Editing Even and odd functions (section)

==Harmonics==
In [[signal processing]], [[harmonic distortion]] occurs when a [[sine wave]] signal is sent through a memory-less [[nonlinear system]], that is, a system whose output at time ''t'' only depends on the input at time ''t'' and does not depend on the input at any previous times. Such a system is described by a response function <math>V_\text{out}(t) = f(V_\text{in}(t))</math>. The type of [[harmonic]]s produced depend on the response function ''f'':<ref>{{Cite web|url=http://www.uaudio.com/webzine/2005/october/content/content2.html|title=Ask the Doctors: Tube vs. Solid-State Harmonics|last=Berners|first=Dave|date=October 2005|website=UA WebZine|publisher=Universal Audio|access-date=2016-09-22|quote=To summarize, if the function f(x) is odd, a cosine input will produce no even harmonics. If the function f(x) is even, a cosine input will produce no odd harmonics (but may contain a DC component). If the function is neither odd nor even, all harmonics may be present in the output.}}</ref>
* When the response function is even, the resulting signal will consist of only even harmonics of the input sine wave; <math>0f, 2f, 4f, 6f, \dots </math>
** The [[fundamental frequency|fundamental]] is also an odd harmonic, so will not be present.
** A simple example is a [[full-wave rectifier]].
** The <math>0f</math> component represents the DC offset, due to the one-sided nature of even-symmetric transfer functions.
* When it is odd, the resulting signal will consist of only odd harmonics of the input sine wave; <math>1f, 3f, 5f, \dots </math>
** The output signal will be half-wave [[symmetric]].
** A simple example is [[clipping (audio)|clipping]] in a symmetric [[Electronic amplifier|push-pull amplifier]].
* When it is asymmetric, the resulting signal may contain either even or odd harmonics; <math>1f, 2f, 3f, \dots </math>
** Simple examples are a half-wave rectifier, and clipping in an asymmetrical [[class-A amplifier]].

This does not hold true for more complex waveforms.  A [[sawtooth wave]] contains both even and odd harmonics, for instance.  After even-symmetric full-wave rectification, it becomes a [[triangle wave]], which, other than the DC offset, contains only odd harmonics.