### Sampled Sinusoids

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

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