Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, which is referred to as the Interpolation Identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time. The Interpolation Identity also leads to new sampling strategies including an extension of Papoulis’ generalized sampling expansion.