From 4b900c759dfa32f4b824e40d45095b848462756c Mon Sep 17 00:00:00 2001 From: Diogo Cordeiro Date: Thu, 31 Dec 2020 23:11:10 +0000 Subject: [PATCH] TP3_8: Noise removal done. --- TP3/DiogoEliseu_TP3_7.m | 1 + TP3/DiogoEliseu_TP3_8.m | 34 ---------- {TP3 => TP3_8}/Canto1.mp3 | Bin TP3_8/DiogoEliseu_TP3_8_butterworth.m | 58 ++++++++++++++++++ ...liseu_TP3_8_butterworth_2nd_order_filter.m | 21 +++++++ TP3_8/DiogoEliseu_TP3_8_butterworth_filter.m | 27 ++++++++ TP3_8/DiogoEliseu_TP3_8_high_pass.m | 55 +++++++++++++++++ TP3_8/canto1_butterworh_2nd_order.flac | Bin 0 -> 1003837 bytes TP3_8/canto1_butterworth.flac | Bin 0 -> 573811 bytes TP3_8/canto1_high_pass.flac | Bin 0 -> 659481 bytes TP3_8/img/filters/butterworth_filter.png | Bin 0 -> 29278 bytes .../filters/butterworth_filter_2nd_order.png | Bin 0 -> 45404 bytes TP3_8/img/plots/ft_signal.jpg | Bin 0 -> 78661 bytes TP3_8/img/plots/ft_signal_zoom.png | Bin 0 -> 5412 bytes .../gain_butterworth_amplitude_points.png | Bin 0 -> 27113 bytes TP3_8/img/plots/marked_ft_signal.jpg | Bin 0 -> 80064 bytes TP3_8/img/plots/plot_ft_signal.jpg | Bin 0 -> 76613 bytes .../plot_ft_signal_filtered_2nd_order.jpg | Bin 0 -> 76665 bytes 18 files changed, 162 insertions(+), 34 deletions(-) delete mode 100644 TP3/DiogoEliseu_TP3_8.m rename {TP3 => TP3_8}/Canto1.mp3 (100%) create mode 100644 TP3_8/DiogoEliseu_TP3_8_butterworth.m create mode 100644 TP3_8/DiogoEliseu_TP3_8_butterworth_2nd_order_filter.m create mode 100644 TP3_8/DiogoEliseu_TP3_8_butterworth_filter.m create mode 100644 TP3_8/DiogoEliseu_TP3_8_high_pass.m create mode 100644 TP3_8/canto1_butterworh_2nd_order.flac create mode 100644 TP3_8/canto1_butterworth.flac create mode 100644 TP3_8/canto1_high_pass.flac create mode 100644 TP3_8/img/filters/butterworth_filter.png create mode 100644 TP3_8/img/filters/butterworth_filter_2nd_order.png create mode 100644 TP3_8/img/plots/ft_signal.jpg create mode 100644 TP3_8/img/plots/ft_signal_zoom.png create mode 100644 TP3_8/img/plots/gain_butterworth_amplitude_points.png create mode 100644 TP3_8/img/plots/marked_ft_signal.jpg create mode 100644 TP3_8/img/plots/plot_ft_signal.jpg create mode 100644 TP3_8/img/plots/plot_ft_signal_filtered_2nd_order.jpg diff --git a/TP3/DiogoEliseu_TP3_7.m b/TP3/DiogoEliseu_TP3_7.m index 30077c2..50e832d 100644 --- a/TP3/DiogoEliseu_TP3_7.m +++ b/TP3/DiogoEliseu_TP3_7.m @@ -10,6 +10,7 @@ s = y(:,1); % F: vector of cyclical frequencies % T: vector of time instants % P: power spectral density (PSD) + % signal, window, noverlap, nfft, fs [S, F, T, P] = spectrogram(s, 128, 96, 128, Fs); figure(1) diff --git a/TP3/DiogoEliseu_TP3_8.m b/TP3/DiogoEliseu_TP3_8.m deleted file mode 100644 index ba92712..0000000 --- a/TP3/DiogoEliseu_TP3_8.m +++ /dev/null @@ -1,34 +0,0 @@ -%% clean environment -clear; close all; clc - -%% read input -[signal, fs] = audioread("Canto1.mp3"); - -%% Compute the FFT -signal_length = length(signal); -fhat = fft(signal, signal_length); -PSD = fhat.*conj(fhat)/signal_length; % Power spectrum density -%[S, freq, T, PSDlel] = spectrogram(signal, 128, 96, 128, Fs); -% signal, window, noverlap, nfft, fs -freq_vector = linspace(1, fs, signal_length); -L = 1:floor(signal_length/2); - -cutoff_indices = abs(PSD)>0.002; -PSD_clean = PSD.*cutoff_indices; -fhat_filtered = cutoff_indices.