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Sampling theorem concepts are applied to certain classes of linear shift-variant systems. Various sampling theorem characterizations arise from different bandlimiting assumptions on the system input and/or impulse response. In two of the three cases considered, the system output is also bandlimited and can be expressed in a sampling theorem expansion. The discrete characterizations arising from these two cases reduce to an identical computational form that can be evaluated with a generalized Z-transform treatment. The Fourier duals of the sampling theorems, wherein the system is characterized by its frequency rather than impulse response, are also presented.