Multi-dimensional linear canonical transform with applications to sampling and multiplicative filtering

• Published in: Multidimensional systems and signal processing Vol. 33; no. 2; pp. 621 - 650
• Main Authors: Shah, Firdous A., Tantary, Azhar Y.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Artificial Intelligence; Circuits and Systems; Convolution; Domains; Electrical Engineering; Engineering; Sampling; Signal,Image and Speech Processing; Theorems; Uncertainty principles; 65R10; Uncertainty principle; 53D22; 26A33; Multiplicative filtering; 93E11; Convolution; 42B10; Linear canonical transform; Sampling; 94A12; Symplectic matrix; 94A20
• ISSN: 0923-6082; 1573-0824
• DOI: 10.1007/s11045-021-00816-6

This paper presents a novel and elegant convolution structure for the multi-dimensional linear canonical transform involving a pure multi-dimensional kernel obtained via a general 2 n × 2 n real, symplectic matrix M with n ( 2 n + 1 ) independent parameters. The primary intention is to develop the convolution theorem associated with the novel linear canonical convolution. The convolution structure is subsequently invoked to establish the sampling theorem for the band-limited signals in the multi-dimensional linear canonical domain. The validity and efficiency of the sampling procedure are demonstrated via a lucid example. Besides, the Heisenberg’s and Beckner’s uncertainty principles associated with the multi-dimensional linear canonical transform are also studied in detail. Finally, we study and design the multiplicative filter in the multi-dimensional linear canonical domain by utilizing the proposed multi-dimensional convolution structure.