[The develop branch is now finished, all the codes are done]
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This is the read me file
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We have 5 codes here.
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The one we need to use is the main one.
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To use it we just run it.
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It will plot 10 graphs representing the signals, the linear frequency and the log frequency
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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(2pi(l_sample)/length(signal)) + 0/08cos(4pi(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 power = frequencySpectrum(signal, fs, resolution, part_signal)
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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 in Hz
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% - resolution: frequency resolution in Hz, signal will be padded with zeros if necessary
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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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% 15/03/2024
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%%%%%%%%%%%%%%%%%%
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n = length(signal); % number of samples
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current_resolution = fs / n;
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if (resolution < current_resolution)
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n_original = n;
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n = fs / resolution;
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signal = [signal zeros(1, n-n_original)];
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end
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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(0:0.1fs:nfs);
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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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title('Plot for signal number', part_signal)
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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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%%%%%%%%%%%%%%%%%%%%%%
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% UNKNOWN SIGNAL
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% Sampling frequency: 300 Hz
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% Duration; 2 s
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% First second: 0.1Hz, 30 Hz, 30.5 Hz, 60 Hz, 61 Hz
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% Second second: 0.1Hz, 32 Hz, 36 Hz, 64 Hz, 72 Hz
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%%%%%%%%%%%%%%%%%%%%%%
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% loads the signal package on Octave
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% pkg load signal
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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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% estimates its original frequency resolution
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resolution = fps / length(signal); % in Hz
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%%%%%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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title('Temporal plot');
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% spectrogram
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step_size = 50; %ms
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window_size = 100; %ms
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spectrogram(signal, fps, step_size, window_size);
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% ccl: signal is not stationary, it is composed of 2 parts
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%%%%%SPLIT SIGNAL INTO 2 PARTS%%%%%
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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, 1);
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% 2nd part of the signal with 1 Hz resolution
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frequencySpectrum(signal_2, fps, 0.5, 2);
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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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zoomFrequencySpectrum(signal_1, fps, 0.5, 1);
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% 2nd part of the signal with 1 Hz resolution
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zoomFrequencySpectrum(signal_2, fps, 0.5, 2);
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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 1 Hz resolution
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frequencySpectrum(signal_1_win, fps, 0.5, 1);
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signal_2_win = blackmanWin(signal_2);
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% 2nd part of the signal with 1 Hz resolution
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frequencySpectrum(signal_2_win, fps, 0.5, 2);
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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 1 Hz resolution
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zoomFrequencySpectrum(signal_1_win, fps, 0.5, 1);
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signal_2_win = blackmanWin(signal_2);
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% 2nd part of the signal with 1 Hz resolution
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zoomFrequencySpectrum(signal_2_win, fps, 0.5, 2);
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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_sizesamplingFreq/1000); % one spectral slice every step_size ms
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window = fix(window_sizesamplingFreq/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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File diff suppressed because one or more lines are too long
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unction power = zoomFrequencySpectrum(signal, fs, resolution, part_signal)
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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 in Hz
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% - resolution: frequency resolution in Hz, signal will be padded with zeros if necessary
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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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% Sébastien Dubois, sebastien.dubois@ecam.fr
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% 18/03/2024
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%%%%%%%%%%%%%%%%%%
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n = length(signal); % number of samples
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current_resolution = fs / n;
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if (resolution < current_resolution)
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n_original = n;
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n = fs / resolution;
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signal = [signal zeros(1, n-n_original)];
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end
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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(0:0.1fs:nfs);
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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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xlim([5, 20]);
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title('Zoomed plot for signal number', part_signal)
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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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