如何在 Cuda 中获取从 2D Real 到 Complex FFT 的所有数据

Question

I am trying to do a 2D Real To Complex FFT using CUFFT.

I realize that I will do this and get W/2+1 complex values back (W being the "width" of my H*W matrix).

The question is - what if I want to build out a full H*W version of this matrix after the transform - how do I go about copying some values from the H*(w/2+1) result matrix back to a full size matrix to get both parts and the DC value in the right place

Thanks

Answer 1

I'm not familiar with CUDA, so take that into consideration when reading my response. I am familiar with FFTs and signal processing in general, though.

It sounds like you start out with an H (rows) x W (cols) matrix, and that you are doing a 2D FFT that essentially does an FFT on each row, and you end up with an H x W/2+1 matrix. A W-wide FFT returns W values, but the CUDA function only returns W/2+1 because real data is even in the frequency domain, so the negative frequency data is redundant.

So, if you want to reproduce the missing W/2-1 points, simply mirror the positive frequency. For instance, if one of the rows is as follows:

Index Data
0 12 + i
1 5 + 2i
2 6
3 2 - 3i
...

The 0 index is your DC power, the 1 index is the lowest positive frequency bin, and so forth. You would thus make your closest-to-DC negative frequency bin 5+2i, the next closest 6, and so on. Where you put those values in the array is up to you. I would do it the way Matlab does it, with the negative frequency data after the positive frequency data.

I hope that makes sense.

Answer 2

There are two ways this can be acheived. You will have to write your own kernel to acheive either of this.

1) You will need to perform conjugate on the (half) data you get to find the other half.
2) Since you want full results anyway, it would be best if you convert the input data from real to complex (by padding with 0 imaginary) and performing the complex to complex transform.

From practice I have noticed that there is not much of a difference in speed either way.

Answer 3

I actually searched the nVidia forums and found a kernel that someone had written that did just what I was asking. That is what I used. if you search the cuda forum for "redundant results fft" or similar you will find it.