Biomedical Engineering Reference
In-Depth Information
noise, the method of suppressing these depends on the frequencies at which they occur;
therefore, the coherence function not only shows the causality between the input and the
output but also may be of use in helping solve the interference or noise problems within
a system.
In summary, the coherence is a frequency domain function with observed values
ranging from 0 to 1. At each frequency where the coherence function is performed, it
represents the fraction of the power output related to input. If the coherence function is
less than 1, then there are three possible explanations:
1.
there is noise in the system or
2.
the system has some nonlinearity generating energy at other frequencies or
3.
there are other inputs into the system that have not be accounted for.
The coherence function can be calculated using the Fast Fourier Transform [1].
If only one transform is performed on a power spectrum, the coherence function will
always be unity. Therefore, it is necessary to average a number of transforms to get a
good estimate of the function.
18.3 MISAPPLICATION OF THE COHERENCE
FUNCTION
Let us look at an example of when a single coherence function by itself may not give
desirable results to a noise problem. Assume that there are multiple inputs to a system
as shown in Fig. 18.3.
The coherence function will be 1 if each suspect input is evaluated separately,
while the other inputs are turned off. If two or more sources are related to or caused by
the primary source, the coherence may not reveal the secondary cause, if both suspect
inputs are wired to the same power source. This problem is similar to the “spurious
correlation” and “multicolinearity” problems in statistics [4,7]. This problem may be
solved by “multiple coherences” [6].
Bendat and Piersol [1] note there may be bias in the coherence function analysis
of a frequency response, if there are other inputs correlated with the “input of interest,” if
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