In

_{s}/2) âˆ’ ''B'' = (800 Hz/2) âˆ’ 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.

signal processing
Signal processing is an electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetis ...

, oversampling is the process of sampling
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
*Sample (graphics), Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a sound ...

a signal at a sampling frequency significantly higher than the Nyquist rate
In signal processing
Signal processing is an electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electr ...

. 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 the bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...

of the signal. Oversampling is capable of improving resolution
Resolution(s) may refer to:
Common meanings
* Resolution (debate), the statement which is debated in policy debate
* Resolution (law), a written motion adopted by a deliberative body
* New Year's resolution, a commitment that an individual make ...

and signal-to-noise ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and ...

, and can be helpful in avoiding aliasing
In signal processing
Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Sig ...

and phase distortion
In signal processing, phase distortion or phase-frequency distortion is distortion, that is, change in the shape of the waveform, that occurs when (a) a filter's phase response is not linear over the frequency range of interest, that is, the Pha ...

by relaxing anti-aliasing filter
An anti-aliasing filter (AAF) is a filter
Filter, filtering or filters may refer to:
Science and technology Device
* Filter (chemistry), a device which separates solids from fluids (liquids or gases) by adding a medium through which only the ...

performance requirements.
A signal is said to be oversampled by a factor of ''N'' if it is sampled at ''N'' times the Nyquist rate.
Motivation

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

Oversampling can make it easier to realize analoganti-aliasing filter
An anti-aliasing filter (AAF) is a filter
Filter, filtering or filters may refer to:
Science and technology Device
* Filter (chemistry), a device which separates solids from fluids (liquids or gases) by adding a medium through which only the ...

s. Without oversampling, it is very difficult to implement filters with the sharp cutoff necessary to maximize use of the available bandwidth without exceeding the Nyquist limit
In signal processing
Signal processing is an electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electr ...

. By increasing the bandwidth of the sampling system, design constraints for the anti-aliasing filter may be relaxed. Once sampled, the signal can be digitally filtered and downsampled to the desired sampling frequency. In modern integrated circuit
An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuit
200px, A circuit built on a printed circuit board (PCB).
An electronic circuit is composed of indiv ...

technology, the digital filter associated with this downsampling is easier to implement than a comparable analog filter required by a non-oversampled system.
Resolution

In practice, oversampling is implemented in order to reduce cost and improve performance of ananalog-to-digital converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a Digital signal (signal processing), digit ...

(ADC) or digital-to-analog converter
In electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons
The electron is a subatomic particle
In physical sciences, subatomic ...

(DAC). When oversampling by a factor of N, the dynamic range
Dynamic range (abbreviated DR, DNR, or DYR) is the ratio
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lem ...

also increases a factor of N because there are N times as many possible values for the sum. However, the signal-to-noise ratio (SNR) increases by $\backslash sqrt$, because summing up uncorrelated noise increases its amplitude by $\backslash sqrt$, while summing up a coherent signal increases its average by N. As a result, the SNR increases by $\backslash sqrt$.
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.
The number of samples required to get $n$ bits of additional data precision is
:$\backslash mbox\; =\; (2^n)^2\; =\; 2^.$
To get the mean sample scaled up to an integer with $n$ additional bits, the sum of $2^$ samples is divided by $2^n$:
:$\backslash mbox\; =\; \backslash frac\; =\; \backslash frac.$
This averaging is only effective if the signal
In signal processing
Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Sig ...

contains sufficient uncorrelated noise to be recorded by the ADC. If not, in the case of a stationary input signal, all $2^n$ 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 some dither
Dither is an intentionally applied form of noise
Noise is unwanted sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psyc ...

ing 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 domainâ€”resulting in a final measurement, in the frequency range of interest, with both higher resolution and lower noise.
Noise

If multiple samples are taken of the same quantity with uncorrelated noise added to each sample, then because, as discussed above, uncorrelated signals combine more weakly than correlated ones, averaging ''N'' samples reduces thenoise power In telecommunication
Telecommunication is the transmission of information by various types of technologies over wire
A wire is a single usually cylindrical
A cylinder (from Greek
Greek may refer to:
Greece
Anything of, from, or rela ...

by a factor of ''N''. If, for example, we oversample by a factor of 4, the signal-to-noise ratio in terms of power improves by factor of 4 which corresponds to a factor of 2 improvement in terms of voltage.
Certain kinds of ADCs known as delta-sigma converters produce disproportionately more quantization noise at higher frequencies. By running these converters at some multiple of the target sampling rate, and low-pass filter
A low-pass filter is a filter
Filter, filtering or filters may refer to:
Science and technology Device
* Filter (chemistry), a device which separates solids from fluids (liquids or gases) by adding a medium through which only the fluid can pass
...

ing the oversampled signal down to half the target sampling rate, a final result with ''less'' noise (over the entire band of the converter) can be obtained. Delta-sigma converters use a technique called noise shaping
Noise shaping is a technique typically used in digital audio
Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal processing), digital form. In digital audio, the sound wave of the audio signal is t ...

to move the quantization noise to the higher frequencies.
Example

Consider a signal with a bandwidth or highest frequency of ''B'' = 100 . Thesampling theorem
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
*Sample (graphics), Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a soun ...

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 a transition bandThe transition band, also called the skirt, is a range of frequencies that allows a transition between a passband and a stopband of a signal processing filter. The transition band is defined by a passband and a stopband cutoff frequency or corne ...

of 300 Hz ((''f''Reconstruction

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 analogue 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
In digital signal processing, upsampling, expansion, and interpolation are terms associated with the process of resampling in a multi-rate digital signal processing system. ''Upsampling'' can be synonymous with ''expansion'', or it can describe an ...

. When the resulting higher-rate samples are converted to analog, a less complex and less expensive analog reconstruction filter
Reconstruction may refer to:
Politics, history, and sociology
* Reconstruction (law), the transfer of a company's (or several companies') business to a new company
*''Perestroika
''Perestroika'' postage stamp, 1988
Perestroika (; russian: Ð ...

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.
See also

* Oversampled binary image sensor *Supersampling
Supersampling or supersampling anti-aliasing (SSAA) is a spatial anti-aliasing method, i.e. a method used to remove aliasing (jagged and pixelated edges, colloquially known as " jaggies") from images rendered in computer games
A PC game, also ...

*Undersampling
In signal processing
Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Signal ...

Notes

References

Further reading

* {{DSPDigital signal processingDigital signal processing (DSP) is the study of signal processing, signals in a Digital data, digital representation and the processing methods of these signals. DSP and analog signal processing are subsets of signal processing. It has three major su ...

Information theory