An Efficient Design of 2-D Digital Filters Using Singular Value Decomposition and Genetic Algorithm with Canonical Signed Digit (CSD) Coefficients

Abstract

In this thesis, the design of 2-D filters by SVD is proposed. This technique reduces the complexity of the designed 2-D digital filters by decomposing it into a set of 1-D digital filters in zl and z2 connected in cascade. The design by SVD can be improved by varying the order of 1-D digital filters in each section based on their corresponding singular values. It is shown that by assigning higher order filters to the sections with greater singular values (SVs), and lower order filters to the sections with lower SVs, a sizable reduction in the total number of required multiplications is achieved. A Genetic Algorithm (GA) is used to design each of the 1-D filters instead of classical optimization. Canonical signed digit system is used to represent filters\u27 coefficients. CSD helps to improve the efficiency of multiplications and thus increase the throughput rate. Examples are provided to demonstrate the effectiveness and usefulness of the proposed technique