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Oversampling
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A signal that is oversampled is said to be oversampled β times where β is defined as

: \beta \equiv rac{f_s}{2 B} \
or
: f_s = 2 \beta B \

where

There are three main reasons for performing oversampling:

  • It aids in Anti-aliasing because realizable analog Anti-aliasing Filter s 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 is 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 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. Note that this averaging is possible only if the Signal contains perfect equally distributed Noise (e.g. 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).

  • Certain kinds of A/D converters known as Delta-sigma Converter s produce disproportionately more Quantization 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. Delta-sigma converters use a technique called Noise Shaping to move the quantization noise to the higher frequencies.



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 \beta = 1.
Sampling at four times over (\beta = 4) would result in a sampling rate of 800 Hz.
This gives the anti-aliasing filter a Transition Band of 600 Hz (f_s - 2 B = 800 - 2 \cdot 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.


REFERENCE

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



SEE ALSO