Non-iterative WLS design of allpass variable fractional-delay digital filters

This paper presents a non-iterative method for the weighted-least-squares (WLS) design of allpass variable fractional-delay (VFD) digital filters. After expressing the coefficients of an allpass VFD filter as the polynomials of the variable fractional-delay parameter p, we develop an analytical WLS method for finding the optimal polynomial coefficients, and show that the allpass VFD filter design problem can be efficiently solved without resort to any iterative procedure or using any nonlinear optimization technique while a closed-form solution can be analytically obtained through solving a matrix equation. Compared with the existing allpass WLS method that iteratively solves a series of linearized WLS minimization problems, the proposed non-iterative WLS approach can yield much better design results with significantly reduced computational complexity and without any convergence issue.