Summary

Hypothetical spectrum of a inadequately sampled bandlimited signal where the images overlap showing how aliases are created. X(f) (blue) and X_A(f) (blue) are continuous Fourier transforms of two different functions, x(t) and x_A(t) (not shown). When the functions are sampled at rate f_s, the images (green) are added to the original transforms (blue) when one examines the discrete-time Fourier transforms (DTFT) of the sequences. In this hypothetical example, the DTFTs are identical, which means the sampled sequences are identical, even though the original functions are not. If these were audio signals, x(t) and x_A(t) would not sound the same. But their samples (taken at rate f_s) would lead to identical reproduced sounds; thus x_A(t) is an alias of x(t) at this sample rate. In this example (of a bandlimited function), such aliasing can be prevented by increasing f_s such that the green images in the top figure do not overlap the blue portion. Created by Robert Bristow-Johnson for use in Wikimedia Commons. No Rights Reserved.

This image is an information graphic created by a computer program from data sets or formulas that have not been fully provided on this page. In order to allow other editors to improve or build such images, and to ensure compliance with free content licenses such as the GFDL, the following should be provided: Software package(s) used Data sets used (if any), including pre-processing instructions Sequence of commands used to create the graphic Short description of any post-processing stages Once all the above are included in the image's description page(s), please remove this template.

Deutsch ∙ English ∙ français ∙ magyar ∙ Nederlands ∙ Plattdüütsch ∙ suomi ∙ македонски ∙ русский ∙ 日本語 ∙ 中文 ∙ 中文（简体）‎ ∙ +/−

This graph image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file “AliasedSpectrum.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Licensing

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.