Discretization-free design of variable fractional-delay FIR digital filters

This paper presents a closed-form solution for obtaining the optimal coefficients of variable finite impulse-response (FIR) filters with continuously adjustable fractional-delay (FD) response. The design is formulated as a weighted-least-squares (WLS) approximation problem without discretizing (sampling) the frequency ω and the variable FD p in the filter design process, and the objective error function of variable frequency response can be derived by numerical integration, thus the variable FD filter coefficients can be obtained in a closed-form. Compared to the existing WLS method, since the discretization-free method does not need parameter discretizations in deriving the objective error function, the closed-form solution is optimal in the sense that the filter design accuracy is not affected by the sampling grid densities, and higher design accuracy can be guaranteed. Furthermore, since the discretization-free method does not need to sum up all the squared errors at a great number of discrete points when evaluating the objective error function, the computational complexity can be reduced considerably