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:




When , we obtain




![\begin{eqnarray*}
y(t) &\isdef & {\cal A}e^{st} \\
&\isdef & A e^{j\phi} e^{(\...
... t} \left[\cos(\omega t + \phi) + j\sin(\omega t + \phi)\right].
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/mdft/img604.png)
Defining
, we see that the generalized complex sinusoid
is just the complex sinusoid we had before with an exponential envelope:

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