Variable Fractional Delay FIR Filter Design with a Bicriteria and Coefficient Relationship

This brief investigates a tradeoff between the integral squared error and the peak deviation error for a variable fractional delay (VFD) filter with a coefficient relationship. The integral squared error is minimized subject to additional constraints on the peak deviation error. The problem is solved by utilizing second-order cone programming. In addition, the performance of the VFD filter with discrete coefficients is investigated, in which the filter coefficients are expressed as the sum of power-of-two terms to reduce the filter operations to shifts and adds. Design examples show that the peak deviation error can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error. Similarly, the integral squared error can be significantly reduced from the minimax solution while maintaining approximately the same peak deviation error. Furthermore, the tradeoff filters are less sensitive with respect to quantization than the least squares and minimax solutions.