FFTW fftwf_plan_r2r_2d() with FFTW_REDFT01 equivalent

问题

I am trying to port code that uses FFTW to use KissFFT.
The code uses fftwf_plan_r2r_2d() with FFTW_REDFT01.

What would be the equivalent call in KissFFT?

If this call (with FFTW_REDFT01) is equivalent to a DCT, could I just use a direct DCT transform instead, e.g. such as OpenCV cv::dct?
Is there some input data modification I'd need to do, like reflections and symmetrizations?

回答1:

Answering my own question...
With the help of these two references, I ended up not using DFT at all, but using OpenCV's cv::dct() and cv::idct() instead.

To answer the question, fftwf_plan_r2r_2d(...,FFTW_REDFT10, FFTW_REDFT10,...) can be replaced by this OpenCV code with the additional scaling:

cv::dct(img, resFFT); // fwd dct. This is like Matlab's dct2()
resFFT *= (4 * sqrt(float(img.rows/2)) * sqrt(float(img.cols/2)));
resFFT.row(0) *= sqrt(2.f);
resFFT.col(0) *= sqrt(2.f);

The inverse with FFTW_REDFT01 can be done like so:

// First re-scale the data for idct():
resFFT /= (4 * sqrt(float(img.rows/2)) * sqrt(float(img.cols/2)));
resFFT.row(0) /= sqrt(2.f);
resFFT.col(0) /= sqrt(2.f);
cv::idct(resFFT, outImg); // this will return the input exactly

// However, the transforms computed by FFTW are unnormalized, exactly like the corresponding, 
// so computing a transform followed by its inverse yields the original array scaled by N, where N is the logical DFT size. 
// The logical DFT size: Logical N=2*n for each axis, this is th implicit symmetrization
// of the image: reflect right and then reflect both halves down.
int logicalSizeN = (2*img.rows) * (2*img.cols);
outImg *= logicalSizeN; // scale to be like FFTW result