Cross Spectrum

The cross spectrum Fxy(f) of fx(t) and fy(t) is the forward Fourier Transform of the cross correlation function Rxy(T). The cross spectrum is in general complex. The cross spectrum can also be obtained from the individual Fourier spectra Fx(f) and Fy(f)
Fxy(f)=F'x(f)Fy(f)
where F'x(f) is the complex conjugate of Fx(f)
The cross spectrum reduces to the power spectrum when Fy(f)=Fx(f).

Applications
  • Determination of transfer functions.
  • Measurement of time delays which vary with frequency since this can be obtained from the phase shift at any frequency.

See also: Autospectrum, Cross Correlation, Spectrum.

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Subjects: Mathematics Noise & Vibration Signal Processing