This representation gives a good picture of what happens around the Nyquist frequency when filtering with the low-pass filter is done.
12.
In discrete-time applications, one only examines the region of frequencies between 0 and the Nyquist frequency, because of periodicity and symmetry.
13.
In applications where the sample-rate is pre-determined, the filter is chosen based on the Nyquist frequency, rather than vice versa.
14.
Often, this is done by adding analog anti-aliasing filters at the input and output, thus avoiding any frequency component above the Nyquist frequency.
15.
Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process.
16.
Depending on the frequency units, the Nyquist frequency may be 0.5, 1.0, ?, or ?of the actual sample-rate.
17.
Note that aliasing will occur, including aliasing below the Nyquist frequency to the extent that the continuous-time filter's response is nonzero above that frequency.
18.
The normalized Nyquist frequency is ? " radians / sample ", and the normalized sample-rate is 2? " radians / sample ".
19.
When the function domain is time, sample rates are usually expressed in samples / second, and the unit of Nyquist frequency is cycles / second ( hertz ).
20.
Ideally, both filters should be brickwall filters, constant phase delay in the pass-band with constant flat frequency response, and zero response from the Nyquist frequency.
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