It is known that a continuous time signal x(i) with Fourier transform X(v) band-limited to |v|<0/2 can be reconstructed from its samples x(T0n) with To-2if/®. In the case that X(y) consists of two bands and is band-limited to i/o < H < v0+&/2, successful reconstruction of x(t) from z(T07i) 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(2T0n) and x(2Ton + d1), with average sampling period To, to recover x(i). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)J. 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.
|Number of pages||12|
|Journal||IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing|
|State||Published - 1 Dec 1998|