A novel description and mathematical analysis of the Fractional Discrete\n Fourier Transform

2019/09/26 by E. Zayas, Zayas, Evan
Computer Science · Mathematics · #Digital Filter Design and Implementation #FOS: Mathematics #General Mathematics (math.GM) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1909.13691

openalex publication_date 2019/09/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT)\ndescribed algorithmically by a combination of chirp transforms and ordinary\nDFTs. The transform is shown to be consistent with a continuous two-dimensional\nrotation between the time and frequency domains. I further present a new\nclosed-form expression for the transformation matrix and some preliminary\nanalysis of its properties.\n

Citations

• An algorithm for the machine calculation of complex Fourier series

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