68 / 2025-05-14 16:56:24

A fast algorithm for the symmetric discrete Fourier transform

DFT; fast algorithm; fast SDFT; symmetry; SDFT; zero padding;

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The Fourier Transform (FT) is extensively applied across a wide range of scientific and technological disciplines, including electronic, mechanical, electrical, information and communication, control, and biomedical engineering, as well as astronomy. In practical spectral analysis, signals are typically discrete and finite, making the Discrete Fourier Transform (DFT) the digital counterpart of the continuous FT. Among the two main forms of the DFT, the ordinary DFT (ODFT) and the symmetric DFT (SDFT), recent studies have shown that the SDFT is more suitable as the discrete counterpart of the FT. However, like ODFT, SDFT suffers from high computational complexity and significant memory usage. To address these challenges, this paper proposes a fast computation method for SDFT. The fundamental principle involves utilizing the FFT to efficiently compute the SDFT by exploiting its theoretical connection to the ODFT. Simulation results demonstrate that the proposed algorithm significantly reduces both computation time and memory consumption, offering an efficient solution for practical applications.