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TABLE 10-1. Example of
FFT
Power
Spectra Bin Averaging (Assuming
1024
time series values
starting in Location
1)
SECTION
10.
PROCESSING INSTRUCTIONS
For example, given that
the power spectra result
shows that the
energy peak of a signal falls
in
bin 32 when it
is
sampled at
a
frequency
of
10
Hzlor
1024 samples and that
the bin averaging
specified
is 4,
the frequency
of
the signal in bin
i
is:
31
*
10 " 4
/
1024
<li<32"
10*
4
I
1024
'l.21 Hz
<
f,
<
1
.25
H2
POWER SPECTRA
The result
of
the FFT with A bins averaged, are
(N/2A)-1 bins of average spectral
energy (APSn)
representing frequencies
from 0
Hzto
112lhe
sampling
frequency.
The value of
ivaries
from
1
to (N/2A)-1. The results are found
in
consecutive
input locations starting with the first
one specified
by Parameter
4.
The value
for
average bin n
(APS.) is related to the spectral
bin values
(PS;
see previous section) by
the
following equation:
No
BIN
NO.
0
1
2
3
4
5
6
7
I
9
10
11
502
503
504
505
506
507
508
509
510
511
Bin
Averaging
LOC.
REPRESENTATIVE
FREQUENCY
APS'=(X PS;+O.5(PSn4_4y2+PSn4*ed),ln
[1
where
i
goes
from nA-(A/2-1) to nA+(A/2-1)
The following
table illustrates how
bin
is
done given
a
time series
of
1024
values
at one per second with
the resulting 512
bins averaged
in
groups of
4 (Parameter
3
=
base 2 of
4 =
2l
to
produce
'127
averaged
bins.
In
the following example, averaging produces
bins
with representative frequencies that are
same
as
if
256 samples had been used with
no
averaging.
Note that when averaging
is
done,
information from the first
few and last few bins
is not included so that the averages
can better
represent frequencies that correspond
to
of
fewer original samples.
Examples
of
the use
of
the FFT are given
in
Section
8,
Averaged in Groups of
4
AVERAGED
LOC.
REPRESENT
BIN
NO.
FREQUENCY
1
411024
or
1
1
2
3
4
5
6
7
8
9
10
11
12
DC
111024
211024
3/1024
411024
511024
611024
7/1024
811024
9t1024
10t1024
11t1024
502/1024
50311024
50411024
s05/1
024
506/1024
507/1024
50811024
509t1024
510/1024
51',|11024
--
126
2
8/1024 or
126
50411024
or
1
10-10
----
127
127
508fi024 or
127,
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