added window programs + frequencySpectrum and spectogram
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Raphaelsav
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function signal_win = blackmanWin(signal, signal_duration, sampling_freq, pad)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%function signal_win = blackmanWin(signal)
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%
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% Inputs:
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% - signal: signal of interest
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%
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% Output:
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% - signal_win: signal of interest on which a blackman window was applied
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%
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% Author: Guillaume Gibert, guillaume.gibert@ecam.fr
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% Date: 15/03/2024
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% create the temporal array
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t=-signal_duration/2:1/sampling_freq:(signal_duration/2)-1/sampling_freq;
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% window duration is half of signal duration
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windowDuration = signal_duration/2;
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blackmanWin = zeros(1, length(t));
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for l_sample=1:length(signal)
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blackmanWin(l_sample) = (0.42 - 0.5 * cos(2*pi*(l_sample)/length(signal)) + 0/08*cos(4*pi*(l_sample)/length(signal)));
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end
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% plot Blackman window
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figure;
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title("Blackman Window"); hold on;
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plot(t, blackmanWin);
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% apply the Blackman window
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for l_sample=1:length(signal)
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signal_win(l_sample) = signal(l_sample) * blackmanWin(l_sample);
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end
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figure;
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title("Original and Windowed signals"); hold on;
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plot(signal); hold on;
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plot(signal_win);
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frequencySpectrum(signal_win, sampling_freq/2,pad);
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function power = frequencySpectrum(signal, fs, pad)
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%%%%%%%%%%%%%%%%%%
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%function power = frequencySpectrum(signal, fs, pad)
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%
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% Task: Display the power spectrum (lin and log scale) of a given signal
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%
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% Input:
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% - signal: the input signal to process
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% - fs: the sampling rate
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% - pad: pad the signal with zeros to the next power of 2
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%
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% Output:
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% - power: the power spectrum
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%
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%
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% Guillaume Gibert, guillaume.gibert@ecam.fr
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% 25/04/2022
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%%%%%%%%%%%%%%%%%%
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n = length(signal); % number of samples
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if (pad)
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n_original = n;
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n = 2^(nextpow2(n));
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signal = [signal zeros(1, n-n_original)];
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end
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y = fft(signal, n);% compute DFT of input signal
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power = abs(y).^2/n; % power of the DFT
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[val, ind] = max(power); % find the mx value of DFT and its index
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% plots
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figure;
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subplot(1,3,1) % time plot
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t=0:1/fs:(n-1)/fs; % time range
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plot(t, signal)
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xticks(0:0.1*fs:n*fs);
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xticklabels(0:0.1:n/fs);
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xlabel('Time (s)');
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ylabel('Amplitude (a.u.)');
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subplot(1,3,2) % linear frequency plot
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f = (0:n-1)*(fs/n); % frequency range
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plot(f,power, 'b*'); hold on;
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plot(f,power, 'r');
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xlabel('Frequency (Hz)')
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ylabel('Power (a.u.)')
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subplot(1,3,3) % log frequency plot
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plot(f,10*log10(power/power(ind)));
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xlabel('Frequency (Hz)')
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ylabel('Power (dB)')
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function signal_win = hammingWin(signal, signal_duration, sampling_freq, pad)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%function signal_win = hammingWin(signal, signal_duration, sampling_freq, pad)
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% ex.: signal_win = hammingWin(signal, 2, 300, 1)
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%
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% Inputs:
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% - signal: location of the signal to window
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% - signal_duration: duration of the signal in seconds
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% - sampling_freq: sampling frequency in Hz
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% - pad: wether or not add zero padding (0 false; 1 true)
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%
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% Output:
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% - signal_win: signal of interest on which a hamming window was applied
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%
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% Author: Guillaume Gibert, guillaume.gibert@ecam.fr
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% Date: 04/03/2024
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% create the temporal array
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t=-signal_duration/2:1/sampling_freq:(signal_duration/2)-1/sampling_freq;
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% window duration is half of signal duration
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windowDuration = signal_duration/2;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% creates the Hamming time window
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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hammingWin = zeros(1, length(t));
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for l_sample=1:windowDuration*sampling_freq
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hammingWin(l_sample+signal_duration*sampling_freq/4) = (0.54 - 0.46*cos(2*pi*(l_sample)/(signal_duration*sampling_freq/2)));
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end
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figure;
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title("Hamming Window"); hold on;
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plot(t,hammingWin);
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% apply the window on input signal
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for l_sample=1:length(t)
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signal_win(l_sample) = signal(l_sample) * hammingWin(l_sample);
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end
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figure;
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title("Original and Windowed signals"); hold on;
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plot(t, signal); hold on;
