新たに導いた3 × 3巡回と疑似巡回行列の恒等式を用いてWinograd 9点FFTを導出する新しいアルゴリズム

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  • A New Simple Algorithm for Deriving the Winograd 9-Point FFT by Using New Identical Equations for 3 × 3 Circulant and Quasi-Circulant Matrices

抄録

<p>The Winograd small fast Fourier transform (FFT) is a method of efficiently computing the discrete Fourier transform (DFT) for data of small block length. The equations of post-additions, constant multiplication factors, and pre-additions for the Winograd 9-point FFT are given in references [3], [5], [6]. A 6 × 6 block matrix is obtained from 9-point DFT matrix by matrix manipulation. By using the 6 × 6 block matrix, 3 × 3 circular and quasi-circular matrices can be derived. New identical equations for 3 × 3 circular and quasi-circular matrices have been derived by the authors. A new simple algorithm is given for the Winograd 9-point FFT correctly by using new identical equations for 3 × 3 circular and quasi-circular matrices.</p>

収録刊行物

  • 信号処理

    信号処理 25 (1), 43-51, 2021-01-01

    信号処理学会

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