Synthesis of narrowband linear-phase FIR filters with a piecewise-polynomial impulse response

A method is presented to synthesize narrowband linear-phase FIR filters. The method is based on a piecewise-polynomial approximation of impulse responses and recursive implementation structures. The arithmetic complexity of these filters is proportional to the number of impulse-response pieces and the overall polynomial order. The filter coefficients are optimized by using linear programming. An example shows the advantage of these filters with regard to reducing the number of coefficients as well as the arithmetic complexity of these filters.