https://icyveins7.github.io/tags/dft/Recent content in Dft on icyveins7's blogHugoen-usThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Mon, 15 Jul 2024 20:00:00 +0800https://icyveins7.github.io/posts/2024/07/some-notes-on-2d-real-to-complex-fourier-transforms/Mon, 15 Jul 2024 20:00:00 +0800https://icyveins7.github.io/posts/2024/07/some-notes-on-2d-real-to-complex-fourier-transforms/<blockquote> <p>IPP in particular has some very niche ways of packing R2C DFT output, but otherwise there&rsquo;s a few pointers here to keep in mind for how they are implemented in most libraries.</p> </blockquote> <p>It&rsquo;s pretty well known that the output of a Fourier transform of real inputs has symmetric properties. This is due to the fact that real waves consist of two conjugate pairs of complex exponentials.</p> <p>What may be a bit less obvious (at least to me, when examining some programming libraries) is exactly how many useful output elements there are, and under which scenarios. In particular, I looked at IPP (which has some special packed structure), and cuFFT/NumPy/SciPy (which follow the FFTW structure I think).</p>