Error estimates associated with sampling series of the linear canonical transforms

The linear canonical and fractional Fourier transforms and their different sampling representations play a major role for signal processing experts. Although there are many works on the derivation of sampling expansions for these transforms as well as their applications, studies on the associated er...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2015-04, Vol.35 (2), p.931-946
Main Authors: Annaby, M. H., Asharabi, R. M.
Format: Article
Language:English
Subjects:
Derivation
Error analysis
Errors
Estimates
Fourier transforms
Representations
Sampling
Transforms
Citations: Items that cite this one
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Summary:The linear canonical and fractional Fourier transforms and their different sampling representations play a major role for signal processing experts. Although there are many works on the derivation of sampling expansions for these transforms as well as their applications, studies on the associated error are rare. This paper is filling a remarkable portion of this gap by deriving accurate estimates for three types of error. We concretely establish error bounds for truncation, amplitude and jitter errors. Illustrative numerical examples with figures and comparisons are demonstrated.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/dru020