### 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:

where and are complex, and further defined as

When , we obtain

which is the complex sinusoid at amplitude , frequency , and phase . More generally, we have

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

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