A singular value decomposition derivation in the discrete frequency domain of optimal noncentro-symmetric 2-D FIR filters

Author

Hanna, Magdy T.

Author_Institution

Dept. of Eng. Math. & Phys., Cairo Univ., Fayoum, Egypt

Volume

46

Issue

5

fYear

1998

fDate

5/1/1998 12:00:00 AM

Firstpage

1397

Lastpage

1402

Abstract

A new derivation is presented for the least squares solution of the design problem of two-dimensional (2-D) finite impulse response (FIR) filters by minimizing the Frobenius norm of the difference between the matrices of the ideal and actual frequency responses sampled at the points of a frequency grid. The mathematical approach is based on the singular value decomposition (SVD) of two complex transformation matrices. Interestingly, the designed filter is proved to be zero-phase if the ideal filter is so without assuming any kind of symmetry

Keywords

FIR filters; frequency-domain synthesis; least squares approximations; matrix algebra; minimisation; singular value decomposition; two-dimensional digital filters; Frobenius norm; complex transformation matrices; design; discrete frequency domain; finite impulse response filters; frequency grid; frequency responses; least squares solution; optimal noncentro-symmetric 2-D FIR filters; singular value decomposition derivation; zero-phase filter; Equations; Finite impulse response filter; Frequency domain analysis; Frequency response; Least squares methods; Matrix decomposition; Signal sampling; Singular value decomposition; Symmetric matrices; Two dimensional displays;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.668801

Filename

668801