Non-uniform time sampling FIR filter design based on least-squares criterion

The finite impulse response (FIR) digital filter for non-uniform time samples is investigated. By the upsampling technique this filter design is reduced to determining filter coefficients with many zeros. Only those coefficients that are not zeros correspond to time samples which are used to obtain the filtered output. Determining such a set of filter coefficients is exactly a best m-term approximation problem. The optimal non-uniform least-squares filter is obtained by a matching pursuit algorithm. In general, nonzero filter coefficients are not distributed consecutively in order to ensure the better performance of a filter. Satisfactory performances of the present method have been demonstrated by simulation.