Fast algorithms for complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913787277213696 |
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| author | Cariow, Aleksandr |
| author_facet | Cariow, Aleksandr |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast algorithms for complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs Cariow, Aleksandr Data Structures and Algorithms 65T50 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. |
| title | Fast algorithms for complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs |
| topic | Data Structures and Algorithms 65T50 |
| url | https://arxiv.org/abs/2504.07264 |