Sampling Rate

Sampling rate determines the sound frequency range (corresponding to pitch) which can be represented in the digital waveform. The range of frequencies represented in a waveform is often called its bandwidth. Waveforms sampled at a high sampling rate can represent a broad range of frequencies and hence have broad bandwidth. In fact, the maximum bandwidth of a sampled waveform is determined exactly by its sampling rate; the maximum frequency representable in a sampled waveform is termed its Nyquist frequency, and is equal to one half the sampling rate. Thus, for example, a waveform sampled at 16,000 Hz can represent all frequencies up to its Nyquist frequency of 8,000 Hz.

A problem called aliasing occurs when a signal to be sampled contains energy at frequencies above the sampling Nyquist frequency. The next figure illustrates how aliasing would occur when the sampling rate is much too low for the frequency of an input signal. The solid curve represents the analog signal at a comparatively high frequency. Circles show where samples were taken at a relatively low sampling rate. The dotted line illustrates the apparent frequency of the sampled waveform, completing about two cycles in the period that the original signal completed 20 cycles.

Obviously, aliasing has the effect of producing sounds of lower frequency from sounds that are higher in frequency than the Nyquist frequency. Once aliasing has occurred, it is absolutely impossible to distinguish a component generated by aliasing from one that was actually present in the input signal. This effect is one of the most common sources of distortion in digitized waveforms. Fortunately, most modern computer hardware for digitizing sound has builtin filters which are tuned to remove sound energy at frequencies beyond the Nyquist frequency for whatever sampling rate is being used.