Natural Basis
The natural basis for a discrete-time signal
is the set
of shifted impulses:
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(12.108) |
or,
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(12.109) |
for all integers





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(12.110) |
so that the expansion of

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(12.111) |
i.e.,
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|
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This expansion was used in Book II [263] to derive the impulse-response representation of an arbitrary linear, time-invariant filter.
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Example: Upsampling by 2