Editing Sampling (signal processing) (section)

== Practical considerations==
In practice, the continuous signal is sampled using an [[analog-to-digital converter]] (ADC), a device with various physical limitations. This results in deviations from the theoretically perfect reconstruction, collectively referred to as [[distortion]].

Various types of distortion can occur, including:
* [[Aliasing]]. Some amount of aliasing is inevitable because only theoretical, infinitely long, functions can have no frequency content above the Nyquist frequency. Aliasing can be made [[arbitrarily small]] by using a [[sufficiently large]] order of the anti-aliasing filter.
* [[Analog-to-digital converter#Jitter|Aperture error]] results from the fact that the sample is obtained as a time average within a sampling region, rather than just being equal to the signal value at the sampling instant.<ref>H.O. Johansson and C. Svensson, "Time resolution of NMOS sampling switches", IEEE J. Solid-State Circuits Volume: 33, Issue: 2, pp. 237–245, Feb 1998.</ref> In a [[capacitor]]-based [[sample and hold]] circuit, aperture errors are introduced by multiple mechanisms. For example, the capacitor cannot instantly track the input signal and the capacitor can not instantly be isolated from the input signal.
* [[Jitter]] or deviation from the precise sample timing intervals.
* [[Noise (physics)|Noise]], including thermal sensor noise, [[analog circuit]] noise, etc..
* [[Slew rate]] limit error, caused by the inability of the ADC input value to change sufficiently rapidly.
* [[Quantization (signal processing)|Quantization]] as a consequence of the finite precision of words that represent the converted values.
* Error due to other [[non-linear]] effects of the mapping of input voltage to converted output value (in addition to the effects of quantization).

Although the use of [[oversampling]] can completely eliminate aperture error and aliasing by shifting them out of the passband, this technique cannot be practically used above a few GHz, and may be prohibitively expensive at much lower frequencies. Furthermore, while oversampling can reduce quantization error and non-linearity, it cannot eliminate these entirely. Consequently, practical ADCs at audio frequencies typically do not exhibit aliasing, aperture error, and are not limited by quantization error. Instead, analog noise dominates. At RF and microwave frequencies where oversampling is impractical and filters are expensive, aperture error, quantization error and aliasing can be significant limitations.

Jitter, noise, and quantization are often analyzed by modeling them as random errors added to the sample values. Integration and zero-order hold effects can be analyzed as a form of [[low-pass filter]]ing. The non-linearities of either ADC or DAC are analyzed by replacing the ideal [[linear function]] mapping with a proposed [[Nonlinear system|nonlinear function]].