A FREQUENCY-DOMAIN APPROACH TO INTERPOLATION FROM A NONUNIFORM GRID

We introduce a linear time-varying (LTV) system framework for the mode ling and design of linear algorithms for interpolating band-limited si gnals from nonuniformly spaced samples. The LTV model characterizes th e interpolation process in the frequency domain via the notion of bifr equency transmission function (BFTF). The BFTF provides a convenient m eans of assessing interpolator quality because it conveys how frequenc y components in the input are mapped to the frequency axis of the inte rpolated output. We show plots of BFTFs for several common linear inte rpolators, with an emphasis on a minimum-mean-squared-error method due to J.L. Yen. We prove that Yen's algorithm can be obtained as a speci al case of an optimal frequency-domain design of its BFTF using a weig hted least-squares criterion. This design procedure is then generalize d by using an unevenly weighted least-squares error measure that can i ncorporate knowledge of the approximate spectral shape of the original analog signal, to reduce interpolation error. Block interpolators are considered for situations where the number of signal samples is large or infinite, and methods are described for avoiding the matrix invers ion to compute the interpolation. Finally, the performances of all int erpolators studied in this paper are compared via simulation.