Periodically nonuniform sampling of a new class of bandpass signals

It is known that a continuous time signal x(t) with Fourier transform X(/spl nu/) band-limited to |/spl nu/|</spl Theta//2 can be reconstructed from its samples x(T/sub 0/n) with T/sub 0/=2/spl pi///spl Theta/. In the case that X(/spl nu/) consists of two bands and is band-limited to /spl nu//sub 0/<|/spl nu/|</spl nu//sub 0/+/spl Theta//2, successful reconstruction of x(t) from x(T/sub 0/n) requires that these two bands be located properly. When the two bands are not located properly, Kohlenberg (1953) showed that we can use a periodically nonuniform sampling (PNS) scheme to recover x(t). In this paper, we show that PNS scheme can be generalized and applied to a wider class. Further generalizations will be made to two-dimensional case and discrete-time case.