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clear all
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close all
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% loads signal and its characteristics
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signal = csvread('unknownsignal.csv');
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%%%%%SIGNAL CHARACTERISTICS%%%%%
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% sets sampling frequency
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fps = 200; % -> freqMax of the signal should be < 150 Hz (Shannon-Nyquisit theorem), in practice freqMax < 60 Hz would be better
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% computes the duration of the signal
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duration = length(signal) / fps; % in s
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disp(duration);
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% estimates its original frequency resolution
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resolution = fps / length(signal); % in Hz
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%Then we study the stationarity
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% temporal plot
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figure;
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plot(signal);
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xticks(0:0.2*fps:length(signal)*fps);
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xticklabels(0:0.2:length(signal)/fps);
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xlabel('Time (s)');
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ylabel('Amplitude (a.u.)');
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% spectrogram
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step_size = 50; %ms
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window_size = 1000; %ms
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spectrogram(signal, fps, step_size, window_size);
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% We conclude that the signal must be cut in 2 stationary parts
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%Thus we cut it in 2 parts of equal length
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% First part: [0 1s]
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signal_1 = signal(1:end/2);
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% Second part: [1s 2s]
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signal_2 = signal(end/2+1:end);
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%%%%%SPECTRAL ANALYSIS (RECTANGULAR WINDOW)%%%%%
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%plots power spectrum with rectangular window
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% 1st part of the signal with 0.5 Hz resolution
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frequencySpectrum(signal_1, fps, 0.5);
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% 2nd part of the signal with 0.5 Hz resolution
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frequencySpectrum(signal_2, fps, 0.5);
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%%%%%SPECTRAL ANALYSIS (BLACKMAN WINDOW)%%%%%
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%plots power spectrum with blackman window
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signal_1_win = blackmanWin(signal_1);
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% 1st part of the signal with 0.5 Hz resolution
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frequencySpectrum(signal_1_win, fps, 0.5);
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signal_2_win = blackmanWin(signal_2);
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% 2nd part of the signal with 0.5 Hz resolution
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frequencySpectrum(signal_2_win, fps, 0.5);
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function signal_win = blackmanWin(signal)
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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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blackmanWin = zeros(1, length(signal));
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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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%~ plot(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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%~ plot(signal);
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%~ hold on;
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%~ plot(signal_win);
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function signal = windowing(signal_freq, signal_duration, signal_phase, sampling_freq)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%function signal = windowing(signal_freq, signal_duration, signal_phase, sampling_freq)
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% ex.: signal = windowing(10, 12, 0, 50)
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%
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% Inputs:
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% - signal_freq: frequency of the cosine function in Hz
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% - signal_duration: duration of the signal in seconds
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% - signal_phase: phase of the signal in rad
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% - sampling_freq: sampling frequency in Hz
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%
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% Output:
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% - signal: an array containing the samples of a cosine function sampled at the given sampling freq and windowed (in a.u.)
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% signal = cos(2*pi*signal_freq*t+signal_phase)
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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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% generates a time array
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t=-signal_duration/2:1/sampling_freq:signal_duration/2;
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% generates a sampled signal
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signal = cos(2*pi*signal_freq*t+signal_phase);
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% window duration is half of signal duration
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windowDuration = signal_duration/2;
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% creates rectangular time window
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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*sampling_freq/4) = 1;
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end
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figure;
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plot(rectangularWin);
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for l_sample=1:signal_duration*sampling_freq
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signal_rect(l_sample) = signal(l_sample) * rectangularWin(l_sample);
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end
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figure;
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plot(signal); hold on;
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plot(signal_rect);
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% creates the Hanning time window
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% creates the Hamming time window
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% creates the Balckman time window
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