An analog signal is any continuous signal for which the time-varying feature of the signal represents some other time-varying quantity, i.e. analogous to another time-varying signal. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves.
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In contrast, a digital signal represents the original time-varying quantity as a sampled sequence of quantized values. This imposes some bandwidth and dynamic range constraints on the representation but, unlike the analog signal, can avoid further electronic noise and distortion.