Hypothetical spectrum of a inadequately sampled bandlimited signal where the images overlap showing how aliases are created.
X(f) (blue) and XA(f) (blue) are continuous Fourier transforms of two different functions, x(t) and xA(t) (not shown). When the functions are sampled at rate fs, 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 xA(t) would not sound the same. But their samples (taken at rate fs) would lead to identical reproduced sounds; thus xA(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 fs 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 PNG 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.
Ta grafika (graph) (lub wszystkie grafiki w tym artykule bądź kategorii) powinny zostać przetworzone na grafiki wektorowe jako plik SVG. O zaletach grafik wektorowych można przeczytać na stronie Commons:Media for cleanup. Jeśli wersja SVG tej grafiki jest już dostępna, załaduj ją. Po załadowaniu SVG zamień ten szablon na stronie tej grafiki na szablon {{vector version available|nazwa nowej grafiki.svg}}.
Licencja
Public domainPublic domainfalsefalse
Ja, właściciel praw autorskich do tej pracy, udostępniam ją jako własność publiczną. Dotyczy to całego świata. W niektórych krajach może nie być to prawnie możliwe, jeśli tak, to: Zapewniam każdemu prawo do użycia tej pracy w dowolnym celu, bez żadnych ograniczeń, chyba że te ograniczenia są wymagane przez prawo.
Podpisy
Dodaj jednolinijkowe objaśnienie tego, co ten plik pokazuje
Hypothetical spectrum of a inadequately sampled bandlimited signal where the images overlap showing how aliases are created. Created by Robert Bristow-Johnson for use in Wikimedia Commons. No Rights Reserved.