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The frequency response is characterized by the magnitude, typically in decibels (dB) or as a generic amplitude of the dependent variable, and the phase, in radians or degrees, measured against frequency, in radian/s, Hertz (Hz) or as a fraction of the sampling frequency.
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.
In electrical engineering and control theory, a Bode plot / ˈ b oʊ d i / 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.
In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction ( filtering) and sample-rate reduction.
The Duffing equation is an example of a dynamical system that exhibits chaotic behavior. Moreover, the Duffing system presents in the frequency response the jump resonance phenomenon that is a sort of frequency hysteresis behaviour.
The frequency response, in terms of normalized frequency ω, is: H ( e j ω ) = 1 3 + 1 3 e − j ω + 1 3 e − j 2 ω = 1 3 e − j ω ( 1 + 2 cos ( ω ) ) . {\displaystyle {\begin{aligned}H\left(e^{j\omega }\right)&={\frac {1}{3}}+{\frac {1}{3}}e^{-j\omega }+{\frac {1}{3}}e^{-j2\omega }\\&={\frac {1}{3}}e^{-j\omega }\left(1+2\cos(\omega ...
Example frequency-response function of a dynamical system with several degrees of freedom, showing distinct resonance-antiresonance behavior in both amplitude and phase. The frequency response function (FRF) of any linear dynamic system composed of many coupled components will in general display distinctive resonance-antiresonance behavior when ...
The sampling frequency or sampling rate, f s, is the average number of samples obtained in one second, thus f s = 1/T, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second. Reconstructing a continuous function from samples is done by interpolation algorithms.
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.
Frequency response distortion. Non-flat frequency response is a form of distortion that occurs when different frequencies are amplified by different amounts in a filter. For example, the non-uniform frequency response curve of AC-coupled cascade amplifier is an example of frequency distortion.