo)
+        xlabel('t'), ylabel('xo[t]'), title('sinal xo');
+        
+        subplot(2,3,2)
+        plot(filtrado)
+        xlabel('t'), ylabel('filtrado[t]'), title('sinal filtrado');
+        
+        subplot(2,3,3)
+        DFT_xo = fft(xo);
+        DFT_xo_pi = DFT_xo(1 : (Ls)/2);
+        plot(w_pi, abs(DFT_xo_pi));
+        xlabel('\omega/\pi'), ylabel('|X(\omega)|'), title('DFT xo em [0, \pi]')
+        
+        subplot(2,3,4)
+        DFT_filtrado = fft(filtrado);
+        DFT_filtrado_pi = DFT_filtrado(1 : (Ls)/2);
+
+        plot(w_pi, abs(DFT_filtrado_pi));
+        xlabel('\omega/\pi'), ylabel('|X(\omega)|'), title('DFT xo filtrado em [0, \pi]')
+        
+        subplot(2,3,5)
+        plot(w_2pi, gain);
+        ylabel("Ganho (dB)"); xlabel("\omega/2\pi"); title('Ganho do filtro');
+        
+        subplot(2,3,6)
+        zplane(z, p)
+        title("Diagrama de Zeros e Polos");
+    end
+end
+

TP3b/DiogoEliseu_TP3_7.m

@@ -0,0 +1,67 @@
+%% Inicialização do ambiente
+clear; close all; clc
+
+%% Exercício 7
+[y, Fs] = audioread("Canto1.mp3");
+s = y(:,1);
+%Ts = 1/Fs;
+
+% S: short-time Fourier transform of the input signal
+% F: vector of cyclical frequencies
+% T: vector of time instants
+% P: power spectral density (PSD)
+[S, F, T, P] = spectrogram(s, 128, 96, 128, Fs);
+
+figure(1)
+% Signal
+subplot(2,3,1)
+surf(T, F, 10*log10(P), 'edgecolor', 'none')
+axis tight, view(0,90)
+title("Original Signal (X)"); ylabel("Frequency (Hz)"); xlabel("Time (s)");
+
+% Noise
+subplot(2,3,2)
+%T_noise = T(1377:4134);
+s_noise = s((Fs * (1 - 1)) + 1 : Fs * (3 - 1)); % [1-3]
+[S_noise, F_noise, T_noise, P_noise] = spectrogram(s_noise, 128, 96, 128, Fs);
+surf(T_noise, F_noise, 10*log10(P_noise), 'edgecolor', 'none')
+axis tight, view(0,90)
+title("Background Noise (Xn) in 1-3s"); ylabel("Frequency (Hz)"); xlabel("Time (s)");
+
+% Song
+subplot(2,3,3)
+s_chirp = s((Fs * (4 - 1)) + 1 : Fs * (6 - 1)); % [4-6]
+[S_chirp, F_chirp, T_chirp, P_chirp] = spectrogram(s_chirp, 128, 96, 128, Fs);
+surf(T_chirp, F_chirp, 10*log10(P_chirp), 'edgecolor', 'none')
+axis tight, view(0,90)
+title("Chirp (Xs) in 4-6s"); ylabel("Frequency (Hz)"); xlabel("Time (s)");
+
+% DFT signal
+subplot(2,3,4)
+L_s = length(s);
+f_s_2pi = linspace(0, Fs, L_s)/1000; % to kHz
+f_s_half = f_s_2pi(1:(length(f_s_2pi)/2));
+DFT_s = fft(s);
+DFT_s_half = DFT_s(1 : (L_s/2));
+plot(f_s_half, abs(DFT_s_half));
+title("X in function of the frequency (kHz)"); ylabel("Amplitude (Hz)"); xlabel("Frequency (kHz)");
+
+% DFT noise
+subplot(2,3,5)
+L_s_noise = length(s_noise);
+f_s_noise_2pi = linspace(0, Fs, L_s_noise)/1000; % to kHz
+f_s_noise_half = f_s_noise_2pi(1:(length(f_s_noise_2pi)/2));
+DFT_s = fft(s_noise);
+DFT_s_noise_half = DFT_s(1 : (L_s_noise/2));
+plot(f_s_noise_half, abs(DFT_s_noise_half));
+title("Xn in function of the frequency (kHz)"); ylabel("Amplitude (Hz)"); xlabel("Frequency (kHz)");
+
+% DFT chirp
+subplot(2,3,6)
+L_s_chirp = length(s_chirp);
+f_s_chirp_2pi = linspace(0, Fs, L_s_chirp)/1000; % to kHz
+f_s_chirp_half = f_s_chirp_2pi(1:(length(f_s_chirp_2pi)/2));
+DFT_s = fft(s_chirp);
+DFT_s_chirp_half = DFT_s(1 : (L_s_chirp/2));
+plot(f_s_chirp_half, abs(DFT_s_chirp_half));
+title("Xs in function of the frequency (kHz)"); ylabel("Amplitude (Hz)"); xlabel("Frequency (kHz)");

