Error Analysis of Reconstruction From Linear Canonical Transform Based Sampling

In this paper, we consider the performance of sampling associated with the linear canonical transform (LCT), which generalizes a large number of classical integral transforms and fundamental operations linked to signal processing and optics. First, we revisit sampling approximation in the LCT domain to introduce a generalized approximation operator. Then, we derive an exact closed-form expression for the integrated squared error that occurs when a signal is approximated by a basis of shifted, scaled, and chirp-modulated versions of a generating function in the LCT domain. Several basic properties of the approximation error are presented. The derived results can be applied to a wide variety of sampling approximation schemes in the LCT domain. Finally, experimental examples are given to illustrate the theoretical derivations.