Operator`s manual

SECTION 10. PROCESSING INSTRUCTIONS
10-10
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
Hz for 1024 samples and that the bin averaging
specified is 4, the frequency of the signal in bin i
is:
31 * 10 * 4 / 1024 < f
i
< 32 * 10 * 4 / 1024
1.21 Hz < f
i
< 1.25 Hz
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 Hz to 1/2 the
sampling frequency. The value of i varies 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
n
) is related to the spectral
bin values (PS
i
see previous section) by the
following equation:
APS
n
=(Σ PS
i
+0.5(PS
nA-A/2
+PS
nA+A/2
))/A [10]
where i goes from nA-(A/2-1) to nA+(A/2-1)
The following table illustrates how bin averaging
is done given a time series of 1024 values taken
at one per second with the resulting 512 spectral
bins averaged in groups of 4 (Parameter 3 = log
base 2 of 4 = 2) to produce 127 averaged bins.
In the following example, averaging produces
bins with representative frequencies that are the
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 results
of fewer original samples.
Examples of the use of the FFT are given in
Section 8.
TABLE 10-1. Example of FFT Power Spectra Bin Averaging (Assuming 1024 time series values
starting in Location 1)
No Bin Averaging Averaged in Groups of 4
BIN NO. LOC. REPRESENTATIVE AVERAGED LOC. REPRESENTATIVE
FREQUENCY BIN NO. FREQUENCY
01 DC
1 2 1/1024
2 3 2/1024
3 4 3/1024
4 5 4/1024 ------------------------ 1 1 4/1024 or 1/256
5 6 5/1024
6 7 6/1024
7 8 7/1024
8 9 8/1024 ------------------------ 2 2 8/1024 or 2/256
9 10 9/1024
10 11 10/1024
11 12 11/1024
. . .
502 502/1024
503 503/1024
504 504/1024 ---------------------126 126 504/1024 or 126/256
505 505/1024
506 506/1024
507 507/1024
508 508/1024 ---------------------127 127 508/1024 or 127/256
509 509/1024
510 510/1024
511 511/1024