Recursive extended window interpolators applied to the design of IIR and fractional delay filters

This paper proposes a conceptual modification of the interpolator used by the extended window design (EWD) of IIR and fractional delay filters. The original EWD digitizes analog filters by performing a trigonometric polynomial interpolation along an extended window that ends at the current sampling time. The proposed changes increase the flexibility and the degrees of freedom of the interpolator in two ways. First, the interpolation space is expanded from the space spanned by a restricted set of sinusoidal functions to the space spanned by any set of linearly independent functions. Second, the Hermite interpolation (which processes the values of both the signal and some of its derivatives at sampling times) is considered in order to smoothen the interpolated signal. Since the input derivatives are not available, related parameters are estimated and updated recursively. The increased accuracy of the proposed recursive EWD relatively to nonrecursive EWD and WLS optimal filter designs is illustrated with an example.