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Publish Date: Dec 20, 2006


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crosspower spectrum

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The spectrum containing the product of the power of correlated frequency vectors of two channels. Consists of both a real and imaginary part, that is, a complex spectrum.

The cross spectrum is the power between the input and the output, and hence is computed by multiplying and averaging (denoted by the hat) the instantaneous spectrum of the input () and output (). Note that these spectra are complex, i.e. they can be viewed as vectors.

where the * indicates the complex conjungate.

The crosspower spectrum is particularly useful in the measurement of frequency response in that it removes the influence of system noise. The “noise reduction” assuming uncorrelated Gaussian noise is

where is the noise reduction in dB for N averages.
See frequency response to see how the cross spectrum is used to make high quality frequency response measurements.

Units:

V2 and rad
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