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Volume 37, Issue 3
Derivative Sampling Expansions for the Linear Canonical Transform: Convergence and Error Analysis

Mahmoud H. Annaby & Rashad M. Asharabi

DOI: 10.4208/jcm.1806-m2017-0215

J. Comp. Math., 37 (2019), pp. 403-418.

Published online: 2018-09

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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 band-limited 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 band-limited 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.

  • Keywords

Linear canonical transform, Sampling theorems, Truncation error, Amplitude error, Jitter-time error.

  • AMS Subject Headings

65D05, 94A20, 30D10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mhannaby@sci.cu.edu.eg (Mahmoud H. Annaby)

rmahezam@nu.edu.sa (Rashad M. Asharabi)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-403, author = {Annaby , Mahmoud H. and Asharabi , Rashad M.}, title = {Derivative Sampling Expansions for the Linear Canonical Transform: Convergence and Error Analysis}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {3}, pages = {403--418}, 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 band-limited 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 band-limited 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1806-m2017-0215}, url = {http://global-sci.org/intro/article_detail/jcm/12730.html} }
TY - JOUR T1 - Derivative Sampling Expansions for the Linear Canonical Transform: Convergence and Error Analysis AU - Annaby , Mahmoud H. AU - Asharabi , Rashad M. JO - Journal of Computational Mathematics VL - 3 SP - 403 EP - 418 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1806-m2017-0215 UR - https://global-sci.org/intro/article_detail/jcm/12730.html KW - Linear canonical transform, Sampling theorems, Truncation error, Amplitude error, Jitter-time error. AB -

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 band-limited 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 band-limited 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.

Annaby , Mahmoud H. and Asharabi , Rashad M.. (2018). Derivative Sampling Expansions for the Linear Canonical Transform: Convergence and Error Analysis. Journal of Computational Mathematics. 37 (3). 403-418. doi:10.4208/jcm.1806-m2017-0215
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