Biomedical Engineering Reference
In-Depth Information
CHAPTER
19
Error in Random Data
Estimate Analysis
(Information Is Paraphrased
from Bendat & Piersol)
This chapter presents the various statistical errors in random data analysis. Emphasis
is on frequency domain properties of joint sample records from two different stationary
(ergodic) random processes. The advanced parameter estimates discussed in this chapter
include magnitude and phase estimates of autospectral density functions, cross-spectral
density functions, transfer functions, and coherence functions. In particular, statistical
error formulas are given without development or proof for the following functions:
1.
frequency response function estimates (gain and phase),
2.
coherence function estimates,
3.
cross-spectral density function estimates, and
4.
autospectral density function estimates.
19.1 CROSS-SPECTRAL DENSITY FUNCTION
ESTIMATES
Recall that the cross-spectral density function between two stationary (ergodic) Gaussian
random processes
{
x
(
t
)
}
and
{
y
(
t
)
}
is defined by (19.1). Specifically, given a pair of sample
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