Periodically nonuniform sampling of bandpass signals

摘要

It is known that a continuous time signal x(i) with Fourierntransform X(Ν) band-limited to |Ν|<Θ/2 can benreconstructed from its samples x(T0n) withnT0=2Π/Θ. In the case that X(Ν) consists of twonbands and is band-limited to Ν0<|Ν|<Ν0n+Θ/2, successful reconstruction of x(t) fromnx(T0n) requires an additional condition on the bandnpositions. When the two bands are not located properly, Kohlenbergnshowed that we can use two sets of uniform samples, x(2T0n)nand x(2T0n+d1), with average sampling periodnT0, to recover x(t). Because two sets of uniform samples arenemployed, this sampling scheme is called Periodically NonuniformnSampling of second order [PNS(2)]. In this paper, we show that PNS(2)ncan be generalized and applied to a wider class. Also, PeriodicallynNonuniform Sampling of Lth-order [PNS(L)] will be developed and used tonrecover a broader class of band-limited signal. Further generalizationsnwill be made to the two-dimensional case and discrete time case