Campbell Scientific CR10X Measurement and Control System - Manual (Page 168)

SECTION 10. PROCESSING INSTRUCTIONS
10-10
BIN FREQUENCY
The band width or the frequency covered by
each averaged bin is equal to FA/N where F is
the sample frequency in Hz (1/scan interval in
seconds) and A is the number of bins being
averaged.
The frequency (f
i
) of any given averaged bin i
where i ranges from 1 to (N/2A)-1 is given by the
following equation:
i-1 * F * A / N < fi < i * F * A / N [9]
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.
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
0 1 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
Examples of the use of the FFT are given in Section 8.