Title :
A singular value decomposition derivation in the discrete frequency domain of optimal noncentro-symmetric 2-D FIR filters
Author_Institution :
Dept. of Eng. Math. & Phys., Cairo Univ., Fayoum, Egypt
fDate :
5/1/1998 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
