Poisson summation formulae associated with the special affine Fourier transform and offset Hilbert transform
type: Item
instance of: scholarly article
title: Poisson summation formulae associated with the special affine Fourier transform and offset Hilbert transform
zbMATH Open document ID: 1426.42005
DOI: 10.1155/2017/1354129
author: Zhi-Hai Zhuo
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: This paper investigates the generalized pattern of Poisson summation formulae from the special affine Fourier transform (SAFT) and offset Hilbert transform (OHT) points of view. Several novel summation formulae are derived accordingly. Firstly, the relationship between SAFT (or OHT) and Fourier transform (FT) is obtained. Then, the generalized Poisson sum formulae are obtained based on above relationships. The novel results can be regarded as the generalizations of the classical results in several transform domains such as FT, fractional Fourier transform, and the linear canonical transform.
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 94A20
zbMATH DE Number: 6971724
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1354129
OpenAlex ID: W2750375755
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description: scientific article; zbMATH DE number 6971724