Oversampling

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In information theory, oversampling is the process of sampling a signal with a sampling frequency higher than the nyquist frequency. A signal that is oversampled is said to be oversampled β times where β is defined as

$\beta = \frac{f_{sampling}}{2 B}$ or

f s a m p l i n g = 2β B

where

$f s a m p l i n g$ is the sampling frequency
$B$ is the bandwidth of the signal

There are three main reasons for performing oversampling:

It aids in anti-aliasing because 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 can be made cheaper by relaxing the requirements of the filter at the cost of a faster sampler. Once sampled, the signal is digitally filtered and then downsampled to the desired sampling frequency. Digital filtering is much easier to implement (and, generally speaking, can be changed at will) and the only cost for a better filter is extra CPU time.
It is a cheaper way of achieving 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 16 times the target sampling rate. Averaging a group of 16 consecutive 20-bit samples adds 4 bits to the resolution of the average, producing a single sample with 24-bit resolution.
Certain kinds of A/D converters produce disproportionately more noise in the upper parts of their frequency response. By running these converters at some multiple of the target sampling rate, and then low-pass-filtering the results down to the right sampling rate, it is possible to obtain a result with less noise than the average over the entire band of the converter. This technique is called noise shaping.

Example

For example, take a signal with a bandwidth of 100 Hz. The sampling theorem states that sampling frequency would then have to be greater than 200 Hz. Sampling at 200 Hz would result in $β = 1$ . Sampling at four times over ( $β = 4$ ) would result in a sampling rate of 800 Hz. This gives the anti-aliasing filter a transition band of 600 Hz ( $f s a m p l i n g - 2 B = 800 - 2 * 100 = 600$ ) instead of 0 Hz if the sampling frequency were at 200 Hz.

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 100 Hz and then further downsampled to closer to 200 Hz.

Oversampling

Example

See also