Abstract
The vector space of two-sided sequences expressible as finite sums of unit sample sequences, complex exponential sequences, the unit step sequence, and their elementwise products forms a natural space for the theory of discrete-time linear shift-invariant operators. This space is (algebraically) closed under translation, elementwise multiplication, and solution of linear constant-coefficient difference equations. Every sequence in this space can be uniquely decomposed into a sum of elementary sequences. An unexpected consequence of this decomposition is that the impulse response and frequency response of an LSI operator can be specified independently.
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