Constrained Design of Two-Dimensional FIR Filters with Sparse Coefficients

We present an algorithm for the constrained design of a 2D FIR filter with sparse coefficients. Existing filter design methods aim to minimize a filter order and maximize filter performance. The 2D FIR filter coefficients designed by the least-squares method with peak error constraints are optimal in the sense of least-squares within a given order. However, they are not necessarily optimal in terms of constructing a filter that satisfies the design specification. That is, a higher-order filter with some zero coefficients can construct a filter that satisfies the design specification with fewer multipliers. Our method minimizes the number of non-zero coefficients of the filter coefficients, while the frequency response of the filter satisfies the design specification. It performs better in terms of maximum error than the least-squares method with peak error constraints having the same number of multipliers.