Optimization and implementation of extrapolated impulse response filters

The impulse response of an FIR lowpass or highpass filter is quasi-periodic and enclosed in an envelope with diminishing magnitude. Its energy concentrates near the center. This diminishing energy and quasi-periodic nature of the impulse response have been exploited in Y.C. Lim (1990) to reduce the complexity of an FIR filter using a scheme called the extrapolated impulse response technique. 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.