An Improved Weighted Least-Squares Design for Variable Fractional Delay FIR Filters

Digital filters capable of changing their frequency response characteristics are often referred to as variable digital filters (VDF’s) and have been found useful in a number of digital signal processing applications. An important class of VDF’s is the class of digital filters with variable fractional delay. This paper describes an enhanced weighted least-squares design for variable-fractional-delay finite-impulse response filters, which offers improved performance of the filters obtained with considerably reduced computational complexity compared to a recently proposed weighted least-squares (WLS) design method. The design enhancement is achieved by deriving a closed-form formula for evaluating the WLS objective function. The formula facilitates accurate and efficient function evaluations as compared to summing up a large number of discrete terms, which would be time consuming and inevitably introduce additional errors into the design.