Nyquist frequency signal, whereas "Nyquist frequency" is a property of a discrete-time system. When the function domain is time, sample rates are usually expressed in samples per second, and the unit of Nyquist frequency is cycles per second (hertz). When the function domain is distance, as in an image sampling system, the sample rate might be dots per inch and the corresponding Nyquist frequency would be in cycles/inch. Referring again to Figure 1, undersampling of the sinusoid at 0.6 f is what allows there to be a lower-frequency "alias", which is a different function that produces the same set of samples. That
Parity of a permutation of formula_1 into disjoint cycles, which can be composed in any order because they commute. A cycle formula_49 involving formula_50 points can always be obtained by composing formula_51 transpositions (2-cycles): so call formula_51 the "size" of the cycle, and observe that, under this definition, transpositions are cycles of size 1. From a decomposition into formula_54 disjoint cycles we can obtain a decomposition of formula_1 into formula_56 transpositions, where formula_57 is the size of the th cycle. The number formula_58 is called the discriminant of formula_1, and can also be computed as if we take care to include the fixed points