Periodically nonuniform sampling of a new class of bandpass signals

It is known that a continuous time signal x(t) with Fourier transform X(ν) band-limited to |ν|<Θ/2 can be reconstructed from its samples x(T₀n) with T₀=2π/Θ. In the case that X(ν) consists of two bands and is band-limited to ν₀<|ν|<ν₀ +Θ/2, successful reconstruction of x(t) from x(T₀n) requires that these two bands be located properly. When the two bands are not located properly, Kohlenberg (1953) showed that we can use a periodically nonuniform sampling (PNS) scheme to recover x(t). In this paper, we show that PNS scheme can be generalized and applied to a wider class. Further generalizations will be made to two-dimensional case and discrete-time case