New results on Yen´s approach to interpolation from nonuniformly spaced samples

The problem of reconstructing a bandlimited signal from a set of nonuniformly spaced samples is addressed, with particular emphasis on a method due to J.L. Yen (1956). A simple proof for the derivation of Yen´s interpolation formula is given. The interpolating process is then modeled as a linear time-varying system and is analyzed in the frequency domain by means of its bifrequency transmission function (BFTF). It is proven that Yen´s interpolator can be obtained as a special case of an optimal frequency-domain design of its BFTF using a weighted least-square criterion. A practical interpolator, based on Yen´s method, is considered for situations where the number of samples is large or infinite and the original Yen interpolation formula is inapplicable. The performance of this modified Yen interpolator is compared with that of other commonly used interpolation methods in terms of achievable S/N