Coherence Function from Spectral Analysis - Signal Processing of Random Physiological Signals - page 210

A.C. powerline

Suspect
output

System

Input

Suspect input 2

Suspect input 1

FIGURE 18.3 : Spurious correlation in the analysis of a system

there is bias in the autospectral and cross-spectral density measurements, and if there are
nonlinear and/or time-varying parameters within the system. Mathematical explanations
of these biases are shown by (9.62) through (9.92) in Bendat and Piersol [1].
A confidence interval may be used with the coherence function. By definition, a
confidence interval of 95%, for example, is “in repeated sampling 95% of all intervals will
include the true fixed value of the parameter of interest” [4], then it is a true random
interval.

18.4 EXAMPLES OF THE USE OF COHERENCE
FUNCTIONS
The first example of how a coherence function might be used is demonstrated [5 and 6]
to measure the vibration spectrum of a small printed circuit board shown in Fig. 18.4.
In this example, the ratio of acceleration/force was measured by connecting an
accelerometer to the output and a pseudorandom signal to the input. In this case, the
modal vibration resonances were measured and converted to the power spectrum. At
100 Hz, the coherence decreased from 1 to 0.83, indicating that the signal-to-noise ratio