An optimal design of FIR filters with discrete coefficients and image sampling application

The paper proposes a new approach for the design of linear phase finite impulse response (FIR) filters with discrete co-efficient values. This problem is a very hard combinatoric discrete optimization, which results in the prohibitive computational complexity for solution. In this paper, we first explicitly express the discrete coefficients of filters as indefinite quadratic but continuous constraints. We then develop an efficient iterative algorithm to tackle the nonconvex optimization problem to locate optimal discrete filter coefficients. By numerical simulation results, we show that our proposed method significantly outperform the methods using quantized coefficients of filters. We also provide an image sampling application to illustrate the performance of our designed filters.