Lesson plan
Pole–zero plot
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 maps the z-plane to the s-plane. The unstable regions for the poles of a linear control system are shaded. 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: s = \sigma + j \omega ** Real frequency components are along its vertical axis (the imaginary line s {=} j \omega where \sigma{=}0 ) * Discrete-time systems use the Z-transform and are plotted in the z-plane: z = A e^{j\phi} ** Real frequency components are along its unit circle
Article summary
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 maps the z-plane to the s-plane. The unstable regions for the poles of a linear control system are shaded. 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: s = \sigma + j \omega ** Real frequency components are along its vertical axis (the imaginary line s {=} j \omega where \sigma{=}0 ) * Discrete-time systems use the Z-transform and are plotted in the z-plane: z = A e^{j\phi} ** Real frequency components are along its unit circle
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.