From 06dee7fa7490107165b09c6de26aebce046b6d2e Mon Sep 17 00:00:00 2001 From: Louis Date: Mon, 18 Mar 2024 09:31:28 +0100 Subject: [PATCH] Continue report and add code to use --- Midterm_Report_Graz_Louis.docx | Bin 45465 -> 1174888 bytes blackmanWin.m | 36 +++++++++++++++ frequencySpectrum.m | 61 +++++++++++++++++++++++++ main.m | 79 +++++++++++++++++++++++++++++++++ spectrogram.m | 35 +++++++++++++++ 5 files changed, 211 insertions(+) create mode 100644 blackmanWin.m create mode 100644 frequencySpectrum.m create mode 100644 main.m create mode 100644 spectrogram.m diff --git a/Midterm_Report_Graz_Louis.docx b/Midterm_Report_Graz_Louis.docx index 01c7328dc25387aa1a6ecd91c75b98c085ad9ebf..a1839cbac0b1ba014f96abd52428c73845fd8418 100644 GIT binary patch literal 1174888 zcmeFY19vQ6*Y4f1ZQHh;?AT6rY}?s8wrx8*wr$(C%^kh@-{*dC#(CaPa88Y??$KRU zUA0#Iu9|Dkx>`XR1QZnj4uAvz07QVD{MdjtAOOG!3IIR>Kmu!v*x5Rp*gET}c-Wgb z>Cn5|SQF-h0#oJ!fWNo@f7AcPJur|wF4xb9DE2JzE^0QF_m z-hHgd4H6zAm2bt}8LTlChqh|lqJ;>`b}W3nm|k2}X1!v1-@Aa=Us8{h7_^{BF#Wh% z?$<7MMXHn%z15sdh_fh|HuBxXlW)>hbUId}|DLXB2U>FZOGZpM4a0GA;^8zq4(Bf& zE2v8T_Mj88LeX|(+0`kHyv=kUl#on{ho@ESDx`~F4@7v^QS<4h0->dOm%B^4Ev;FC zq<_2Zepqcn#n~GWe((wHuj3(vlAeI*A8v%*fG31(QSzs``7dl0+^-DVHY{Z!?x@Ja zS{=&;VnKpAeEHnr2pM(E^FPFIV_v8F+}XX#W_XTlw|*s3kc0m{=^1N70X{_xIcoh% zscCqnil#M+60{-4+XC-wh}_5I(PUJ>7G+0O_ocpdN&Fx#oP){9vn z$6z$Gj=2f}sVymkvc6)u{Q1GVvI4AgY9Ky7H=i)$>6H1yWhYVR20K|5F1!n$rkQCHW#N@tYzXzLf^kn)mMj}Zy77(F{7Cwy)9`_QOI@yDANGwlyOIS!SGJ1vK_e$LyJBL3hbuSP(5#9#j~^o44stWUbHR@FOe%_G==|2EAQ7 zoJ<{|`|rT_f9j)~ZS38R2mlb<0|1b|JH^e;(U`&5&d9~)J1+hc5HI-F9SbCquW@R> z1l>uF3<`Ao52{Y9G^-XH6&DZfTiXd-*|`y=G_8sB0jq~=D?VvelxTuqYU(;4n_!S}ew{O#&o8uxq#)(8-W}_v&sWo6 z_H79s#PQE90mXp;gb>1N;H5Tj5}Ac7mH?6vK)@ACgrgxsXQ!Etn51>^l6uscK>Bx5U_&tZ3=sODc8iGU zd(L){XXZ%q7L;-{l(+I2z*Lq9WBxn13A9p3c1A_b0gN`1MKGH)pbvrZQvD)`s z+Er++7k*H|8Q|_yW1k8CypwP**bcD{*XQd(xHWaz{ifZ0R-CA&m7 z@OyO)1s3p4hs^(N1POh~P9uZf)B7hF0XuzY2O1XThI!4Hl%b&)w(NxslAy)yB$ZqXOc-{(f6@o$A>Jn`3|^g*k}NN$q=9#7(dQ* zB5Q=%Ax8Fj5L6lnlo$r7f8!42x_6r3?_bhF?v{;zGC|JBp4Ih*9s9I`?TISq0U$1a z-Qe$;=r*&$bj?|O%;X!q%o>#jIR`fa8u>fsc3it|Z%bidGNSewROQ`!4HzcH<0`~11G#645|odT}h(GjHQtEf+ZTVYwE z5_{NXD7KiCZKxQpHmO>9K*bAs?d1u#a+686Ob? zO*vT%!waNnr{F-NJo$?nz;W?w6PZspO zqvUo|Jbh~pT1$$^P~x6KUwWW=fYKr=M9Nva7VOuXJ1pjY{!B589oEtLVs*_(VyMxo zwO|5pn&X5LNAw+Rxn~-IuPw`556taiE0W2im%ty}6-?O`J$C9v4J1`m)>?O5&siH) zxq@*wQ!dnsMa3}C&t#B>An$ZaD!vC1{*O#|#m&D7rHMQwu(s#yMi-fG>xm{%GkDE?XM3fCfnt6Qr9NiwAR5%k|wK5 za)7e!-{AB&!dK<&S&<;&+?7|C#1}NDx1@A-AyQOY(1}I8QtZ#NH)7`LwMVJ?s*m>G zBH=rAcD_vQ61+Ld#WkpAQNv%BKuzIu#h~gjJ(Fol-g(IzKjxBM6F5s@K-hawxFhDJ=sfE)iC+pZKT?{`Xh_J_3T-fJ%dJC@ zGJ=$?u85)!7vYTZp*rF6%a2Z z#;S|laLh$X(3_sy)Qdzjoty8P2?D4__VW)Z__vY_Q|P|PViKTZu4n9!f3CZ@FaAbX z^=kW_P%c^3dNyR*Et!lfOSC_y_nj?D z#*sFKgtY%3%_%--amh>!We8@X;)!#zc>$(haB<5rd6L@+w;jPuKp6|0y`YDpFEo2V zL8(>xD|@#dJ-(QmY+Ahf?eQm^znDL{d?3%$qMj8oMOllG?1SVTPMZ#b#AR=BC!u_l ze!6)IFW-_*fe7q>9?-=LIDyyn`P0QXg{4eicZMX#ESw-b{isu!#oW2*G{@j@KjQ1! 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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)');

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