Optimization of extrapolated impulse response filters using semi-infinite programming

Narrow band lowpass or highpass digital finite impulse response filters can be synthesized by using extrapolated impulse response techniques to achieve reduced complexity. However, the non-linear optimization problem of the extrapolated impulse response filters was simplified to a linear programming problem in previous literature leading to suboptimum. In this paper, a semi-infinite programming is proposed to jointly optimize the filter coefficients and the extrapolated scaling factors. A realization structure making use of the coefficient symmetry is also presented. An example taken from literature is included illustrating that the number of multipliers for the resulting filter is less than 65 percent of existing results.