An improved weighted least-squares design of FIR digital filters with variable fractional delay

Digital filters capable of changing their frequency response characteristics are often referred to as variable digital filters (VDFs) and have found useful in a number of digital signal processing applications. An important class of VDFs is the digital filters with variable fractional delay. This paper describes an improved WLS design for variable-fractional-delay FIR filters, which offers improved performance of the filters obtained with considerably reduced computational complexity compared to a recently proposed WLS design method. The design improvement 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.