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| Keywords: AliasedSpectrum.png Hypothetical spectrum of a inadequately sampled bandlimited signal where the images overlap showing how aliases are created X f blue and X<sub>A</sub> f blue are continuous Fourier transforms of two <u>different</u> functions x t and x<sub>A</sub> t not shown When the functions are sampled at rate f<sub>s</sub> 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 <u>the sampled sequences are identical</u> even though the original functions are not If these were audio signals x t and x<sub>A</sub> t would not sound the same But their samples taken at rate f<sub>s</sub> would lead to identical reproduced sounds; thus x<sub>A</sub> 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<sub>s</sub> 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 source code please graph Aliasing Nyquist Shannon theorem | ||||