TP3b/sintetico.csv

@@ -0,0 +1 @@
+1,-0.67391,1.1587,0.3128,0.93612,1.2837,0.90455,1.7785,1.3046,1.8455,1.852,1.9125,2.1352,2.2587,2.0989,2.7274,2.0553,2.978,2.2675,2.918,2.6486,2.7807,2.9186,2.8027,2.9677,2.9523,2.9453,3.0443,2.9973,3.0398,3.0493,3.0945,2.9478,3.2825,2.76,3.3982,2.78,3.1627,3.1682,2.6183,3.6665,2.1883,3.8052,2.2527,3.418,2.7086,2.8574,3.0586,2.6196,2.9617,2.7891,2.6157,2.9553,2.5121,2.7074,2.8485,2.1298,3.2838,1.7182,3.3201,1.825,2.8541,2.283,2.2651,2.622,1.9757,2.5832,2.0273,2.3258,2.14,2.143,2.1069,2.1005,2.001,2.0436,1.9762,1.8962,1.9922,1.8025,1.8617,1.9099,1.551,2.1063,1.2945,2.1095,1.323,1.8299,1.5411,1.5277,1.6054,1.5121,1.3558,1.7244,1.0681,1.7491,1.166,1.298,1.6937,0.60739,2.1863,0.24468,2.1365,0.50781,1.5443,1.0989,0.91705,1.4504,0.71957,1.3261,0.90774,1.0143,1.0578,0.93038,0.89404,1.1331,0.57644,1.3133,0.44862,1.2107,0.60587,0.9152,0.81754,0.70896,0.84929,0.70402,0.73493,0.75323,0.66173,0.71245,0.67024,0.65786,0.60662,0.74438,0.39813,0.90648,0.25176,0.85117,0.44768,0.41943,0.94474,-0.12966,1.3207,-0.3255,1.1964,-0.00067769,0.67569,0.49292,0.25683,0.65994,0.28125,0.41659,0.55213,0.17407,0.57822,0.34358,0.1627,0.84136,-0.35305,1.172,-0.47064,0.9837,-0.086321,0.4438,0.42079,0.022946,0.62844,-0.019783,0.4955,0.1566,0.30214,0.25911,0.25538,0.22224,0.28247,0.2009,0.22958,0.2713,0.13727,0.28929,0.19285,0.10775,0.4301,-0.16131,0.61471,-0.2356,0.51604,-0.025333,0.22939,0.2092,0.098326,0.15893,0.28298,-0.11741,0.50752,-0.20443,0.34821,0.18615,-0.23908,0.81811,-0.78944,1.1239,-0.79564,0.80571,-0.25768,0.16132,0.31715,-0.24173,0.46395,-0.16727,0.2268,0.096406,0.029416,0.13387,0.1476,-0.11362,0.4212,-0.33705,0.50661,-0.27613,0.30851,-0.020671,0.057516,0.14698,-0.012093,0.1148,0.065862,0.029884,0.10406,0.036342,0.061896,0.057948,0.093187,-0.060251,0.27064,-0.25277,0.38721,-0.22665,0.16269,0.17708,-0.36181,0.6993,-0.76408,0.86938,-0.66503,0.51987,-0.16845,0.0026036,0.22725,-0.18708,0.18064,0.034568,-0.11148,0.2563,-0.1579,0.066897,0.23816