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 - <p style="text-align: justify;">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.</p>