We examine the problem of sampling and reconstructing non-bandlimited signals with sample sets of finite density. Three approaches are considered in the paper. The first approach, based on a method of Clark, involves time warping, or demodulating, a class of generalized phase modulated signals into bandlimited signals, which can then be sampled and reconstructed with the standard Shannon sampling theory. The second method applies Kramer generalization of Shannon's theory, and it is seen that the reconstruction processes derived from this application are, in general, for non-bandlimited signals. The final approach combines the first approach and a special case of the second approach wherein non-harmonic Fourier kernels are used. This approach allows the specification of a sampling and reconstruction process for certain classes of non-bandlimited signals for which uniform sampling is used.
James J. Clark,
"Sampling and Reconstruction of Non-Bandlimited Signals", Proc. SPIE 1199, Visual Communications and Image Processing IV, (1 November 1989); doi: 10.1117/12.970164; https://doi.org/10.1117/12.970164