diff --git a/Midterm_Report_Graz_Louis.docx b/Midterm_Report_Graz_Louis.docx index 01c7328..a1839cb 100644 Binary files a/Midterm_Report_Graz_Louis.docx and b/Midterm_Report_Graz_Louis.docx differ 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..ce1271d --- /dev/null +++ b/frequencySpectrum.m @@ -0,0 +1,61 @@ +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.)'); + +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.)') + +subplot(1,3,3) % log frequency plot +plot(f,10*log10(power/power(ind))); +xlabel('Frequency (Hz)') +ylabel('Power (dB)') + diff --git a/main.m b/main.m new file mode 100644 index 0000000..f6fb49e --- /dev/null +++ b/main.m @@ -0,0 +1,79 @@ +%%%%%%%%%%%%%%%%%%%%%% +% UNKNOWN SIGNAL +% Sampling frequency: 200 Hz +% Duration; 2 s +% First second: 0.1Hz, 30 Hz, 30.5 Hz, 60 Hz, 61 Hz +% Second second: 0.1Hz, 32 Hz, 36 Hz, 64 Hz, 72 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 = 200; % -> 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); +title('Temporal Plot of the Unknown Signal'); + +% 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); + + + + + diff --git a/spectrogram.m b/spectrogram.m new file mode 100644 index 0000000..ca44b95 --- /dev/null +++ b/spectrogram.m @@ -0,0 +1,35 @@ +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 + + +[S, f, t] = specgram(signal); +specgram(signal, 2^nextpow2(window), samplingFreq, window, window-step); +xlabel('Time (s)'); +ylabel('Frequency (Hz)');