engleski

Design of Sparse FIR-Filters With No Phase Specifications Using Signomial Programming

Finite impulse response filters are used in many digital signal processing applications because of their stability and simple implementation. More popular are FIR filters with linear phase, but if phase specification is not mandatory, additional filter selectivity can be gained by omitting phase constraints. On the other hand, when analyzing filters from hardware complexity point of view, it is beneficial to reduce the number of filter’s coefficients since each filter coefficient leads to one general purpose multiplier. By reducing the number of multipliers, power consumption of the complete design is decreased. One method for reducing filter’s coefficients is sparse filter design. However, this design leads to optimization problem with combinatorial complexity. Here, we focus on the design of sparse lowpass FIR filters with no phase specifications, constrained in a minimax sense, by using nonlinear optimization technique called signomial programming. Instead of classic minimization of the l0-norm, we minimize the lp-norm of filter’s coefficients with 0 < p < 1, which is known to force sparsity. We illustrate by examples that our method yields sparse filters whose magnitude attenuation is higher than those of their nonsparse counterparts.

digital filter ; FIR filter ; lp-norm ; nonlinear phase ; signomial programming ; sparsity

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