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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:

u(t)=Ausinωt

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

y(t)=Aysin(ωt+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.

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