*fhat; -signal_filtered = ifft(fhat_filtered); - -figure(1) -plot(PSD) - -figure(2) -plot(PSD_clean) - -figure(3) -plot(signal) - -figure(4) -plot(signal_filtered) - -%% output -audiowrite('restored.flac', signal_filtered, fs); \ No newline at end of file diff --git a/TP3/Canto1.mp3 b/TP3_8/Canto1.mp3 similarity index 100% rename from TP3/Canto1.mp3 rename to TP3_8/Canto1.mp3 diff --git a/TP3_8/DiogoEliseu_TP3_8_butterworth.m b/TP3_8/DiogoEliseu_TP3_8_butterworth.m new file mode 100644 index 0000000..8bf7f7c --- /dev/null +++ b/TP3_8/DiogoEliseu_TP3_8_butterworth.m @@ -0,0 +1,58 @@ +%% Inicialização do ambiente +clear; close all; clc + +%% >Exercício 8< +%% Input +[y, Fs] = audioread("Canto1.mp3"); % Signal and Sampling Frequency +signal = y(:,1); % Discard second channel +Fn = Fs/2; % Nyquist Frequency (Hz) +L = length(signal); % Signal Length + +%% Find the noise +dft_signal = fft(signal)./L; % Fourier Transform +Fv = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector + +%% Filter +%signal_filtered = filter(DiogoEliseu_TP3_8_butterworth_2nd_order_filter,signal); +signal_filtered = filter(DiogoEliseu_TP3_8_butterworth_filter,signal); + +%% Filtered signal +dft_signal_filtered = fft(signal_filtered)/L; % Fourier Transform + +%% Output +signal_power = abs(dft_signal(1:(L/2+1))); +figure(1) +subplot(2,3,1) +hold on +plot(Fv, signal_power) +grid +marks = [2850, 3020, 7000, 7150]; +plot(2850, signal_power(2850), 'r*') +plot(3020, signal_power(3020), 'r*') +plot(7000, signal_power(7000), 'r*') +plot(7150, signal_power(7150), 'r*') +xlabel("Frequência (Hz)"); ylabel("|H_{1}(f)|"); title("DFT do Sinal") +hold off +subplot(2,3,4) +plot(Fv, abs(dft_signal_filtered(1:(L/2+1)))) +grid +xlabel("Frequência (Hz)"); ylabel("|H_{1}(f)|"); title("DFT do Sinal Filtrado") +subplot(2,3,2) +plot(Fv, signal(1:(L/2+1))) +grid +xlabel("Frequência (Hz)"); ylabel("Amplitude"); title("Sinal") +subplot(2,3,5) +plot(Fv, signal_filtered(1:(L/2+1))) +grid +xlabel("Frequência (Hz)"); ylabel("Amplitude"); title("Sinal Filtrado") +subplot(2,3,3) +plot(Fv, mag2db(signal_power)) +grid +xlabel("Frequência (Hz)"); ylabel("Ganho (dB)"); title("Ganho do Sinal") +subplot(2,3,6) +plot(Fv, mag2db(abs(dft_signal_filtered(1:(L/2+1))))) +grid +xlabel("Frequência (Hz)"); ylabel("Ganho (dB)"); title("Ganho do Sinal Filtrado") + +%sound(signal_filtered, Fs); +%audiowrite('canto1_butterworth.flac', signal_filtered, Fs); \ No newline at end of file diff --git a/TP3_8/DiogoEliseu_TP3_8_butterworth_2nd_order_filter.m b/TP3_8/DiogoEliseu_TP3_8_butterworth_2nd_order_filter.m new file mode 100644 index 0000000..6069aed --- /dev/null +++ b/TP3_8/DiogoEliseu_TP3_8_butterworth_2nd_order_filter.m @@ -0,0 +1,21 @@ +function Hd = DiogoEliseu_TP3_8_final2 +%DIOGOELISEU_TP3_8_FINAL2 Returns a discrete-time filter object. + +% MATLAB Code +% Generated by MATLAB(R) 9.8 and Signal Processing Toolbox 8.4. +% Generated on: 31-Dec-2020 16:39:59 + +% Butterworth Bandpass filter designed using FDESIGN.BANDPASS. + +% All frequency values are in Hz. +Fs = 44100; % Sampling Frequency + +N = 2; % Order +Fc1 = 2850; % First Cutoff Frequency +Fc2 = 7150; % Second Cutoff Frequency + +% Construct an FDESIGN object and call its BUTTER method. +h = fdesign.bandpass('N,F3dB1,F3dB2', N, Fc1, Fc2, Fs); +Hd = design(h, 'butter'); + +% [EOF] diff --git a/TP3_8/DiogoEliseu_TP3_8_butterworth_filter.m b/TP3_8/DiogoEliseu_TP3_8_butterworth_filter.m new file mode 100644 index 0000000..6d99768 --- /dev/null +++ b/TP3_8/DiogoEliseu_TP3_8_butterworth_filter.m @@ -0,0 +1,27 @@ +function Hd = DiogoEliseu_TP3_8_final_filter +%DIOGOELISEU_TP3_8_FINAL_FILTER Returns a discrete-time filter object. + +% MATLAB Code +% Generated by MATLAB(R) 9.8 and Signal Processing Toolbox 8.4. +% Generated on: 31-Dec-2020 19:24:38 + +% Butterworth Bandpass filter designed using FDESIGN.BANDPASS. + +% All frequency values are in Hz. +Fs = 44100; % Sampling Frequency + +Fstop1 = 2850; % First Stopband Frequency +Fpass1 = 3020; % First Passband Frequency +Fpass2 = 7000; % Second Passband Frequency +Fstop2 = 7150; % Second Stopband Frequency +Astop1 = 96; % First Stopband Attenuation (dB) +Apass = 1; % Passband Ripple (dB) +Astop2 = 104; % Second Stopband Attenuation (dB) +match = 'stopband'; % Band to match exactly + +% Construct an FDESIGN object and call its BUTTER method. +h = fdesign.bandpass(Fstop1, Fpass1, Fpass2, Fstop2, Astop1, Apass, ... + Astop2, Fs); +Hd = design(h, 'butter', 'MatchExactly', match); + +% [EOF] diff --git a/TP3_8/DiogoEliseu_TP3_8_high_pass.m b/TP3_8/DiogoEliseu_TP3_8_high_pass.m new file mode 100644 index 0000000..d956026 --- /dev/null +++ b/TP3_8/DiogoEliseu_TP3_8_high_pass.m @@ -0,0 +1,55 @@ +%% Inicialização do ambiente +clear; close all; clc + +%% >Exercício 8< + +%% Input +[y, Fs] = audioread("Canto1.mp3"); % Signal and Sampling Frequency +signal = y(:,1); % Discard second channel +Fn = Fs/2; % Nyquist Frequency (Hz) +L = length(signal); % Signal Length + +%% Compute the DFT +dft = fft(signal)./L; +magnitude = 10.*log10(abs(dft).^2); % power is squared, thus 10 +Fv = linspace(0, 1, L)*Fn; % Frequency Vector + +%% High-pass Filter +not_to_cutoff_indices = magnitude > -96; +dft_filtered = not_to_cutoff_indices.*dft; +magnitude_filtered = not_to_cutoff_indices.*magnitude; +signal_filtered = ifft(dft_filtered.*L); + +%% Output +Fv_half = linspace(0, 1, fix(L/2)+1)*Fn; +y = abs(dft(1:(L/2+1))); +y_filtered = abs(dft_filtered(1:(L/2+1))); +figure(1) +subplot(2,3,1) +plot(Fv_half, y) +grid +xlabel("Frequência (Hz)"); ylabel("|H_{1}(f)|"); title("DFT do Sinal") +subplot(2,3,4) +plot(Fv_half, y_filtered) +grid +xlabel("Frequência (Hz)"); ylabel("|H_{1}(f)|"); title("DFT do Sinal Filtrado") +subplot(2,3,2) +plot(Fv_half, signal(1:(L/2+1))) +grid +xlabel("Frequência (Hz)"); ylabel("Amplitude"); title("Sinal") +subplot(2,3,5) +plot(Fv_half, y_filtered) +grid +xlabel("Frequência (Hz)"); ylabel("Amplitude"); title("Sinal Filtrado") +subplot(2,3,3) +%plot(Fv, magnitude); +plot(Fv_half, mag2db(y)) +grid +xlabel("Frequência (Hz)"); ylabel("Ganho (dB)"); title("Ganho do Sinal") +subplot(2,3,6) +plot(Fv_half, mag2db(y_filtered)) +grid +xlabel("Frequência (Hz)"); ylabel("Ganho (dB)"); title("Ganho do Sinal Filtrado") + +%sound(signal_filtered, Fs); +%audiowrite('canto1_high_pass.flac', signal_filtered, Fs); \ No newline at end of file diff --git a/TP3_8/canto1_butterworh_2nd_order.flac b/TP3_8/canto1_butterworh_2nd_order.flac new file mode 100644 index 0000000000000000000000000000000000000000..0815cb967d2892f8492f7bfeb8a1e8844a1046e4 GIT binary patch literal 1003837 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