Pole–zero_plot
Pole–zero plot
Diagram showing the singularities of a given control system's transfer function
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 is plotted in the plane of a complex frequency domain, which can represent either a continuous-time or a discrete-time system:
- Continuous-time systems use the Laplace transform and are plotted in the s-plane:
- Real frequency components are along its vertical axis (the imaginary line where )
- Discrete-time systems use the Z-transform and are plotted in the z-plane:
- Real frequency components are along its unit circle