Sampling rate

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The sampling rate, sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz (inverse seconds, 1/s, s−1). The inverse of the sampling frequency is the sampling period or sampling interval, which is the time between samples.[1]

Sample rate is usually noted in Sa/s (non-SI) and expanded as kSa/s, MSa/s, etc. The common notation for sampling frequency is fs which stands for frequency (subscript) sampled.

Contents

Sampling theorem

The Nyquist–Shannon sampling theorem states that perfect reconstruction of a signal is possible when the sampling frequency is greater than twice the maximum frequency of the signal being sampled,[2] or equivalently, when the Nyquist frequency (half the sample rate) exceeds the highest frequency of the signal being sampled. If lower sampling rates are used, the original signal's information may not be completely recoverable from the sampled signal.

For example, if a signal has an upper band limit of 100 Hz, a sampling frequency greater than 200 Hz will avoid aliasing and allow theoretically perfect reconstruction.

Oversampling

In some cases, it is desirable to have a sampling frequency more than twice the desired system bandwidth so that a digital filter can be used in exchange for a weaker analog anti-aliasing filter. This process is known as oversampling.[3]

Undersampling

Conversely, one may sample below the Nyquist rate. For a baseband signal (one that has components from 0 to the band limit), this introduces aliasing, but for a passband signal (one that does not have low frequency components), there are no low frequency signals for the aliases of high frequency signals to collide with, and thus one can sample a high frequency (but narrow bandwidth) signal at a much lower sample rate than the Nyquist rate.

Audio

In digital audio, notable sampling rates are:

Video systems

In digital video, the temporal sampling rate is defined the frame rate – or rather the field rate – rather than the notional pixel clock. The image sampling frequency is the repetition rate of the sensor integration period. Since the integration period may be significantly shorter than the time between repetitions, the sampling frequency can be different from the inverse of the sample time.

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