Robust and efficient filterbank structure for reconstruction from recurrent nonuniform samples

In this paper, we present a robust and efficient structure for the reconstruction of uniform samples of a signal from its recurrent nonuniform samples. This structure makes use of the synthesis part of a uniform discrete Fourier transform (DFT) modulated filterbank. The proposed structure is a refinement over an existing filterbank structure that utilizes the inverse of a nonuniform DFT matrix, the numerical stability of which cannot be guaranteed. The poor numerical stability of the inverse is overcome in a modified structure by inverting a preconditioned matrix having an improved numerically stable inverse. Necessary and sufficient conditions that ensure numerical stability of the preconditioned matrix inverse have been presented.