Exact reconstruction from periodic nonuniform samples

We examine the problem of reconstructing a discrete-time signal given only n of its M-phase components. Borrowing analysis from the field of perfect reconstruction filter banks enables us to derive necessary and sufficient conditions under which reconstruction is possible. Essentially, in a perfect reconstruction system, the conditions required to reconstruct from partial information are equivalent to the conditions needed to ensure that the rest of the information does not contribute to the reconstructed signal. This allows us to reconstruct multiband signals which have an overall bandwidth of no more than B, yet cannot be reconstructed from uniformly spaced samples at the minimum rate of B/2π