Oversampling

Encyclopedia

In signal processing

,

a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled. Oversampling helps avoid aliasing

, improves resolution and reduces noise

.

or

where:

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 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.

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.

Number of samples required to get bits of additional data:

The result in software from samples is then divided by 2

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 added to each sample, then averaging

by a factor of 1/

in terms of power improves by factor of 4 which corresponds to factor of 2 improvement in terms of voltage.

Certain kinds of A/D converters known as delta-sigma converter

s 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 filter

ing the oversampled down to half the target sampling rate, it is possible to obtain a result with

to move the quantization noise to the higher frequencies.

.

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 (β = 4) would result in a sampling rate of 800 Hz.

This gives the anti-aliasing filter a transition band

of 600 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 less expensive due to relaxation of the transition band requirements.

After being sampled at 800 Hz, the signal (ostensibly with a bandwidth of 400 Hz) could be digitally filtered to have a bandwidth of 100 Hz and then further downsampled

to closer to 200 Hz.

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

,

**oversampling**is the process of samplingSampling (signal processing)

In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....

a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled. Oversampling helps avoid aliasing

Aliasing

In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

, improves resolution and reduces noise

Noise

In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...

.

## Oversampling factor

An oversampled signal is said to be oversampled by a factor of β, defined asor

- .

where:

*f*is the sampling frequency_{s}*B*is the bandwidth or highest frequency of the signal; the Nyquist rateNyquist rateIn signal processing, the Nyquist rate, named after Harry Nyquist, is two times the bandwidth of a bandlimited signal or a bandlimited channel...

is 2*B*.

### Anti-aliasing

It aids in anti-aliasingAnti-aliasing

In digital signal processing, spatial anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution image at a lower resolution...

because realizable analog anti-aliasing filter

Anti-aliasing filter

An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem....

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 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

Downsampling

In signal processing, downsampling is the process of reducing the sampling rate of a signal. This is usually done to reduce the data rate or the size of the data....

to the desired sampling frequency. In modern integrated circuit

Integrated circuit

An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

technology, digital filters are much easier to implement than comparable analog filters of high order.

### Resolution

In practice, oversampling is implemented in order to achieve cheaper higher-resolution A/DAnalog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

and D/A

Digital-to-analog converter

In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...

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.

Number of samples required to get bits of additional data:

The result in software from samples is then divided by 2

^{n}:Note that this averaging is possible only if the signal contains perfect equally distributed noise

Noise

In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical 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

If multiple samples are taken of the same quantity with uncorrelatedUncorrelated

In probability theory and statistics, two real-valued random variables are said to be uncorrelated if their covariance is zero. Uncorrelatedness is by definition pairwise; i.e...

noise added to each sample, then averaging

*N*samples reduces the noise powerNoise power

In telecommunication, the term noise power has the following meanings:# The measured total noise per bandwidth unit at the input or output of a device when the signal is not present.# The power generated by a random electromagnetic process....

by a factor of 1/

*N*. If, for example, we oversample by a factor of 4, the signal-to-noise ratioSignal-to-noise ratio

Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...

in terms of power improves by factor of 4 which corresponds to factor of 2 improvement in terms of voltage.

Certain kinds of A/D converters known as delta-sigma converter

Delta-sigma modulation

Delta-sigma modulation is a method for encoding high-resolution or analog signals into lower-resolution digital signals. The conversion is done using error feedback, where the difference between the two signals is measured and used to improve the conversion...

s produce disproportionately more quantization

Quantization (signal processing)

Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

noise in the upper portion of their output spectrum. By running these converters at some multiple of the target sampling rate, and low-pass filter

Low-pass filter

A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

ing 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 shapingNoise shaping

Noise shaping is a technique typically used in digital audio, image, and video processing, usually in combination with dithering, as part of the process of quantization or bit-depth reduction of a digital signal...

to move the quantization noise to the higher frequencies.

## Example

For example, consider a signal with a bandwidth or highest frequency of*B*= 100 HzHertz

The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

.

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 (β = 4) would result in a sampling rate of 800 Hz.

This gives the anti-aliasing filter a transition band

Transition band

The transition band 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 corner frequency....

of 600 Hz ((

*f*−_{s}*B*) −*B*= (800 Hz−100 Hz) − 100 Hz = 600 Hz) instead of 0 Hz if the sampling frequency was virtually 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 less expensive due to relaxation of the transition band requirements.

After being sampled at 800 Hz, the signal (ostensibly with a bandwidth of 400 Hz) could be digitally filtered to have a bandwidth of 100 Hz and then further downsampled

Downsampling

In signal processing, downsampling is the process of reducing the sampling rate of a signal. This is usually done to reduce the data rate or the size of the data....

to closer to 200 Hz.

## See also

- Nyquist-Shannon sampling theorem
- DownsamplingDownsamplingIn signal processing, downsampling is the process of reducing the sampling rate of a signal. This is usually done to reduce the data rate or the size of the data....

, UpsamplingUpsamplingUpsampling is the process of increasing the sampling rate of a signal. For instance, upsampling raster images such as photographs means increasing the resolution of the image.... - Sampling frequency
- UndersamplingUndersamplingIn signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate below the usual Nyquist rate In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate...
- Oversampling and undersampling in data analysisOversampling and undersampling in data analysisOversampling and undersampling in data analysis are techniques used to adjust the class distribution of a data set ....