PERIODICALLY NONUNIFORM SAMPLING OF BANDPASS SIGNALS

It is known that a continuous time signal x(t) with Fourier transform X(nu) band-limited to \nu\ < Theta/2 can be reconstructed from its sam ples x(T(o)n) with T-o = 2 pi/Theta. In the case that X(nu) consists O f two bands and is band-limited to nu(o) < \nu\ < nu(o) + Theta/2, suc cessful reconstruction of x(t) from x(T(o)n) requires an additional co ndition on the band positions, When the two bands are not located prop erly, Kohlenberg showed that we can use two sets of uniform samples, x (2T(o)n) and x(2T(o)n+d(1)), with average sampling period T-o, to reco ver x(t). Because two sets of uniform samples are employed, this sampl ing scheme is called Periodically Nonuniform Sampling of second order [PNS(2)], In this paper, we show that PNS(2) can be generalized and ap plied to a wider class, Also, Periodically Nonuniform Sampling of Lth- order [PNS(L)] will be developed and used to recover a broader class o f band-limited signals, Further generalizations will be made to the tw o-dimensional case and discrete time case.