Frequency response is the quantitative measure of the output
spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and
phase of the output as a function of
frequency, in comparison to the input. In simplest terms, if a
sine wave is injected into a system at a given frequency, a
linear system will respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Also for a linear system, doubling the amplitude of the input will double the amplitude of the output. In addition, if the system is
time-invariant (so
LTI), then the frequency response also will not vary with time. Thus for LTI systems, the frequency response can be seen as applying the system's
transfer function to a
purely imaginary number argument
representing the frequency of the sinusoidal excitation.