The Nyquist criterion is a fundamental principle in signal processing and control theory that determines the stability of a system by analyzing the frequency response. It states that for a system to be stable, the Nyquist plot of its open-loop transfer function must not encircle the critical point (-1,0) in the complex plane when the plot is traced as the frequency varies from zero to infinity.

Nyquist Criterion

Nyquist criterion

fundamental principle

Signal processing involves the analysis, manipulation, and synthesis of signals such as sound, images, and scientific measurements to improve transmission, storage, and quality. It is fundamental in various applications, including telecommunications, audio engineering, and biomedical engineering, where it enhances signal clarity and extracts useful information.

signal processing

Control theory is a field of study that focuses on the behavior of dynamical systems and the use of feedback to modify the behavior of these systems to achieve desired outcomes. It is widely applied in engineering and science to design systems that maintain stability and performance despite external disturbances and uncertainties.

control theory

stability of a system

Frequency response describes how a system or device reacts to different frequencies of input signals, crucial for understanding its behavior across the spectrum. It is essential in fields like audio engineering, telecommunications, and control systems to ensure optimal performance and fidelity.

frequency response

A Nyquist Plot is a graphical representation used in control systems and signal processing to analyze the stability of a system by plotting the complex frequency response. It provides insights into the system's gain margin and phase margin, which are crucial for assessing stability and performance in the frequency domain.

Nyquist plot

open-loop transfer function

In mathematics, a critical point of a function is where its derivative is zero or undefined, indicating potential local maxima, minima, or saddle points. In thermodynamics, a critical point refers to the end point of a phase equilibrium curve, beyond which distinct liquid and gas phases do not exist, marking the critical temperature and pressure of a substance.

critical point

The complex plane is a two-dimensional plane used to represent complex numbers, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. This visualization allows for a geometric interpretation of complex number operations, such as addition, multiplication, and finding magnitudes and angles.

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