Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?
Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur Graph Search.
Concept
Pole–zero plot
Résumé
In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as:
Stability
Causal system / anticausal system
Region of convergence (ROC)
Minimum phase / non minimum phase
A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system, such as a controller, compensator, sensor, equalizer, filter, or communications channel. By convention, the poles of the system are indicated in the plot by an X while the zeros are indicated by a circle or O.
A pole-zero plot can represent either a continuous-time (CT) or a discrete-time (DT) system. For a CT system, the plane in which the poles and zeros appear is the s plane of the Laplace transform. In this context, the parameter s represents the complex angular frequency, which is the domain of the CT transfer function. For a DT system, the plane is the z plane, where z represents the domain of the Z-transform.
In general, a rational transfer function for a continuous-time LTI system has the form:
where
and are polynomials in ,
is the order of the numerator polynomial,
is the m-th coefficient of the numerator polynomial,
is the order of the denominator polynomial, and
is the n-th coefficient of the denominator polynomial.
Either M or N or both may be zero, but in real systems, it should be the case that ; otherwise the gain would be unbounded at high frequencies.
the zeros of the system are roots of the numerator polynomial: such that
the poles of the system are roots of the denominator polynomial: such that
The region of convergence (ROC) for a given CT transfer function is a half-plane or vertical strip, either of which contains no poles. In general, the ROC is not unique, and the particular ROC in any given case depends on whether the system is causal or anti-causal.
If the ROC includes the imaginary axis, then the system is bounded-input, bounded-output (BIBO) stable.
Source officielle
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.