Least lp-norm design of complex exponential structure variable fractional delay FIR filters

Most of variable fractional delay (VFD) filters adopt the well-known Farrow structure that assumes an algebraic polynomial approximation to the varying impulse response. The recently proposed complex exponential (CE) structure for VFD filters can achieve a great improvement in design accuracy and a marked reduction in complexity compared with the Farrow structure by using complex exponential functions as the approximants. The least l(p)-norm design problem of the CE -based VFD FIR filters is considered in this paper, which is viewed as a good tradeoff between the least squares and minimax designs. The iteratively reweighted least squares (IRLS) approach is adopted to solve this problem, in which the least l(p)-norm approximation is decomposed into a series of weighted least squares (WLS) subproblems. A matrix -based conjugate gradient (CG) algorithm is presented to solve those WLS subproblems, which is very efficient due to the use of matrix variables. Moreover, the filter performance will be improved further by optimizing the shape parameter in the CE structure using a one-dimensional search technique. Design examples are provided to demonstrate the effectiveness of the proposed method. The comparison of the CE structure filters with the Farrow structure filters is included.