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The Nyquist stability criterion is widely used in electronics and control system engineering, as well as other fields, for designing and analyzing systems with feedback. While Nyquist is one of the most general stability tests, it is still restricted to linear time-invariant (LTI) systems.
In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel (including responses of transmit and receive filters), result in no intersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference.
Nyquist criterion may refer to: Nyquist stability criterion, a graphical technique for determining the stability of a feedback control system; Nyquist frequency, ½ of the sampling rate of a discrete signal processing system; Nyquist rate, a rate used in signal processing; Nyquist ISI criterion, a condition to avoid intersymbol interference
One of the possible reasons is to reduce the Nyquist rate for more efficient storage. And it turns out that one can directly achieve the same result by sampling the bandpass function at a sub-Nyquist sample-rate that is the smallest integer-sub-multiple of frequency A that meets the baseband Nyquist criterion: f s > 2B.
The Nyquist aliasing criteria is expressed graphically in the z-plane by the x-axis, where ωnT = π. The line of constant damping just described spirals in indefinitely but in sampled data systems, frequency content is aliased down to lower frequencies by integral multiples of the Nyquist frequency.
A number of stability criteria are in common use: Circle criterion; Jury stability criterion; Liénard–Chipart criterion; Nyquist stability criterion; Routh–Hurwitz stability criterion; Vakhitov–Kolokolov stability criterion; Barkhausen stability criterion; Stability may also be determined by means of root locus analysis.
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But if the Nyquist criterion is not satisfied, adjacent copies overlap, and it is not possible in general to discern an unambiguous (). Any frequency component above / is indistinguishable from a lower-frequency component, called an alias, associated with one of the copies. In such cases, the customary interpolation techniques produce the alias ...