I have some FFT data, 257 dimensions, every 10 ms, with 121 frames, i.e. 1.21 secs. I think the first dimension is probably something else and the remaining are the FFT coefficients, I guess.
From there, I want to calculate back some PCM signal for 44.1 Hz so I can play the sound. I asked the same question in a more mathematical way here but maybe here is a better place because I actually want to implement this.
How would I do that? Maybe I need some more information (which I have to find out somehow) - which? Maybe these missing information can be intelligently guessed somehow? What is a likely interpretation of those 257 dimensions?
This question is about the theory. The implementation is trivial I guess. But a concrete example in some language would be nice to help understanding the theory. Maybe C++ with FFTW? I skipped through the FFTW docs but I fail to understand all the terminology and some background, e.g. here. Why is it from complex to real or the other way, I only want real to real. What are those REDFT? What's a DCT, DFT, DST? FFTW_HC2R?
(I asked mostly the same question on SO here, but that was intended to be more about the practical side. Here on DSP I want to ask about the theory to get some understanding.)