Periodically nonuniform sampling of bandpass signals

Abstract

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.