Variable fractional delay filter design with discrete coefficients

Abstract

This paper investigates the optimal design of variable fractional delay (VFD) filter with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two (SPT) terms with a restriction on the total number of power-of-two terms. An optimization problem with least squares criterion is formulated as a mixed-integer programming problem. An optimal scaling factor quantization scheme is applied to the problem resulting in an optimal scaling factor quantized solution. This solution is then improved further by applying a discrete filled function, that has been extended for a mixed integer optimization problem. To apply the discrete filled function method, it requires multiple calculations of the objective function around the neighborhood of a searched point. Thus, an updating scheme is developed to efficiently calculate the objective function in a neighborhood of a point. Design examples demonstrate the effectiveness of the proposed optimization approach.