A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters
Multidimensional Systems and Signal Processing
A graph representation of filter networks
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions
Multidimensional Systems and Signal Processing
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This paper solves the weighted least mean square (WLMS) design of two-dimensional (2-D) finite impulse response (FIR) filters with general half plane symmetric frequency responses and nonnegative weighting functions. The optimal solution is characterized by a pair of coupled integral equations, and the existence and uniqueness of the WLMS solution for 2-D FIR filter design are established. Two efficient numerical algorithms using a 2-D fast Fourier transform (FFT) are proposed to solve the WLMS solution. One is based on the contraction mapping and fix point theorem characterizing the coupled integral equation; the other uses conjugate gradient techniques, which guarantees finite convergence. The associated computational complexity is analyzed and compared with existing algorithms. Examples are used to illustrate the effectiveness of the proposed design algorithms. The selection of weighting functions to improve the minimax performance of the filter is also discussed