# Speeding up Fourier-related transform computations in python

I have an image and I need to compute a fourier-related transform over it called Short Time Fourier Transform (for extra mathematical info check:http://en.wikipedia.org/wiki/Short-time_Fourier_transform).

In order to do that I need to :

(1) place a window at the starting pixel of the image (x,y)=(M/2,M/2)

(2) Truncate the image using this window

(3) Compute the FFT of the truncated image, save results.

(4) Incrementally slide the window to the right

(5) Go to step 3, until window reaches the end of the image

However I need to perform the aformentioned calculation in real time... But it is rather slow !!!

Is there anyway to speed up the aformentioned process ??

I also include my code:

height, width = final_frame.shape
M=2
for j in range(M/2, height-M/2):
for i in range(M/2, width-M/2):
face_win=final_frame[j-M/2:j+M/2, i-M/2:i+M/2]

#these steps are perfomed in order to speed up the FFT calculation process
height_win, width_win = face_win.shape
fftheight=cv2.getOptimalDFTSize(height_win)
fftwidth=cv2.getOptimalDFTSize(width_win)
right = fftwidth - width_win
bottom = fftheight - height_win
bordertype = cv2.BORDER_CONSTANT
nimg = cv2.copyMakeBorder(face_win,0,bottom,0,right,bordertype, value = 0)

dft = cv2.dft(np.float32(face_win),flags = cv2.DFT_COMPLEX_OUTPUT)
dft_shift = np.fft.fftshift(dft)
magnitude_spectrum = 20*np.log(cv2.magnitude(dft_shift[:,:,0],dft_shift[:,:,1])

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