Editing Aliasing (section)

== More examples ==

=== Audio example ===
{{Listen|filename=Sawtooth-aliasingdemo.ogg|title=Sawtooth aliasing demo|description=440&nbsp;Hz bandlimited, 440&nbsp;Hz aliased, 880&nbsp;Hz bandlimited, 880&nbsp;Hz aliased, 1760&nbsp;Hz bandlimited, 1760&nbsp;Hz aliased|format=[[Ogg]]}}
The qualitative effects of aliasing can be heard in the following audio demonstration. Six [[sawtooth wave]]s are played in succession, with the first two sawtooths having a [[fundamental frequency]] of 440 Hz (A4), the second two having fundamental frequency of 880 Hz (A5), and the final two at 1760&nbsp;Hz (A6). The sawtooths alternate between [[bandlimited]] (non-aliased) sawtooths and aliased sawtooths and the sampling rate is 22050 Hz. The bandlimited sawtooths are synthesized from the sawtooth waveform's [[Fourier series]] such that no harmonics above the [[Nyquist frequency]] (11025 Hz = 22050 Hz / 2 here) are present.

The aliasing distortion in the lower frequencies is increasingly obvious with higher fundamental frequencies, and while the bandlimited sawtooth is still clear at 1760 Hz, the aliased sawtooth is degraded and harsh with a buzzing audible at frequencies lower than the fundamental.

=== Direction finding ===
A form of spatial aliasing can also occur in antenna arrays or microphone arrays used to estimate the direction of arrival of a wave signal, as in geophysical exploration by seismic waves. Waves must be sampled more densely than two points per [[wavelength]], or the wave arrival direction becomes ambiguous.<ref name=flangan/>