# 6.5 - 6.5 Digital Signal Processing Summary of the...

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103 6.5 Digital Signal Processing Summary of the practical consequences of the sampling theorem in frequency space Recall the general formula for calculating the frequency of an aliased signal that has been sampled at some rate less than f ny , the Nyquist frequency, obs s f ff = , and the graphical demonstration of the same: f (Hz) E 80 90 100 fj fny fs 180 f The following are important general principles of dealing with aliasing in discrete signals. Let the true frequency be denoted f, f obs is the observed frequency, f s is the sampling frequency, and f ny = f s /2 is the Nyquist frequency. 1. Frequencies f f ny are recovered correctly. 2. When f > f ny , the information does not disappear, it reappears as phantom peaks, contaminating the signal at f obs = f s f . 3. In any single realization, there is no way to distinguish phantoms from the real thing, unless you have some other information about likely values. 4. If the apparent signal is a phantom, then f obs will change when f s changes. Thus real and phantom peaks can be distinguished, if f s can be modified.

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6.5 - 6.5 Digital Signal Processing Summary of the...

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