In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled. An oversampled signal is said to be oversampled by a factor of β, defined as Signal processing is the processing, amplification and interpretation of signals, and deals with the analysis and manipulation of signals. ... In signal processing, sampling is the reduction of a continuous signal to a discrete signal. ... In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... The sampling frequency or sampling rate defines the number of samples per second taken from a continuous signal to make a discrete signal. ... This article does not cite any references or sources. ...

or

.

where

• is the sampling frequency
• is the bandwidth or highest frequency of the signal; the Nyquist frequency is .

There are three main reasons for performing oversampling: The sampling frequency or sampling rate defines the number of samples per second taken from a continuous signal to make a discrete signal. ... This article does not cite any references or sources. ...

• It aids in anti-aliasing because realizable analog anti-aliasing filters are very difficult to implement with the sharp cutoff necessary to maximize use of the available bandwidth without exceeding the Nyquist limit. By increasing the bandwidth of the sampled signal, the anti-aliasing filter has less complexity and can be made less expensively by relaxing the requirements of the filter at the cost of a faster sampler. Once sampled, the signal can be digitally filtered and downsampled to the desired sampling frequency. In modern integrated circuit technology, digital filters are much easier to implement than comparable analog filters of high order.
• In practice, oversampling is implemented in order to achieve cheaper higher-resolution A/D and D/A conversion. For instance, to implement a 24-bit converter, it is sufficient to use a 20-bit converter that can run at 256 times the target sampling rate. Averaging a group of 256 consecutive 20-bit samples adds 4 bits to the resolution of the average, producing a single sample with 24-bit resolution. Note that this averaging is possible only if the signal contains perfect equally distributed noise (i.e. if the A/D is perfect and the signal's deviation from an A/D result step lies below the threshold, the conversion result will be as inaccurate as if it had been measured by the low-resolution core A/D and the oversampling benefits will not take effect).
• Noise reduction/cancellation. If multiple samples are taken of the same quantity with a random noise signal, then averaging several samples reduces the noise by a factor of . See standard error (statistics). This means that the SNR ratio improves by a factor of 2 (6dB) if we oversample by a factor of 4 relative to the Nyquist rate (ie a β of 4).

Certain kinds of A/D converters known as delta-sigma converters produce disproportionately more quantization noise in the upper portion of their output spectrum. By running these converters at some multiple of the target sampling rate, and low-pass filtering the oversampled down to half the target sampling rate, it is possible to obtain a result with less noise than the average over the entire band of the converter. Delta-sigma converters use a technique called noise shaping to move the quantization noise to the higher frequencies. In digital signal processing, anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution signal at a lower resolution. ... An anti-aliasing filter is commonly used in conjuction with digital signal processing and is a filter to restrict the bandwidth to approximately satisfy the Shannon-Nyquist sampling theorem. ... Downsampling (or subsampling) is the process of reducing the sampling rate of a signal. ... Integrated circuit of Atmel Diopsis 740 System on Chip showing memory blocks, logic and input/output pads around the periphery Microchips with a transparent window, showing the integrated circuit inside. ... In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... For the Irish mythological figure, see Naoise. ... Look up Threshold in Wiktionary, the free dictionary. ... The standard error of a method of measurement or estimate is the estimated standard deviation of the error in that method. ... The Delta-Sigma (ΔΣ) modulation is a kind of analog-to-digital or digital-to-analog conversion. ... Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ... A low-pass filter is a filter that passes low frequencies but attenuates (or reduces) frequencies higher than the cutoff frequency. ... Similar to dither, noise shaping is a bit reduction technique used to minimize quantization error. ...

Example

For example, consider a signal with a bandwidth or highest frequency of f_H = 100 Hz. The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at 200 Hz would result in β = 1. Sampling at four times that rate () would result in a sampling rate of 800 Hz. This gives the anti-aliasing filter a transition band of 600 Hz () instead of 0 Hz if the sampling frequency were at 200 Hz. The hertz (symbol: Hz) is the SI unit of frequency. ... The Nyquist-Shannon sampling theorem is the fundamental theorem in the field of information theory, in particular telecommunications. ... The transition band is a range of frequencies, usually defined as a bandwidth, that allows the transition from one stage of an electronic filter to the other. ...

An anti-aliasing filter with a transition band of 600 Hz is much more realizable than that of 0 Hz (which would require a perfect filter). If the sampler went to eight times over then the transition band would increase to 1400 Hz, which means the anti-aliasing filter could be made cheaper due to a relaxation of the requirements.

After being sampled at 800 Hz, the signal could be digitally filtered to have a bandwidth of 400 Hz and then further downsampled to closer to 200 Hz. Downsampling (or subsampling) is the process of reducing the sampling rate of a signal. ...

Reference

• John Watkinson, The Art of Digital Audio, ISBN 0-240-51320-7

See also

• Nyquist-Shannon sampling theorem
• Aliasing, Anti-aliasing, Anti-aliasing filter
• Downsampling, Upsampling
• Sampling frequency
• Undersampling