Frequency response

Frequency response describes how a system’s steady-state output amplitude and phase vary with the frequency of a sinusoidal input.

Transfer function: A mathematical description of a linear time-invariant system relating its input to its output. Evaluating a transfer function at different frequencies yields the system’s frequency response.
Sinusoidal steady state: The long-term response of a system to a sinusoidal input after transient effects have decayed. Frequency response is measured from this steady-state output.
Control theory: The study of how to influence the behavior of dynamic systems through feedback and control inputs. Frequency-response methods assess feedback-system performance and stability.
Time-domain analysis: The study of system behavior as signals vary over time. It describes transients directly, while frequency response describes steady-state sinusoidal behavior.
Bode plot: A graph of a system’s gain and phase versus frequency, usually with logarithmic frequency axes. It displays the two main parts of frequency response across a broad range.
Fourier transform: A mathematical transform that represents a signal in terms of its frequency components. It connects a system’s time-domain behavior with its behavior across frequencies.
Feedback: A process in which a system’s output is returned as part of its input. Frequency response helps determine whether feedback improves tracking or causes oscillation.
Transient response: A system’s temporary behavior after an input or operating condition changes. It captures effects that a steady-state frequency response does not show by itself.
Resonance: A strong response that occurs when a system is driven near one of its natural frequencies. A frequency-response peak often identifies a resonant mode.
Linear time-invariant system: A system whose behavior obeys superposition and does not change over time. Its frequency response fully characterizes sinusoidal steady-state behavior.

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