2019/05/10 by William D. Kirwin, José M. Mourão, Kirwin, William D. +5
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Digital Filter Design and Implementation #FOS: Electrical engineering #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1905.04116
openalex publication_date 2019/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in the same wide range of applications with improved properties. The HFrFT of signals spans a one-parameter family of (essentially) holomorphic functions, where the parameter takes values in the bounded interval t∈ (0,π/2). At the boundary values of the parameter, one obtains the original signal at t=0 and its Fourier transform at the other end of the interval t=π/2. If the initial signal is L2 , then, for an appropriate choice of inner product that will be detailed below, the transform is unitary for all values of the parameter in the interval. This transform provides a heat kernel smoothening of the signals while preserving unitarity for L2-signals and continuously interpolating between the original signal and its Fourier transform.