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In Spectrum Averaging Zero Pad and Signal Enhancement modes the original Time
Records a(n) and a(n) are extended by an additional record with a(n)
=
0 or a(n)
=
0
giving a biased estimate,
P~aa(n).
To remove the error caused by zero padding, a "bow-
tie" correction can be applied:
Similar for Ch.B.
13.2.16. Cross Corelation
In Spectrum Averaging mode:
Rzab(n)
=
y-
1
[
W(k) · GAs(k)]
0
~
n
~
N-1 ,
0
~
k
~
N-1 ,
N
=
2048
W(k) is the weighting function applied to .the Cross Spectrum.
The Analytical Cross Correlation Function is defined as:
~
Rzab(n) = Rab(n)
+
j Rab(n)
where
~(n) =
Jr[
Rab(n)]
The displayed function is the normalised Cross Correlation Coefficient:
where
1
N-1
_
1
N-1
_
Raa(O) = -
.E
W(k) · GAA(k) and Rbb(o) = -
.E
W(k) · Gss(k)
N
k=O
N
k=O
In Signal Enhancement mode:
Rzab(n)
=
y-
1
[
I
Gt (k) · Ge(k)
1
2
]
0
~
n
~
N-1, N
=
4096, a(n) and 6(n)
=
0 for N/2
~
n
~N-1
where GA(k) and Ge(k) are the 1-sided spectra of the Enhanced Time Functions a(n)
and b(n) extended with zero padding. Pzab is displayed for -2048
~
n
~
2047.
155
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