Biomedical Engineering Reference
In-Depth Information
For a constant parameter linear system with a single, clearly defined input and
output, the coherence function will be unity. If
x
(
t
) and
y
(
t
) are completely unrelated,
the coherence function will be zero. Coherence function values greater than 0 but less than
1 may be due to the presence of noise in the measurements, or there may be nonlinearities
in the system relating
x
(
t
) and
y
(
t
), or it may be that the output
y
(
t
) may be a function
of or related to other endogenous inputs in addition to the input signal
x
(
t
). For linear
systems, the coherence function can be interpreted as the fractional portion of the mean
square value at the output
y
(
t
) that is contributed by
x
(
t
) at frequency
f
. Conversely,
the quantity [1
2
xy
(
f
)] is a measure of the mean square value of
y
(
t
) not accounted for
by
x
(
t
) at frequency
f
.
−
γ
17.7 SUMMARY
The ability to derive the transfer function for a system's response is an integral part of
the design process. Of the graphical and analytical techniques available to the engineer,
the spectral density functions prove to be powerful computational tools for this purpose.
In addition, through the coherence function, the spectral density functions provide an
effective means for evaluating error in the transfer function model.
17.8
REFERENCES
1.
Bendat, J. S., and Piersol, A. G.,
Random Data: Analysis and Measurement Procedures
,
2nd Edition, John Wiley and Sones, 1986.
2.
D'Azzo, J. J., and Houpis, C.,
Linear Control System Analysis and Design: Conventional
and Modern
. McGraw-Hill, 1981.
3.
Lessard, C. S. “Analysis of Nystagmus Response to Pseudorandom Velocity
0
Input,” In
Computer Methods and Programs in Biomedicine
, Vol. 23, 1986, pp. 11-
τ
=
4.
Lynn, P. A.
An Introduction to the Analysis and Processing of Signals
. Halsted Press,
1973.
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