Periodically nonuniform sampling of bandpass signals

It is known that a continuous time signal [Chi](t) with Fourier transform X([Nu]) band-limited to [absolute value of [Nu]] [less than] [Theta]/2 can be reconstructed from its samples [Chi]([T.sub.o] n) with [T.sub.o] = 2[Pi]/[Theta]. In the case that x([Nu]) consists of two bands and is band-limited to [[Nu].sub.o] [less than] [absolute value of [Nu]] [less than] [[Nu].sub.o] + [Theta] 2, successful reconstruction of [Pi](t) from [Pi]([T.sub.o] 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, [Pi]([2T.sub.o]n) and [Pi]([2T.sub.o] n+[d.sub.1]), with average sampling period [T.sub.o], to recover [Pi](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 signals. Further generalizations will be made to the two-dimensional case and discrete time case.