Quantization effect on phase response and its application to multiplierless ANC

Adaptive filtering is a widely used technique in active noise control (ANC). In order to make the adaptive filter in an FXLMS (filtered-x LMS) ANC system stable, the reference signal must pass through an estimation filter whose phase response is within ±90° of the phase of the secondary path. In this paper, we study the quantization effects on the filter phase response and the relationship between the phase response and the location of the zeros and poles. In addition, we propose a filter structure and nonuniform quantization method in which we quantize the filter coefficients so they each contain a small number of nonzero bits, based on the distance of the zeros/poles to the unit circle, to guarantee that the ±90° allowable phase deviation is met - greatly reducing the implementation cost. We combine these ideas with that of multiplierless implementations of adaptive FIR filters to realize an efficient active noise control using field programmable gate arrays or other digital hardware.