TOPICS
Search

Frequency Response

The frequency response H(omega) of a linear time-invariant system is defined by the response to an input e^(iomegat): the corresponding output is H(omega)e^(iomegat). If h(t) is the impulse response function, then

H(omega)=int_(-infty)^inftyh(t)e^(-iomegat)dt,

so the frequency response is the Fourier transform of the impulse response function. Its absolute value and phase describe the amplitude change and phase shift at each frequency.

See also

Fourier Transform, Impulse Response Function, Linear Time-Invariant System, Transfer Function

Explore with Wolfram|Alpha

References

Oppenheim, A. V.; Willsky, A. S.; and Nawab, S. H. Signals and Systems, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1997.

Cite this as:

Weisstein, Eric W. "Frequency Response." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FrequencyResponse.html

Subject classifications