Insignal processing,oversampling is the process ofsampling a signal at a sampling frequency significantly higher than theNyquist rate. Theoretically, a bandwidth-limited signal can be perfectly reconstructed if sampled at the Nyquist rate or above it. The Nyquist rate is defined as twice thebandwidth of the signal. Oversampling is capable of improvingresolution andsignal-to-noise ratio, and can be helpful in avoidingaliasing andphase distortion by relaxinganti-aliasing filter performance requirements.

A signal is said to be oversampled by a factor ofN if it is sampled atN times the Nyquist rate.

There are three main reasons for performing oversampling: to improve anti-aliasing performance, to increase resolution and to reduce noise.

Oversampling can make it easier to realize analoganti-aliasing filters.^[1][2] Without oversampling, it is very difficult to implement filters with the sharp cutoff necessary to maximize use of the available bandwidth without exceeding theNyquist limit. By increasing the bandwidth of the sampling system, design constraints for the anti-aliasing filter may be relaxed.^[3] Once sampled, the signal can bedigitally filtered anddownsampled to the desired sampling frequency. In modernintegrated circuit technology, the digital filter associated with this downsampling is easier to implement than a comparableanalog filter required by a non-oversampled system.

In practice, oversampling is implemented in order to reduce cost and improve performance of ananalog-to-digital converter (ADC) ordigital-to-analog converter (DAC).^[1] When oversampling by a factor of N, the signal-to-noise ratio (SNR) increases by${\displaystyle \sqrt{N}}$, because summing up uncorrelated noise increases its amplitude by${\displaystyle \sqrt{N}}$, while summing up a coherent signal increases its average by N.

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. Combining 256 consecutive 20-bit samples can increase the SNR by a factor of 16, effectively adding 4 bits to the resolution and producing a single sample with 24-bit resolution.^[4][a]

The number of samples required to get${\displaystyle n}$ bits of additional data precision is

${\displaystyle \text{number of samples}=(2^n{)}^2=2^{2n}.}$

To get the mean sample scaled up to an integer with${\displaystyle n}$ additional bits, the sum of${\displaystyle 2^{2n}}$ samples is divided by${\displaystyle 2^n}$:

${\displaystyle \text{scaled mean}=\frac{\sum _{i=0}^{2^{2n}-1}{2}^n{\text{data}}_i}{2^{2n}}=\frac{\sum _{i=0}^{2^{2n}-1}{\text{data}}_i}{2^n}.}$

This averaging is only effective if thesignal contains sufficientuncorrelated noise to be recorded by the ADC.^[4] If not, in the case of a stationary input signal, all${\displaystyle 2^n}$ samples would have the same value and the resulting average would be identical to this value; so in this case, oversampling would have made no improvement. In similar cases where the ADC records no noise and the input signal is changing over time, oversampling improves the result, but to an inconsistent and unpredictable extent.

Adding somedithering noise to the input signal can actually improve the final result because the dither noise allows oversampling to work to improve resolution. In many practical applications, a small increase in noise is well worth a substantial increase in measurement resolution. In practice, the dithering noise can often be placed outside the frequency range of interest to the measurement, so that this noise can be subsequently filtered out in the digital domain—resulting in a final measurement, in the frequency range of interest, with both higher resolution and lower noise.^[5]

If multiple samples are taken of the same quantity with uncorrelated noise^[b] added to each sample, then because, as discussed above, uncorrelated signals combine more weakly than correlated ones, averagingN samples reduces thenoise power by a factor ofN. If, for example, we oversample by a factor of 4, the signal-to-noise ratio in terms of power improves by a factor of four, which corresponds to a factor of two improvement in terms of voltage.

Certain kinds of ADCs known asdelta-sigma converters produce disproportionately morequantization noise at higher frequencies. By running these converters at some multiple of the target sampling rate, andlow-pass filtering the oversampled signal down to half the target sampling rate, a final result withless noise (over the entire band of the converter) can be obtained. Delta-sigma converters use a technique callednoise shaping to move the quantization noise to the higher frequencies.

Consider a signal with a bandwidth or highest frequency ofB = 100 Hz. Thesampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at four times that rate requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter atransition band of 300 Hz ((f_s/2) −B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz. Achieving an anti-aliasing filter with 0 Hz transition band is unrealistic, whereas an anti-aliasing filter with a transition band of 300 Hz is not difficult.

The term oversampling is also used to denote a process used in the reconstruction phase of digital-to-analog conversion, in which an intermediate high sampling rate is used between the digital input and the analog output. Here, digital interpolation is used to add additional samples between recorded samples, thereby converting the data to a higher sample rate, a form ofupsampling. When the resulting higher-rate samples are converted to analog, a less complex and less expensive analogreconstruction filter is required. Essentially, this is a way to shift some of the complexity of reconstruction from analog to the digital domain. Oversampling in the ADC can achieve some of the same benefits as using a higher sample rate at the DAC.

• Oversampled binary image sensor
• Sample abundance
• Supersampling
• Undersampling

• John Watkinson (1994).The Art of Digital Audio. Focal Press.ISBN 0-240-51320-7.
• Dr. Richard C. CabotPerformance Aspects of Digital Oversampling^[1]

• Digital signal processing
• Information theory

• Articles with short description
• Short description is different from Wikidata
• Use American English from March 2019
• All Wikipedia articles written in American English
• Pages with reference errors
• Pages with broken reference names