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

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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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University