<Table> <Tr> <Td> </Td> <Td> This introduction and first section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (September 2011) (Learn how and when to remove this template message) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This introduction and first section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (September 2011) (Learn how and when to remove this template message) </Td> </Tr> <P> 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 . </P> <P> Two applications of frequency response analysis are related but have different objectives . </P>

Properties of frequency response of an lti system
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