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