# Cross Spectrum

- The cross spectrum F
- F
_{xy}(f)=F^{'}_{x}(f)×F_{y}(f) - where F
^{'}_{x}(f) is the complex conjugate of F_{x}(f) - The cross spectrum reduces to the power spectrum when F
_{y}(f)=F_{x}(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.

_{xy}(f) of f

_{x}(t) and f

_{y}(t) is the forward Fourier Transform of the cross correlation function R

_{xy}(T). The cross spectrum is in general complex. The cross spectrum can also be obtained from the individual Fourier spectra F

_{x}(f) and F

_{y}(f)

**See also: **Autospectrum, Cross Correlation, Spectrum.

**Subjects: ** Mathematics Noise & Vibration Signal Processing