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In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. [1] The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by ...
In electrical engineering and control theory, a Bode plot / ˈboʊdi / is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift . As originally conceived by Hendrik Wade Bode ...
These lead to a description of the system using terms like bandwidth, frequency response, eigenvalues, gain, resonant frequencies, zeros and poles, which give solutions for system response and design techniques for most systems of interest.
One can use the system response directly to determine how any particular frequency component is handled by a system with that Laplace transform. If we evaluate the system response (Laplace transform of the impulse response) at complex frequency s = jω , where ω = 2 πf , we obtain | H ( s )| which is the system gain for frequency f .
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series.
The damping ratio is a parameter, usually denoted by ζ (Greek letter zeta), that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory .
A lead–lag compensator is a component in a control system that improves an undesirable frequency response in a feedback and control system. It is a fundamental building block in classical control theory .
Impulse response. The impulse response from a simple audio system. Showing, from top to bottom, the original impulse, the response after high frequency boosting, and the response after low frequency boosting. In signal processing and control theory, the impulse response, or impulse response function ( IRF ), of a dynamic system is its output ...
ω 0 = k / m {\textstyle \omega _ {0}= {\sqrt {k/m}}} is called the undamped angular frequency of the oscillator or the natural frequency, ζ = c 2 m k {\displaystyle \zeta = {\frac {c} {2 {\sqrt {mk}}}}} is called the damping ratio. Many sources also refer to ω0 as the resonant frequency.
Zero frequency (DC) corresponds to (1, 0), positive frequencies advancing counterclockwise around the circle to the Nyquist frequency at (−1, 0). Two poles are located at the origin, and two zeros are located at z 1 = − 1 2 + j 3 2 {\textstyle z_{1}=-{\frac {1}{2}}+j{\frac {\sqrt {3}}{2}}} , z 2 = − 1 2 − j 3 2 {\textstyle z_{2}=-{\frac ...