Optimal Design of All-Pass Variable Fractional-Delay Digital Filters

This paper presents a computational method for the optimal design of all-pass variable fractional-delay (VFD) filters aiming to minimize the squared error of the fractional group delay subject to a low level of squared error in the phase response. The constrained optimization problem thus formulated is converted to an unconstrained least-squares (LS) optimization problem which is highly nonlinear. However, it can be approximated by a linear LS optimization problem which in turn simply requires the solution of a linear system. The proposed method can efficiently minimize the total error energy of the fractional group delay while maintaining constraints on the level of the error energy of the phase response. To make the error distribution as flat as possible, a weighted LS (WLS) design method is also developed. An error weighting function is obtained according to the solution of the previous constrained LS design. The maximum peak error is then further reduced by an iterative updating of the error weighting function. Numerical examples are included in order to compare the performance of the filters designed using the proposed methods with those designed by several existing methods.