### Generalized Complex Sinusoids

We have defined sinusoids and extended the definition to include complex
sinusoids. We now extend one more step by allowing for *exponential
amplitude envelopes*:

*complex*, and further defined as

When , we obtain

Defining
, we see that the generalized complex sinusoid
is just the complex sinusoid we had before with an *exponential envelope*:

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Sampled Sinusoids

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Analytic Signals and Hilbert Transform Filters