Why does Python welch give me a different answer from MATLAB's pwelch?

Question

I am trying to implement the following line of MATLAB code:

[pxx, f] = pwelch(data,[],[],4096,F_S)

in Python. Knowing that MATLAB using a Hamming window type that uses 8 segment with 50% overlap, my attempt was

freq, PSD =
signal.welch(data, F_S, window='hamming', nperseg=None, noverlap=None, nfft=4096)

However, I receive different results that on the eye look similar but aren't. MATLAB predicts a power peak of 0.13 at the 2nd entry of the pxx vector, while Python predicts a power peak of 0.33 at the 32nd entry of the PSD vector. Did I do something wrong?

Answer 1

Your parameters for the sciPy implementation look wrong. Matlab does divide the input data into 8 segments so you need to do the same with Python. SciPy by default sets each segment to 256 samples (see sciPy.welch)

You need something like:

N = np.floor(len(data)/8) #sets the frame length the same as Matlab's default
freq, PSD = 
   signal.welch(data, F_S, window='hamming', nperseg=N, noverlap=None, nfft=4096)

Better yet, define your own window_length (i.e nperseg) and hop_length (i.e noverlap), and re-do your comparison without relying on the default parameters of either functions.

I'd also suggest looking up the documentation for each, the scaling might be different depending on the implementation.

EDIT Seems the default scaling is the same for both implementation ;)