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Spectral Power Density


 P_y(nu)=lim_(T->infty)2/T|int_(-T/2)^(T/2)[y(t)-y^_]e^(-2piinut)dt|^2,
(1)

so

int_0^inftyP_y(nu)dnu=lim_(T->infty)1/Tint_(-T/2)^(T/2)[y(t)-y^_]^2dt
(2)
=<(y-y^_)^2>
(3)
=sigma_y^2.
(4)

See also

Power Spectrum

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Cite this as:

Weisstein, Eric W. "Spectral Power Density." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpectralPowerDensity.html

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