How to get the input unit back with the spectrogram function

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Tanguy Cléton 2021-5-11

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评论： Tanguy Cléton 2021-5-11

Hello,

I have a signal (acceleration) in witch I want to know how much of a certain frequency is excited. For that I use spectrogram and I want to extract, at a point in time and frequency, the level of excitation in acceleration unit.

If I take sig as a signal then abs( fft(sig) )*2/window gives me the rigth amplitude (window is the size of the window). I tested it with sig = 300*cos(2*pi*f*t) and it indeed gave me 300 at the frequency f. So it works fine with fft.

But when I use it on the 's' output of spectrogram it dont give me that at all.

Any ideas to recover my acceleration unit from the spectrogram ?

Thx

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Mathieu NOE 2021-5-11

myspecgram_demo.m

hello

sometimes it's not so easy to understand how things are scaled inside matlab's functions

that's why I ended up rebuilding the spectrogram with fft so I know the amplitude of the spectrum matches the input signal

FYI I use hanning window and the corresponding corrrection factor

Tanguy Cléton 2021-5-11

Thanks,

I did end up to start my own spectrogram function but my knowledge wasn't deep enougth in signal analysis.

I also tried the formula : A = abs(s)*4/window and it gave me a relative error of about -17% (for my set of widow, noverlap etc and for any amplitude) that I could correct afterward.

It is actually working so I'll stick with that but I do know the interest of writing a new spectrograam function on witch one can know any unit changes.

I explain here what I did in case someone read it later :

first I noticed that A = abs(s)*4/window is relatively close to the right value but an error still exist.

Then I wrote a piece of code that calulate the relative error of the estimated amplitude :

L = 1:10:1000;

j=0;

for k = L

j=j+1;

signal = k*cos(2*pi*BF(1)*t_1);

spec = spectrogram(signal,blackman(window),Overlap,BF,fs,'yaxis');

Amp = max(max(abs(spec)))*4/window;

err_rel(j) = (Amp-k)/k;

end

err = mean(err_rel);

IMPORTANT : You must put the axact same intputs than the spectrogram on witch you want to extract the value bc the relative error actually depend on all of that.

I took t_1 as the same time vector of my original signal.

Finally I can correct my values using this formula : A = abs(s)*4/window/(error+1) ;

If I plot the relative error against the amplitude I get about -17% (with my sittings) but with this correction I get a relative error of about 10^-14%.

We can see that the relative error is not dependent on the amplitude so taking the mean is not a problem and we don't have to put I=1:10:1000 bc the first values are already acurate.

Good luck !

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