Design of allpass variable fractional delay filter with signed powers-of-two coefficients

• A new procedure is proposed to reduce the computational complexity for the design of discrete allpass variable fractional delay filters.
• A new exact penalty function method is developed for the design problem.
• Design examples show that the proposed method is highly effective.

This paper investigates the optimal design of allpass variable fractional delay (VFD) filters with coefficients expressed as sums of signed powers-of-two terms, where the weighted integral squared error is the cost function to be minimized. The design can be classified as an integer programming problem. To solve this problem, a new procedure is proposed to generate a reduced discrete search region to decrease the computational complexity. A new exact penalty function method is developed to solve the optimal design problem for allpass VFD filter with signed powers-of-two coefficients. Design examples show that the proposed method can achieve a higher accuracy when compared with the quantization method.