Compute PSD from fft compared with spectrogram

Question

Yifei 2012-11-29

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https://ww2.mathworks.cn/matlabcentral/answers/55224-compute-psd-from-fft-compared-with-spectrogram

评论： HYZ 2021-10-15

Hi there,

Recently I am working on translating some Matlab code to Java, as I want to do some pattern recognition in mobile phones. In the Matlab code from my teammate, he used this function "spectrogram" to get PSD, which I couldn't find a complete open-source implementation online. Therefore I have to do it by my own.(who doesn't!!)

I got some algorithms from the forum such as:

y = data;
Fs = 90;
L = length(y);
y  = y(:) - mean(y);
NFFT = 2^nextpow2(L);
Y = fft(y,NFFT);
f = Fs/2*linspace(0,1,NFFT/2+1);
psd = abs(Y(1:NFFT/2+1)).^2/L;
psd = psd/Fs;

which has the same result with

periodogram

But NONE of them has the same result as the spectrogram. Would any one help me out here? Thank you very much.

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Answer 1

Wayne King 2012-12-3

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https://ww2.mathworks.cn/matlabcentral/answers/55224-compute-psd-from-fft-compared-with-spectrogram#answer_67375

编辑：Wayne King 2012-12-3

在 MATLAB Online 中打开

spectrogram optionally returns the short-time periodogram estimates. I'll show you how to establish the correspondence for the default Hamming window used in spectrogram. I'll establish the correspondence only for the 1st segment in the following example, but it is straightforward to extend it over the entire data record with the proper overlap.I'll just use a noise vector and assume a sampling rate of 1 kHz.

   x = randn(1000,1);
   [y,f,t,p] = spectrogram(x,256,250,256,1000);
   % now to create an equivalence between the column vectors
   % in p
   win = hamming(256);
   xdft = fft(x(1:256).*win);
   psdx = abs(xdft(1:length(xdft)/2+1)).^2;
   psdx = 1/(1000*norm(win,2)^2)*psdx;
   psdx(2:end-1) = 2*psdx(2:end-1);
   % now compare
   subplot(211)
   plot(psdx)
   subplot(212)
   plot(p(:,1))

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Brandon Madsen 2017-6-8

编辑：Brandon Madsen 2017-6-8

This is a very helpful explanation, but I am unsure about the purpose of a certain line of code, namely: psdx = 1/(1000*norm(win,2)^2)*psdx; . Could someone explain what this part is doing and why it is needed?

EDIT: Oh, nm, it's for normalization to Hz I assume.

HYZ 2021-10-15

If I want to plot for different frequencies, let's say 0 to 300Hz in the y-axis [y,f,t,p] = spectrogram(x,256,250,1:300,1000); how can I change the below?

win = hamming(256);

xdft = fft(x(1:256).*win);

psdx = abs(xdft(1:length(xdft)/2+1)).^2;

psdx = 1/(1000*norm(win,2)^2)*psdx;

psdx(2:end-1) = 2*psdx(2:end-1);

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Answer 2

Vieniava 2012-12-2

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Spectrogram is time-frequency (3D=time vs freq. vs amplitude) representation of a signal and periodogram/fft is frequency only (2D= freq vs amplitude) representation. Spectrogram shows how the frequency spectrum is changing over the time. Spectrogram is a set of consecutive fft's. Spectrogram is a matrix and fft/peridogram is a vector.

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Yifei 2012-12-3

Hi,

Thanks for the answer first.

Sorry for the vague description about my question. Actually what I am looking for is the mathematical implementation for spectrogram PSD via standard fft.

After looking into documents and Matlab implementations, I found that PSD in spectrogram is x^2 of the STFT, which is based on DFT via Goertzel algorithm over hamming window. Honestly I am still a little confused about the algorithm and will continue working on that later(have one final tmrw, so...). If you have ideas about how and why it is computed this way, please let me know.

Thank you for your time~

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