Editing Distortion (section)

==Electronic signals==
In [[telecommunications]] and [[signal processing]], a noise-free [[system]] can be characterised by a [[transfer function]], such that the output <math>y(t)</math> can be written as a function of the input <math>x</math> as

: <math>y(t) = F(x(t))</math>

When the transfer function comprises only a perfect [[gain (electronics)|gain]] constant ''A'' and perfect [[propagation delay|delay]] ''T''

: <math>y(t) = A\cdot x(t-T)</math>

the output is undistorted. Distortion occurs when the transfer function ''F'' is more complicated than this. If ''F'' is a [[linear function]], for instance a filter whose gain and/or delay varies with frequency, the signal suffers linear distortion. Linear distortion does not introduce new frequency components to a signal but does alter the balance of existing ones.

[[File:Distorted waveforms square sine.svg|353px|thumb|right|Graph of a waveform and some distorted versions of the same waveform]]

This diagram shows the behaviour of a signal (made up of a [[Square wave (waveform)|square wave]] followed by a [[sine wave]]) as it is passed through various distorting functions.

# The first trace (in black) shows the input.  It also shows the output from a non-distorting transfer function (straight line).
# A [[high-pass filter]] (green trace) distorts the shape of a square wave by reducing its low frequency components.  This is the cause of the "droop" seen on the top of the pulses. This "pulse distortion" can be very significant when a train of pulses must pass through an AC-coupled (high-pass filtered) amplifier. As the sine wave contains only one frequency, its shape is unaltered.
# A [[low-pass filter]] (blue trace) rounds the pulses by removing the high frequency components. All systems are low pass to some extent. Note that the [[Phase (waves)|phase]] of the sine wave is different for the lowpass and the highpass cases, due to the phase distortion of the filters.
# A slightly [[non-linear]] transfer function (purple), this one gently compresses the peaks of the sine wave, as may be typical of a [[tube audio amplifier]]. This generates small amounts of low order harmonics.
# A hard-[[Clipping (audio)|clipping]] transfer function (red) generates high order harmonics. Parts of the transfer function are flat, which indicates that all information about the input signal has been lost in this region.

The transfer function of an ideal amplifier, with perfect gain and delay, is only an approximation. The true behavior of the system is usually different. [[Nonlinearity|Nonlinearities]] in the transfer function of an [[active device]] (such as [[vacuum tube]]s, [[transistor]]s, and [[operational amplifier]]s) are a common source of non-linear distortion; in passive [[electronic component|components]] (such as a [[coaxial cable]] or [[optical fiber]]), linear distortion can be caused by inhomogeneities, [[Reflection (electrical)|reflections]], and so on in the [[wave propagation|propagation]] path.

===Amplitude distortion===
{{Main|Amplitude distortion}}
{{See also|Clipping (signal processing)}}
Amplitude distortion is distortion occurring in a system, subsystem, or device when the output amplitude is not a linear function of the input amplitude under specified conditions.

===Harmonic distortion===
Harmonic distortion adds [[overtone]]s that are [[Integer|whole number]] multiples of a sound wave's frequencies.<ref>{{Cite book
  | last = Moscal
  | first = Tony
  | title = Sound Check: The Basics of Sound and Sound Systems
  | publisher = Hal Leonard 
  | year = 1994
  | page = 55
  | url = https://books.google.com/books?id=_omgNjqf7GAC&q=harmonic+distortion+whole+integer&pg=PA55
  | isbn = 9780793535590}}</ref> Nonlinearities that give rise to amplitude distortion in audio systems are most often measured in terms of the [[harmonic]]s (overtones) added to a pure [[sinewave]] fed to the system. Harmonic distortion may be expressed in terms of the relative strength of individual components, in [[decibel]]s, or the [[root mean square]] of all harmonic components: [[Total harmonic distortion]] (THD), as a percentage. The level at which harmonic distortion becomes  audible depends on the exact nature of the distortion.  Different types of distortion (like [[crossover distortion]]) are more audible than others (like [[soft clipping]]) even if the THD measurements are identical.  Harmonic distortion in [[radio frequency]] applications is rarely expressed as THD.

===Frequency response distortion===
{{See also|Frequency response}}
Non-flat frequency response is a form of distortion that occurs when different frequencies are amplified by different amounts in a [[Filter (signal processing)|filter]]. For example, the non-uniform frequency response curve of AC-coupled [[cascade amplifier]] is an example of frequency distortion. In the audio case, this is mainly caused by room acoustics, poor loudspeakers and microphones, long loudspeaker cables in combination with frequency dependent loudspeaker [[Electrical impedance|impedance]], etc.

===Phase distortion===
{{Main|Phase distortion}}
This form of distortion mostly occurs due to [[electrical reactance]]. Here, all the components of the input signal are not amplified with the same phase shift, hence making some parts of the output signal out of phase with the rest of the output.

===Group delay distortion===
Can be found only in [[dispersion (optics)|dispersive media]]. In a [[waveguide]], [[phase velocity]] varies with frequency. In a filter, group delay tends to peak near the [[cut-off frequency]], resulting in pulse distortion.  When analog long distance trunks were commonplace, for example in [[12 channel carrier]], group delay distortion had to be corrected in [[repeater]]s.