Extended-window interpolation applied to digital filter design

This paper develops a procedure for the design of frequency-selective interpolation operators that can be computed and saved once and for all. These operators are used to design real-time digital operators: interpolators, FIR differentiators, IIR filters, and composed interpolation and filtering operators. Each real-time operator is a matrix relating sets of data points to sets of interpolated values. Since these matrices are characterized by low norms, they permit reduced-word implementations, and are suitable for real-time processing with array processors and massively parallel machines. The design of the interpolation operators uses windows that, unlike traditional approaches, extend beyond the data interval up to the length permitted by the dimensionality theorem. A new form of the dimensionality theorem is used to minimize the minimax interpolation error within a predetermined frequency range, which may be either the passband of the antialiasing filter or the passband of an analog prototype filter. The main application presented in the paper is the design of combined digital filters and interpolators, which will be referred to as interpolating filters. The frequency responses of such filters, as well as the interpolated time responses, almost coincide with those of the corresponding analog prototypes