Editing Analog-to-digital converter (section)

===Sampling rate===
{{Main|Sampling rate}}

An analog signal is [[continuous function|continuous]] in [[time]] and it is necessary to convert this to a flow of digital values. It is therefore required to define the rate at which new digital values are sampled from the analog signal. The rate of new values is called the ''sampling rate'' or ''[[sampling frequency]]'' of the converter. A continuously varying bandlimited signal can be [[Sampling (signal processing)|sampled]] and then the original signal can be reproduced from the discrete-time values by a [[reconstruction filter]]. The Nyquist–Shannon sampling theorem implies that a faithful reproduction of the original signal is only possible if the sampling rate is higher than twice the highest frequency of the signal.

Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion (called the ''conversion time''). An input circuit called a [[sample and hold]] performs this task—in most cases by using a [[capacitor]] to store the analog voltage at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC [[integrated circuit]]s include the sample and hold subsystem internally.

====Aliasing====
{{Main|Aliasing}}
An ADC works by sampling the value of the input at discrete intervals in time. Provided that the input is sampled above the [[Nyquist rate]], defined as twice the highest frequency of interest, then all frequencies in the signal can be reconstructed. If frequencies above half the Nyquist rate are sampled, they are incorrectly detected as lower frequencies, a process referred to as aliasing. Aliasing occurs because instantaneously sampling a function at two or fewer times per cycle results in missed cycles, and therefore the appearance of an incorrectly lower frequency. For example, a 2&nbsp;kHz sine wave being sampled at 1.5&nbsp;kHz would be reconstructed as a 500&nbsp;Hz sine wave.

To avoid aliasing, the input to an ADC must be [[low-pass filter]]ed to remove frequencies above half the sampling rate. This filter is called an ''[[anti-aliasing filter]]'', and is essential for a practical ADC system that is applied to analog signals with higher frequency content. In applications where protection against aliasing is essential, oversampling may be used to greatly reduce or even eliminate it.

Although aliasing in most systems is unwanted, it can be exploited to provide simultaneous down-mixing of a band-limited high-frequency signal (see [[undersampling]] and [[frequency mixer]]). The alias is effectively the lower [[heterodyne]] of the signal frequency and sampling frequency.<ref>{{cite web|title=RF-Sampling and GSPS ADCs – Breakthrough ADCs Revolutionize Radio Architectures|url=http://www.ti.com/lit/sg/snwt001/snwt001.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.ti.com/lit/sg/snwt001/snwt001.pdf |archive-date=2022-10-09 |url-status=live|publisher=Texas Instruments|access-date=4 November 2013}}</ref>

====Oversampling====
{{Main|Oversampling}}
For economy, signals are often sampled at the minimum rate required with the result that the quantization error introduced is [[white noise]] spread over the whole [[passband]] of the converter. If a signal is sampled at a rate much higher than the [[Nyquist rate]] and then [[Digital filter|digitally filtered]] to limit it to the signal bandwidth produces the following advantages:
* Oversampling can make it easier to realize analog anti-aliasing filters
* Improved [[audio bit depth]]
* Reduced noise, especially when [[noise shaping]] is employed in addition to oversampling.

Oversampling is typically used in audio frequency ADCs where the required sampling rate (typically 44.1 or 48&nbsp;kHz) is very low compared to the clock speed of typical transistor circuits (>1&nbsp;MHz). In this case, the performance of the ADC can be greatly increased at little or no cost. Furthermore, as any aliased signals are also typically out of band, aliasing can often be eliminated using very low cost filters.