DERIVATIVE SAMPLING EXPANSIONS FOR THE LINEAR CANONICAL TRANSFORM: CONVERGENCE AND ERROR ANALYSIS

In recent decades, the fractional Fourier transform as well as the linear canonical transform became very efficient tools in a variety of approximation and signal processing applications. There are many literatures on sampling expansions of interpolation type for bandlimited functions in the sense o...

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Published inJournal of computational mathematics Vol. 37; no. 3; pp. 403 - 418
Main Authors Annaby, Mahmoud H., Asharabi, Rashad M.
Format Journal Article
LanguageEnglish
Published Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences 01.01.2019
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ISSN0254-9409
1991-7139
DOI10.4208/jcm.1806-m2017-0215

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Abstract In recent decades, the fractional Fourier transform as well as the linear canonical transform became very efficient tools in a variety of approximation and signal processing applications. There are many literatures on sampling expansions of interpolation type for bandlimited functions in the sense of these transforms. However, rigorous studies on convergence or error analysis are rare. It is our aim in this paper to establish sampling expansions of interpolation type for bandlimited functions and to investigate their convergence and error analysis. In particular, we introduce rigorous error estimates for the truncation error and both amplitude and jitter-time errors.
AbstractList In recent decades, the fractional Fourier transform as well as the linear canonical transform became very efficient tools in a variety of approximation and signal processing applications. There are many literatures on sampling expansions of interpolation type for bandlimited functions in the sense of these transforms. However, rigorous studies on convergence or error analysis are rare. It is our aim in this paper to establish sampling expansions of interpolation type for bandlimited functions and to investigate their convergence and error analysis. In particular, we introduce rigorous error estimates for the truncation error and both amplitude and jitter-time errors.
Author Annaby, Mahmoud H.
Asharabi, Rashad M.
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CitedBy_id crossref_primary_10_1016_j_sigpro_2019_07_008
crossref_primary_10_1002_mma_7403
crossref_primary_10_1109_LCOMM_2020_2988947
crossref_primary_10_1007_s11075_023_01535_8
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Title DERIVATIVE SAMPLING EXPANSIONS FOR THE LINEAR CANONICAL TRANSFORM: CONVERGENCE AND ERROR ANALYSIS
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