added frequencySpectrum.m

frequencySpectrum.m

@@ -0,0 +1,64 @@
+function power = frequencySpectrum(signal, fs, resolution)
+%%%%%%%%%%%%%%%%%%
+%function power = frequencySpectrum(signal, fs, pad)
+%
+% Task: Display the power spectrum (lin and log scale) of a given signal
+%
+% Input:
+%    - signal: the input signal to process
+%    - fs: the sampling rate in Hz
+%    - resolution: frequency resolution in Hz, signal will be padded with zeros if necessary
+%
+% Output: 
+%    - power: the power spectrum
+%    
+%
+% Guillaume Gibert, guillaume.gibert@ecam.fr
+% 15/03/2024
+%%%%%%%%%%%%%%%%%%
+
+n = length(signal);          % number of samples
+current_resolution = fs / n;
+if (resolution < current_resolution)
+    n_original = n;
+    n = fs / resolution;
+    signal = [signal zeros(1, n-n_original)];
+end
+
+%~ if (pad)
+    %~ n_original = n;
+    %~ n = 2^(nextpow2(n));
+    %~ signal = [signal zeros(1, n-n_original)];
+%~ end
+
+y = fft(signal, n);% compute DFT of input signal
+power = abs(y).^2/n;    % power of the DFT
+
+[val, ind] = max(power); % find the mx value of DFT and its index
+
+% plots
+figure;
+
+subplot(1,3,1) % time plot 
+t=0:1/fs:(n-1)/fs; % time range
+plot(t, signal)
+xticks(0:0.1*fs:n*fs);
+xticklabels(0:0.1:n/fs);
+xlabel('Time (s)');
+ylabel('Amplitude (a.u.)');
+title('Time');
+
+subplot(1,3,2) % linear frequency plot
+f = (0:n-1)*(fs/n);     % frequency range
+plot(f,power, 'b*'); hold on;
+plot(f,power, 'r');
+xlim([5, 20]);
+xlabel('Frequency (Hz)')
+ylabel('Power (a.u.)')
+title('Linear Frequency');
+
+subplot(1,3,3) % log frequency plot
+plot(f,10*log10(power/power(ind)));
+xlabel('Frequency (Hz)')
+ylabel('Power (dB)')
+title('Log Frequency');

main.m

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+```% loads signal and its characteristics
+signal = csvread('unknownsignal.csv');
+
+%%%%%SIGNAL CHARACTERISTICS%%%%%
+% sets sampling frequency
+fps = 300; % -> freqMax of the signal should be < 150 Hz (Shannon-Nyquisit theorem), in practice freqMax < 60 Hz would be better
+
+% computes the duration of the signal
+duration = length(signal) / fps; % in s
+
+% estimates its original frequency resolution
+resolution = fps /  length(signal); % in Hz
+
+%%%%%STATIONARITY%%%%%
+% temporal plot
+figure;
+plot(signal);
+xticks(0:0.2*fps:length(signal)*fps);
+xticklabels(0:0.2:length(signal)/fps);
+xlabel('Time (s)');
+ylabel('Amplitude (a.u.)');
+
+% spectrogram
+step_size = 50; %ms
+window_size = 100; %ms
+spectrogram(signal, fps, step_size, window_size);
+
+% ccl: signal is not stationary, it is composed of 2 parts
+
+%%%%%SPLIT SIGNAL INTO 2 PARTS%%%%%
+% First part: [0 1s]
+signal_1 = signal(1:end/2);
+% Second part: [1s 2s]
+signal_2 = signal(end/2+1:end);
+
+%%%%%SPECTRAL ANALYSIS (RECTANGULAR WINDOW)%%%%%
+%plots power spectrum with rectangular window
+% 1st part of the signal with 1 Hz resolution
+frequencySpectrum(signal_1, fps, 1);
+% 1st part of the signal with 0.5 Hz resolution
+frequencySpectrum(signal_1, fps, 0.5);
+
+% 2nd part of the signal with 1 Hz resolution
+frequencySpectrum(signal_2, fps, 1);
+% 2nd part of the signal with 0.5 Hz resolution
+frequencySpectrum(signal_2, fps, 0.5);
+
+
+
+%%%%%SPECTRAL ANALYSIS (BLACKMAN WINDOW)%%%%%
+%plots power spectrum with blackman window
+signal_1_win = blackmanWin(signal_1);
+% 1st part of the signal with 1 Hz resolution
+frequencySpectrum(signal_1_win, fps, 1);
+% 1st part of the signal with 0.5 Hz resolution
+frequencySpectrum(signal_1_win, fps, 0.5);
+
+signal_2_win = blackmanWin(signal_2);
+% 2nd part of the signal with 1 Hz resolution
+frequencySpectrum(signal_2_win, fps, 1);
+% 2nd part of the signal with 0.5 Hz resolution
+frequencySpectrum(signal_2_win, fps, 0.5);```