In discrete-time audio processing, such as we must do on a computer, we work with samples of continuous-time signals. Let denote thesampling rate in Hz. For audio, we typically have kHz, since the audio band nominally extends to kHz. For compact discs (CDs), kHz (or very close to that–I once saw Sony device using a sampling rate of Hz), while for digital audio tape (DAT), kHz.
Let denote the sampling period 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 (which includes all other cases) is then