On the relationship between uniform and recurrent nonuniform discrete-time sampling schemes

Recurrent nonuniform discrete-time signal samples can be regarded as a combination of K mutual delayed sequences of uniform discrete-time signal samples taken at one Kth of the Nyquist sampling rate. This paper introduces a new alternative discrete-time analysis model of the recurrent nonuniform sampling scenario. This model can be described by the analysis part of a uniform discrete Fourier transform (DFT) modulated filterbank from which the K uniformly distributed and down sampled frequency bands are mixed in a very specific way. This description gives a clear relationship between uniform and recurrent nonuniform discrete-time sampling schemes. A side benefit of this model is an efficient structure with which one can reconstruct uniform discrete-time Nyquist signal samples from recurrent nonuniform samples with known mutual delays between the nonuniform distributed samples. This reconstruction structure can be viewed as a natural extension of the synthesis part of an uniform DFT modulated filterbank.