fft - scipy.signal.spectrogram

I want to do time-frequency analysis of a signal. So i decided to use spectrogram function from scipy. This function returns, three parameters f,t,Sxx. I am using below arguements:

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  x : my signal

  
  


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  fs : 1000 Hz

  
  


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  window : hann, with size = 300

  
  



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  nperseg : 300, same as window size

  
  


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  noverlap : 25

  
  

My question is about returned time segments of this function.

As far as I understand the first time segment for which we calculate fft must be 300 samples, then subtract 25 from it calculate fft for next window of 300 samples,and so on. So the signal of length 1s must be divided in 4 time segments. .275,.500,.775,1. , but the function returns :

f,t,Sxx=spectrogram(sig1,fs=1000,window=get_window('hann',300),noverlap=25,scaling='spectrum',nperseg=300) t Out[172]: array([ 0.15 , 0.425, 0.7 ])

can someone please suggest if I am thinking wrong or there is a bug in spectrogram function.

Answer

As the returned value shows, the first spectrum is computed at time $t=0.15$ s. With a sampling rate of 1000 Hz, that means that the first analysis window is centred at sample $n=150$. So the first analysis frame spans the samples $n \in [0,300[$.

Because your overlap is set to 25 samples, the second analysis frame spans the samples $n \in [275,575[$, thus overlapping in its first 25 samples with the first analysis frame. The second analysis frame is then centred at time $t=0.425$ s or in samples $n=425$.

The third analysis frame again overlaps 25 samples with the second one. Thus, it spans the samples $n \in [550,850[$ and is centred at time $t=0.7$ s or in samples $n=700$.

The next analysis frame would span the samples $n \in [825,1125]$ and is not computed because it would go over the range of samples in the input signal.