Filtering Nonuniformly Sampled Grid-Based Signals

This paper presents an example application of digital alias-free signal processing, where a sequence of irregularly spaced, yet uniformly gridded, samples of a bandlimited discrete-time signal is filtered by using an oversampled finite impulse response filter. The mathematical model of the proposed filter is introduced, and a new interpolation formula for calculating the convolution operation of the filter, based on nonuniform sampling, is derived. In addition, uniform grid versions of Total Random, Stratified and Antithetical Stratified random sampling techniques are demonstrated. We carry out numerical comparison between these techniques and the proposed one in terms of Fourier transform estimates of the filtered output signal. The proposed interpolation technique shows enhancements over other sampling techniques after certain number of sampling points. Furthermore, it has a faster uniform convergence rate of the normalized root mean squared error than other techniques.