Editing Nyquist frequency (section)

== Folding frequency ==
{{main|Aliasing}}
[[File:Aliasing-folding-2.svg|thumb|400px|The black dots are aliases of each other. The solid red line is an <u>example</u> of amplitude varying with frequency. The dashed red lines are the corresponding paths of the aliases.]]

In this example, {{math|''f''{{sub|s}}}} is the sampling rate, and {{math|0.5 ''cycle/sample'' × ''f''{{sub|s}}}} is the corresponding Nyquist frequency. The black dot plotted at {{math|0.6 ''f''{{sub|s}}}} represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that would produce the same set of samples as the actual sinusoid that was sampled.  Undersampling of the sinusoid at {{math|0.6 ''f''{{sub|s}}}} is what allows there to be a lower-frequency [[Aliasing#Sampling sinusoidal functions|alias]].  If the true frequency were {{math|0.4 ''f''{{sub|s}}}}, there would still be aliases at 0.6, 1.4, 1.6, etc.

The red lines depict the paths ([[wikt:loci|loci]]) of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between &nbsp;{{math|''f''{{sub|s}}/2}}&nbsp; and &nbsp;{{math|''f''{{sub|s}}}}).&nbsp; No matter what function we choose to change the amplitude vs frequency, the graph will exhibit symmetry between 0 and &nbsp;{{math|''f''{{sub|s}}.}}&nbsp;  This symmetry is commonly referred to as '''folding''', and another name for &nbsp;{{math|''f''{{sub|s}}/2}}&nbsp; (the Nyquist frequency) is '''folding frequency'''.<ref name=Zawistowski/>