diff --git a/blackmanWin.m b/blackmanWin.m new file mode 100644 index 0000000..d103593 --- /dev/null +++ b/blackmanWin.m @@ -0,0 +1,36 @@ +function signal_win = blackmanWin(signal) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%function signal_win = blackmanWin(signal) +% +% Inputs: +% - signal: signal of interest +% +% Output: +% - signal_win: signal of interest on which a blackman window was applied +% +% Author: Guillaume Gibert, guillaume.gibert@ecam.fr +% Date: 15/03/2024 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +blackmanWin = zeros(1, length(signal)); +for l_sample=1:length(signal) + blackmanWin(l_sample) = (0.42 - 0.5 * cos(2*pi*(l_sample)/length(signal)) + 0/08*cos(4*pi*(l_sample)/length(signal))); +end + +% plot Blackman window +%~ figure; +%~ plot(blackmanWin); + +% apply the Blackman window +for l_sample=1:length(signal) + signal_win(l_sample) = signal(l_sample) * blackmanWin(l_sample); +end + +%~ figure; +%~ plot(signal); +%~ hold on; +%~ plot(signal_win); + + + + diff --git a/frequencySpectrum.m b/frequencySpectrum.m new file mode 100644 index 0000000..8909735 --- /dev/null +++ b/frequencySpectrum.m @@ -0,0 +1,57 @@ +function power = frequencySpectrum(signal, fs, pad) +%%%%%%%%%%%%%%%%%% +%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 +% - pad: pad the signal with zeros to the next power of 2 +% +% Output: +% - power: the power spectrum +% +% +% Guillaume Gibert, guillaume.gibert@ecam.fr +% 25/04/2022 +%%%%%%%%%%%%%%%%%% + +n = length(signal); % number of samples + +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.)'); + +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'); +xlabel('Frequency (Hz)') +ylabel('Power (a.u.)') +xlim([30,40]); + +subplot(1,3,3) % log frequency plot +plot(f,10*log10(power/power(ind))); +xlabel('Frequency (Hz)') +ylabel('Power (dB)') +xlim([30,40]); + diff --git a/main.m b/main.m new file mode 100644 index 0000000..08f89c2 --- /dev/null +++ b/main.m @@ -0,0 +1,74 @@ +%%%%%%%%%%%%%%%%%%%%%% +% UNKNOWN SIGNAL +% Sampling frequency: 200 Hz +% Duration; 2 s +% First second: 6.25Hz, 13.28 Hz, 17.19 Hz +% Second second: 17.97Hz, 6.25 Hz, 8.59 Hz, 13.28 Hz +%%%%%%%%%%%%%%%%%%%%%% + +% loads the signal package on Octave +% pkg load signal + +% 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); + + +% 2nd part of the signal with 1 Hz resolution +frequencySpectrum(signal_2, fps, 1); + + + + +%%%%%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); + + +signal_2_win = blackmanWin(signal_2); +% 2nd part of the signal with 1 Hz resolution +frequencySpectrum(signal_2_win, fps, 1); + + + + + + diff --git a/spectrogram.m b/spectrogram.m new file mode 100644 index 0000000..dd9070e --- /dev/null +++ b/spectrogram.m @@ -0,0 +1,38 @@ +function spectrogram(signal, samplingFreq, step_size, window_size) +%%%%%%%%%%%%%%%%%%%%%%% +%function spectrogram(signal, samplingFreq, step_size, window_size) +% ex.: spectrogram(signal, 300, 50, 1000) +% +% Task: Plot the spectrogram of a given signal +% +% Inputs: +% -signal: temporal signal to analyse +% -samplingFreq: sampling frequency of the temporal signal +% -step_size: how often the power spectrum will be computed in ms +% -window_size: size of the analysing window in ms +% +% Ouput: None +% +% author: Guillaume Gibert (guillaume.gibert@ecam.fr) +% date: 14/03/2023 +%%%%%%%%%%%%%%%%%%%%%%% + +figure; + subplot(2,1,1); +t=0:1/samplingFreq:length(signal)/samplingFreq-1/samplingFreq; +plot(t, signal'); +xlim([0 length(signal)/samplingFreq-1/samplingFreq]); +ylabel('amplitude (norm. unit)'); + subplot(2,1,2); +step = fix(step_size*samplingFreq/1000); % one spectral slice every step_size ms +window = fix(window_size*samplingFreq/1000); % window_size ms data window +fftn = 2^nextpow2(window); % next highest power of 2 +[S, f, t] = specgram(signal, fftn, samplingFreq, window, window-step); +S = abs(S(2:fftn*samplingFreq/2/samplingFreq,:)); % magnitude in range 0