A New Algorithm for Computing a 2<sup>m</sup>×2<sup>m</sup>-Point Two-Dimensional Discrete Fourier Transform

Yang wan-quan

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A New Algorithm for Computing a 2^m×2^m-Point Two-Dimensional Discrete Fourier Transform

更新时间：2025-12-08

- A New Algorithm for Computing a 2^m×2^m-Point Two-Dimensional Discrete Fourier Transform
- Acta Electronica Sinica Issue 6, Pages: 72-81(1987)
- 作者机构：
  
  四川大学
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- Published：1987
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[1]杨万全.计算2~m×2~m点二维离散Fourier变换的新算法[J].电子学报,1987(06):72-81.

Yang wan-quan. A New Algorithm for Computing a 2^m×2^m-Point Two-Dimensional Discrete Fourier Transform[J]. Acta Electronica Sinica, 1987, (6): 72-81.
[1]杨万全.计算2~m×2~m点二维离散Fourier变换的新算法[J].电子学报,1987(06):72-81. DOI：

Yang wan-quan. A New Algorithm for Computing a 2^m×2^m-Point Two-Dimensional Discrete Fourier Transform[J]. Acta Electronica Sinica, 1987, (6): 72-81. DOI：

摘要

本文提出了一种计算2

×2

点二维离散Fourier变换的新算法。此法与一维FFT逐行逐列计算二维DFT的算法相比

优点是减少25～71％的复数乘法运算。文中还讨论了产生旋转因子和二维反序重排的快速算法。

Abstract

A new algorithm for computing a 2m×2m-point two-dimensional discrete Fourier transform is presented. The main advantage of the algorithin is the 25-71% reduction of complex multiplication compared with conventional method of a two-dimensional DFT by using one-dimensional FFT on the rows and columns separately. The fast algorithm of the generation of twiddle factor and bit reversal and unscrambling are developed as well.

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A New Algorithm for Computing a 2m×2m-Point Two-Dimensional Discrete Fourier Transform

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A New Algorithm for Computing a 2^m×2^m-Point Two-Dimensional Discrete Fourier Transform