I have some difficulty in implementing RODFT00 and REDFT00. I want to use them for fluid simulations.

I would really appreciate some help with my following problems:

  1. I have read the documentation (http://www.fftw.org/fftw3_doc/Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029.html#Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029) and have been unable to understand

The r2r kinds for the various REDFT and RODFT types supported by FFTW, along with the boundary conditions at both ends of the input array (n real numbers in[j=0..n-1]), are:

FFTW_REDFT00 (DCT-I): even around j=0 and even around j=n-1. FFTW_RODFT00 (DST-I): odd around j=-1 and odd around j=n.

Note that these symmetries apply to the “logical” array being transformed; there are no constraints on your physical input data.

What does it explains about the implementation of cosine and sine transforms?

  1. Since I want to obtain the differentiation using the transforms. How should I arrange the wavenumbers to multiply with the matrix in both the cases??

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