Derivative Sampling Expansions for the Linear Canonical Transform: Convergence and Error Analysis

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.