What Is a Frequency Response Model?

Frequency response describes the steady-state response of a system to sinusoidal inputs.

For a linear system, a sinusoidal input of frequency ω:


results in an output that is also a sinusoid with the same frequency, but with a different amplitude and phase θ:


Frequency response G(s) for a stable system describes the amplitude change and phase shift as a function of frequency:

G(s)=Y(s)U(s)|G(s)|=|G(jω)|=AyAuθ=Y(jω)X(jω)=tan1(imaginary part of G(jω)real part of G(jω))

where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively.

Frequency Response Model Applications

You can estimate the frequency response of a Simulink® model as a frequency response model (frd object), without modifying your Simulink model.

Applications of frequency response models include:

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