I found the solution I needed for my peculiar case after reading your email based of the following stages:
I have a N x N frequency-domain matrix Z 1. Use fftshift to obtain a DC centered matrix Note: fftshift(fft(a)) replaces np.fft.fft(np.power(-1,np.arange(64))*a) Zs = np.fft.fftshift(Z) 2. pad Zs with zeros scale = int(ceil(float(N)/M)) MM = scale*M Ztemp = np.zeros((MM,MM), dtype=complex) Ztemp[(MM-N)//2:(N-MM)//2,(MM-N)//2:(N-MM)//2] = Zs 3. Shift back to a "normal order" Ztemp = np.fft.ifftshift(Ztemp) 4. Transform to the "time domain" and sub-sample z = np.fft.ifft2(Ztemp)[::scale, ::scale] I went this was since I needed the aliasing, otherwise I could just truncate Zs to size MxM. Thank you, Nadav. -----הודעה מקורית----- מאת: numpy-discussion-boun...@scipy.org בשם M Trumpis נשלח: ה 05-מרץ-09 21:51 אל: Discussion of Numerical Python נושא: Re: [Numpy-discussion] Interpolation via Fourier transform Hi Nadav.. if you want a lower resolution 2d function with the same field of view (or whatever term is appropriate to your case), then in principle you can truncate your higher frequencies and do this: sig = ifft2_func(sig[N/2 - M/2:N/2 + M/2, N/2 - M/2:N/2+M/2]) I like to use an fft that transforms from an array indexing negative-to-positive freqs to an array that indexes negative-to-positive spatial points, so in both spaces, the origin is at (N/2,N/2). Then the expression works as-is. The problem is if you've got different indexing in one or both spaces (typically positive frequencies followed by negative) you can play around with a change of variables in your DFT in one or both spaces. If the DFT is defined as a computing frequencies from 0,N, then putting in n' = n-N/2 leads to a term like exp(1j*pi*q) that multiplies f[q]. Here's a toy example: a = np.cos(2*np.pi*5*np.arange(64)/64.) P.plot(np.fft.fft(a).real) P.plot(np.fft.fft(np.power(-1,np.arange(64))*a).real) The second one is centered about index N/2 Similarly, if you need to change the limits of the summation of the DFT from 0,N to -N/2,N/2, then you can multiply exp(1j*pi*n) to the outside of the summation. Like I said, easy enough in principle! Mike On Thu, Mar 5, 2009 at 11:02 AM, Nadav Horesh <nad...@visionsense.com> wrote: > > I apology for this off topic question: > > I have a 2D FT of size N x N, and I would like to reconstruct the original > signal with a lower sampling frequency directly (without using an > interpolation procedure): Given M < N the goal is to compute a M x M "time > domain" signal. > > In the case of 1D signal the trick is simple --- given a length N freq. > domain Sig: > > sig = np.fft.ifft(Sig, M) > > This trick does not work in 2D: > > sig = np.fft.ifft2(Sig, (M,M)) > > is far from being the right answer. > > Any ideas? > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
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