In discrete-time audio processing, such as we normally do on a computer,
we work with
samples of continuous-time
signals. Let

denote the
sampling rate in Hz. For audio, we typically have

kHz, since the audio band nominally extends to

kHz. For compact
discs (CDs),

kHz,
while for digital audio tape (DAT),

kHz.

Let

denote the
sampling interval in seconds. Then to
convert from continuous to discrete time, we replace

by

, where

is an integer interpreted as the
sample number.
The sampled generalized complex
sinusoid
is then
Thus, the sampled case consists of a sampled
complex sinusoid
multiplied by a sampled
exponential envelope
![$ \left[e^{\sigma
T}\right]^n = e^{-nT/\tau}$](http://www.dsprelated.com/josimages_new/mdft/img614.png)
.
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