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plot(t, signal_win);
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frequencySpectrum(signal_win, sampling_freq/2,pad);
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function signal_win = hanningWin(signal, signal_duration, sampling_freq, pad)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%function signal_win = hanningWin(signal, signal_duration, sampling_freq, pad)
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% ex.: signal_win = hanningWin(signal, 2, 300, 1)
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%
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% Inputs:
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% - signal: location of the signal to window
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% - signal_duration: duration of the signal in seconds
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% - sampling_freq: sampling frequency in Hz
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% - pad: wether or not add zero padding (0=false; 1=true)
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%
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% Output:
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% - signal_win: signal of interest on which a hanning window was applied
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%
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% Author: Guillaume Gibert, guillaume.gibert@ecam.fr
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% Date: 04/03/2024
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% create the temporal array
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t=-signal_duration/2:1/sampling_freq:(signal_duration/2)-1/sampling_freq;
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% window duration is half of signal duration
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windowDuration = signal_duration/2;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% creates the Hanning time window
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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hanningWin = zeros(1, length(t));
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for l_sample=1:windowDuration*sampling_freq
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hanningWin(l_sample+signal_duration*sampling_freq/4) = (0.5 - 0.5*cos(2*pi*(l_sample)/(signal_duration*sampling_freq/2)));
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end
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figure;
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title("Hanning Window"); hold on;
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plot(t,hanningWin);
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% apply the window on input signal
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for l_sample=1:length(t)
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signal_win(l_sample) = signal(l_sample) * hanningWin(l_sample);
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end
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figure;
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title("Original and Windowed signals"); hold on;
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plot(t, signal); hold on;
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plot(t, signal_win);
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frequencySpectrum(signal_win, sampling_freq/2,pad);
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function signal_win = rectWin(signal, signal_duration, sampling_freq, pad)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%function signal_win = rectWin(signal, signal_duration, sampling_freq, pad)
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% ex.: signal_win = rectWin(signal, 2, 300, 1)
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%
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% Inputs:
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% - signal: location of the signal to window
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% - signal_duration: duration of the signal in seconds
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% - sampling_freq: sampling frequency in Hz
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% - pad: wether or not add zero padding (0=false; 1=true)
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%
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% Output:
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% - signal_win: signal of interest on which a rectangular window was applied
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%
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% Author: Guillaume Gibert, guillaume.gibert@ecam.fr
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% Date: 04/03/2024
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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signal_duration = length(signal)/sampling_freq;
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% create the temporal array
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t=-signal_duration/2:1/sampling_freq:(signal_duration/2)-1/sampling_freq;
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% window duration is half of signal duration
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windowDuration = signal_duration/2;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% creates the Rectangular time window
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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rectangularWin = zeros(1, length(t));
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for l_sample=1:windowDuration*sampling_freq
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rectangularWin(l_sample + signal_duration) = 1;
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end
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figure;
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title("Rectangular Window"); hold on;
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plot(t,rectangularWin);
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% apply the rectangular window
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for l_sample=1:length(t)
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signal_win(l_sample) = signal(l_sample) * rectangularWin(l_sample);
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end
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figure;
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title("Original and Windowed signals"); hold on;
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plot(t, signal); hold on;
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plot(t, signal_win);
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frequencySpectrum(signal_win, sampling_freq/2,pad);
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function spectrogram(signal, samplingFreq, step_size, window_size)
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%%%%%%%%%%%%%%%%%%%%%%%
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%function spectrogram(signal, samplingFreq, step_size, window_size)
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% ex.: spectrogram(signal, 300, 50, 1000)
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%
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% Task: Plot the spectrogram of a given signal
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%
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% Inputs:
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% -signal: temporal signal to analyse
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% -samplingFreq: sampling frequency of the temporal signal
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% -step_size: how often the power spectrum will be computed in ms
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% -window_size: size of the analysing window in ms
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%
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% Ouput: None
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%
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% author: Guillaume Gibert (guillaume.gibert@ecam.fr)
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% date: 14/03/2023
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%%%%%%%%%%%%%%%%%%%%%%%
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figure;
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subplot(2,1,1);
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t=0:1/samplingFreq:length(signal)/samplingFreq-1/samplingFreq;
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plot(t, signal');
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xlim([0 length(signal)/samplingFreq-1/samplingFreq]);
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ylabel('Amplitude (norm. unit)');
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subplot(2,1,2);
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step = fix(step_size*samplingFreq/1000); % one spectral slice every step_size ms
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window = fix(window_size*samplingFreq/1000); % window_size ms data window
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[S, f, t] = specgram(signal);
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specgram(signal, 2^nextpow2(window), samplingFreq, window, window-step);
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xlabel('Time (s)');
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ylabel('Frequency (Hz)');
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