Overlapping windows using the fft for time discrete data

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AC_GBX 2020-10-15

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/614653-overlapping-windows-using-the-fft-for-time-discrete-data

评论： Mathieu NOE 2020-10-20

Hello,

I want to calculate the frequency domain of a measured signal by using the fft. My measurements have the samplerate of 5000Hz over 45s. The signals are acceleration in x,y,z direction of my coordinate system. I need the frequency domain signal for every second. The window I use is the Hann-Window and I decided to use the overlap of 50% as usual.

The problem is:

if I say the win_length is 5000Hz as the samplerate, then the result is for every half second
if I say the win_length is 10.000Hz then the result is for every second, but the algorithm cosiders 2s.

I must be wrong in understand the fft for a time discrete signal, but I read a lot about that. So what am I doing wrong?

sens_length = length(sensordata);
w = hann(win_length);
num_freq = win_length/2 ;
num_w = 2*sens_length/win_length-1;
for t=1:num_axis % for every axis of the coordinate system
    for i = 1:num_w   %for every window
        sensor_freq(:,i,t) = fft(w .* sensordata((i-1)*num_freq+1:(i-1)*num_freq+win_length,t));
        sensor_freq_abs(:,i,t) = abs(sensor_freq(1:num_freq,i,t));
    end
end

This is how one of my signals after measurement looks like:

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Mathieu NOE 2020-10-20

在 MATLAB Online 中打开

spectrog_peak.m

I prefer to "redesign" your code according to my own ideas... hope it matches your needs

so I ended up doing 2 things :

one example how to use pwelch on a buffer of 4096 samples, on each I do a pwelch averaging fft (with nfft = 512). That gives me 62 spectra that I display on a graph
second example is based on spectrogram. It's very similar in naturen bt data are displayed as time / frequency / amplitude (color coded , levels are in dB). It uses the funtion : spectrog_peak.m (attached)

hope this helps you .

% dummy signal
Fs = 5000;
samples = 255001;
dt = 1/Fs;
t = (0:dt:(samples-1)*dt);
omega = 2*pi*(25+20*t);
sensordata = randn(size(t)) + 5*sin(omega.*t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
samples = length(sensordata);
num_axis = 1;
NFFT = 512;    % to have highest frequency resolution , NFFT should be greater than typical max length of files ( 1 second duration at Fs = 16 kHz = 1600 samples);
NOVERLAP = round(0.75*NFFT);
samples_per_frame = NFFT*8;
num_w = floor(samples/samples_per_frame);
% your code modified - multiple spectra 
w = hamming(NFFT);
sensor_spectrum_all = [];
for t=1:num_axis % for every axis of the coordinate system
    for ci = 1:num_w   %for every window
        ind_start = 1+(ci-1)*samples_per_frame;
        ind_stop = ind_start + samples_per_frame-1;
        [sensor_spectrum, freq] = pwelch(sensordata(ind_start:ind_stop),w,NOVERLAP,NFFT,Fs);
        % concatenate spectra
        sensor_spectrum_all = [sensor_spectrum_all sensor_spectrum];
        
    end
end
figure(1),plot(freq,20*log10(sensor_spectrum_all));
title(['Spectra  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz  / Data buffer ' num2str(samples_per_frame) ' samples' ]);
xlabel('Time (s)');ylabel('Frequency (Hz)');
% spectrogram demo
Satur = 80;  % dB range scale (means , the lowes displayed level is 80 dB below the max level)
fmin = 1;
fmax = Fs/2;
% option_fw = 1; % FFT pond L
% option_fw = 2; % FFT pond A
option_fw = 1;
tmin = min(t);    tmax = max(t);
[sg,fsg,tsg] = spectrog_peak(sensordata,NFFT,Fs,0.75,Satur,tmin,tmax,fmin,fmax,option_fw);
% plots sg
figure(2);
imagesc(tsg,fsg,sg);axis('xy');colorbar('vert');
title(['Spectrogram  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');

AC_GBX 2020-10-20

Yes this answers my questions. Thank you very much. You helped a lot. I will try to interpolate the first half of the vector up to 2500 values due to shannon .

Mathieu NOE 2020-10-20