Periodically nonuniform sampling of bandpass signals

It is known that a continuous time signal x(i) 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 an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, x(2T/sub 0/n) and x(2T/sub 0/n+d/sub 1/), with average sampling period T/sub 0/, to recover x(t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order PNS(2). In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order PNS(L) will be developed and used to recover a broader class of band-limited signal. Further generalizations will be made to the two-dimensional case and discrete time case.