The Poisson sum formulae associated with the fractional Fourier transform

DOI10.1016/j.sigpro.2008.10.030zbMath1161.94339OpenAlexW2031825742MaRDI QIDQ1016818

Yue Wang, Ran Tao, Bing-Zhao Li, Tian-Zhou Xu

Publication date: 14 May 2009

Published in: Signal Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sigpro.2008.10.030

zbMATH Keywords

band-limited signalfractional Fourier transformfractional Fourier seriesPoisson sum formula

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical methods for discrete and fast Fourier transforms (65T50) Application of orthogonal and other special functions (94A11)

Related Items

Sampling analysis in the complex reproducing kernel Hilbert space ⋮ Windowed special affine Fourier transform ⋮ The generalization of the Poisson sum formula associated with the linear canonical transform ⋮ Spectral analysis of sampled signals in the linear canonical transform domain ⋮ Poisson summation formulae associated with the special affine Fourier transform and offset Hilbert transform ⋮ Parseval relationship of samples in the fractional Fourier transform domain ⋮ Convolution theorem for fractional cosine‐sine transform and its application ⋮ Special affine wavelet transform and the corresponding Poisson summation formula ⋮ On the duality of discrete and periodic functions

Cites Work

• Unnamed Item
• Sampling and series expansion theorems for fractional Fourier and other transforms
• Research progress of the fractional Fourier transform in signal processing
• Discrete fractional Fourier transform based on orthogonal projections
• Method for defining a class of fractional operations
• Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform
• Unified fractional Fourier transform and sampling theorem
• The discrete fractional Fourier transform
• Closed-form discrete fractional and affine Fourier transforms
• Parseval's relationship for nonuniform samples of signals with several variables
• Spectral Analysis and Reconstruction for Periodic Nonuniformly Sampled Signals in Fractional Fourier Domain
• An uncertainty principle for real signals in the fractional Fourier transform domain