Relationship between sampling and multirate filterbanks in the linear canonical transform domain

Feng Zhang,Ran Tao,Yue Wang

doi:10.1186/1687-6180-2013-102

Abstract

Abstract Multirate filterbanks have found applications in speech processing, image processing, communications, and in the development of new sampling theorems. This paper explores the relationship between sampling theorems and multirate filterbanks in the linear canonical transform (LCT) domain. The sampling identity and the interpolation identity for bandlimited signals in the LCT domain are discussed and then employed to obtain a discrete-time implementation for bandlimited signals in the LCT domain from their multichannel samples. Furthermore, we relate the multichannel sampling for bandlimited signals in the LCT domain as well as the corresponding continuous-time LCT filterbank to the discrete-time LCT filterbank, which can lead to new sampling strategies for bandlimited signals in the LCT domain.

Highlights

Over the recent years, multirate filterbanks have found applications in speech processing, image processing, communications, radar systems, etc. [1,2]
The derived results reveal a method for processing signals nonbandlimited in the Fourier transform (FT) domain but bandlimited in the linear canonical transform (LCT) domain, and can be seen as a step towards generalizing the relationship between the multichannel sampling and filterbanks from the FT to other transforms that are special cases of the LCT
We can see that if a signal is nonbandlimited in the FT domain, it can be bandlimited in the LCT domain [29]

Summary

Introduction

Multirate filterbanks have found applications in speech processing, image processing, communications, radar systems, etc. [1,2]. In another advance in signal processing, the linear canonical transform (LCT) has been introduced and used in processing nonstationary signals [11]. This paper generalizes the relationship between the multichannel sampling theorem and multirate filterbanks from the FT case to the LCT case. The derived results reveal a method for processing signals nonbandlimited in the FT domain but bandlimited in the LCT domain, and can be seen as a step towards generalizing the relationship between the multichannel sampling and filterbanks from the FT to other transforms that are special cases of the LCT

Preliminaries

Convolution theorem for the LCT

Conclusions