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arXiv · 2504.07264

Fast algorithms for complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs

Aleksandr Cariow
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Abstract

Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of complex-valued data when each element of the sequence represents a single whole. However, in some cases, it is more advantageous to represent each element of the input and output sequences by a pair of real numbers. Such a need arises, for example, when further post-processing of spectral coefficients is carried out through two independent channels. Taking into account the noted need, the article proposes an algorithm for fast complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs. A vector-matrix computational procedure is given that allows one to adequately describe and formalize the sequence of calculations when implementing the proposed algorithm.

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Aleksandr Cariow. 2025-04-09. Fast algorithms for complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs. https://arxiv.org/abs/2504.07264

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