Design of extrapolated impulse response FIR filters with residual compensation in subexpression space

Abstract

In this paper, an extrapolated impulse response filter

with residual compensation is proposed for the design of discrete

coefficient finite-impulse response (FIR) filters using subexpression

sharing. The proposed technique utilizes the quasi-periodic

nature of the filter impulse response to approximate the filter coefficients.

The reduced degree of freedom of filter coefficients due

to the quasi-periodic approximation is perfectly restored by introducing

a residual compensation technique. The resulting subexpression

sharing synthesis of discrete coefficient FIR filters has

lower complexities than that of the conventional synthesis techniques

in terms of number of adders. To further reduce the synthesis

complexity, filter coefficients and residuals may be optimized

in subexpression spaces. Mixed integer linear programming is formulated

for the optimization. Numerical examples show that the

number of adders required by synthesizing the filters in the proposed

structure is significantly reduced compared to that of the

conventional synthesis schemes synthesized in direct or transposed

direct form.