2-D symmetry: theory and filter design applications

Author

Reddy, Hari C. ; Khoo, I-Hung ; Rajan, P.K.

Volume

3

Issue

3

fYear

2003

fDate

6/25/1905 12:00:00 AM

Firstpage

4

Lastpage

33

Abstract

In this comprehensive review article, we present the theory of symmetry in two-dimensional (2-D) filter functions and in 2-D Fourier transforms. It is shown that when a filter frequency response possesses symmetry, the realization problem becomes relatively simple. Further, when the frequency response has no symmetry, there is a technique to decompose that frequency response into components each of which has the desired symmetry. This again reduces the complexity of two-dimensional filter design. A number of filter design examples are illustrated.

Keywords

FIR filters; IIR filters; circuit complexity; discrete Fourier transforms; fast Fourier transforms; frequency response; polynomials; symmetry; two-dimensional digital filters; 2-D Fourier transforms; 2-D symmetry; complexity; continuous-time continuous-frequency case; continuous-time discrete-frequency case; discrete Fourier transform; discrete-time continuous-spectrum case; filter design; filter frequency response; filter polynomials; finite impulse response filters; infinite impulse response filters; phase functions; tutorial; two-dimensional filter functions; Crystallography; Digital filters; Fast Fourier transforms; Filtering theory; Finite impulse response filter; Fourier transforms; IIR filters; Polynomials; Quantum mechanics; Transfer functions;

fLanguage

English

Journal_Title

Circuits and Systems Magazine, IEEE

Publisher

ieee

ISSN

1531-636X

Type

jour

DOI

10.1109/MCAS.2003.1263396

Filename

1263396