Reconstruction of sequences from nonuniform samples

If a discrete time signal x(n) is obtained as the output of an interpolation filter F(z), it is natural to expect that it can be recovered from the decimated samples x(Mn), even though the signal is not bandlimited except in the ideal case. However, unless F(z) is a Nyquist filter, stability of reconstruction is not guaranteed. There are cases where x(n) cannot be recovered from the uniformly spaced samples x(Mn) in a stable manner, for example, when all the polyphase components of F(z) have unit-circle zeros. We provide precise theorems which show that even under such situations, stable reconstruction from a nonuniformly decimated version is often possible.