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What's the easiest way to get the DFT matrix for 2-d DFT in python? I could not find such function in numpy.fft. Thanks!
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Then the basic DFT is given by the following formula: X(k)=n−1∑t=0x(t)e−2πitk/n. The interpretation is that the vector x represents the signal level at various points in time, and the vector X represents the signal level at various frequencies.
Length=P Length=Q Length=P+Q-1 For the convolution property to hold, M must be greater than or equal to P+Q-1. As in the 1D case, 2D-DFT, though a self-consistent transform, can be considered as a mean of calculating the transform of a 2D sampled signal defined over a discrete grid.
The easiest and most likely the fastest method would be using fft from SciPy.
import scipy as sp
def dftmtx(N):
return sp.fft(sp.eye(N))
If you know even faster way (might be more complicated) I'd appreciate your input.
Just to make it more relevant to the main question - you can also do it with numpy:
import numpy as np
dftmtx = np.fft.fft(np.eye(N))
When I had benchmarked both of them I have an impression scipy one was marginally faster but I have not done it thoroughly and it was sometime ago so don't take my word for it.
Here's pretty good source on FFT implementations in python: http://nbviewer.ipython.org/url/jakevdp.github.io/downloads/notebooks/UnderstandingTheFFT.ipynb It's rather from speed perspective, but in this case we can actually see that sometimes it comes with simplicity too.
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