Python FFT (average) Hanning spectrum size 4096 and 50% overlap

Question

I want compute a FFT (average) with these parameters:

• Spectrum size: 4096
• Windows function: Hanning
• Overlap: 50%

This is my python code:

data = np.genfromtxt(file_path)
Freq = data[:,0]
Pdyn = data[:,1]
ft = np.fft.rfft(PdynA*np.hanning(len(Pdyn)))
mgft = np.abs(ft)

fig = plt.figure()
xVals = np.abs(np.fft.fftfreq(len(PdynA),d=1/12000))
plt.plot(xVals[:len(mgft)], mgft)
plt.show()

So I have my Hanning windows. But now, I don't know how I can set the Overlap to 50% and the spectrum size to 4096 ?

Answer 1

I can tell you what to do but I can't tell you how to do it in Python code. To average four spectra, do the following:

1) Multiply input samples x[0] –thru- x[4095] by a 4096-point Hanning sequence.

2) Compute a 4096-pt FFT of the above product sequence producing an X1[m] spectrum.

3) Multiply input samples x[2048] –thru- x[6143] by a 4096-point Hanning sequence.

4) Compute a 4096-pt FFT of the above product sequence producing an X2[m] spectrum.

5) Multiply input samples x[4096] –thru- x[8191] by a 4096-point Hanning sequence.

6) Compute a 4096-pt FFT of the above product sequence producing an X3[m] spectrum.

7) Multiply input samples x[6144] –thru- x[10239] by a 4096-point Hanning sequence.

8) Compute a 4096-pt FFT of the above product sequence producing an X4[m] spectrum.

9) Finally, average the magnitude-squared samples of the four spectra to produce a final |Xf[m]| magnitude spectrum. That is,

|Xf[0]| = (|X1[0]| + |X2[0]| + |X3[0]| + |X4[0]|)/4.

|Xf[1]| = (|X1[1]| + |X2[1]| + |X3[1]| + |X4[1]|)/4.

|Xf[2]| = (|X1[2]| + |X2[2]| + |X3[2]| + |X4[2]|)/4.

...

...

|Xf[4095]| = (|X1[4095]| + |X2[4095]| + |X3[4095]| + |X4[4095]|)/4.

If you desire a power spectrum, then merely square each of the |Xf[m]| magnitude samples. user25139, you're implementing Welch's Method of spectrum analysis. You can search the web for "Welch's Method" for more information.

Answer 2

SciPy has a spectrogram function.

Assuming x is your input signal your code would be:

import numpy as np
from scipy.signal import spectrogram, hanning

M = 4096
NFFT = M
win = hanning(M)
overlap = 0.5
overlap_samples = int(round(M*overlap)) # overlap in samples
t, f, S = spectrogram(x,window=win,nperseg=M,noverlap=overlap_samples,nfft=NFFT)

# Compute average spectrum
avg_S = np.mean(S,axis=1)