Campbell Scientific CR10X Measurement and Control System - Manual (Page 166)

SECTION 10. PROCESSING INSTRUCTIONS
10-8
the magnitude and phase components. Bin
averaging is not allowed with this option.
Second Digit: A "0" in the second digit specifies
that no taper be applied, whereas a "1" specifies
that a taper be applied. If the original data set is
not known to be periodic with an integral number
of periods in the data set, then it is necessary to
apply a taper to the beginning and end of the
data. The taper that is applied is a four term
Blackman-Harris as specified by Fredric J.
Harris, Proceedings of the IEEE, Vol. 66, No. 1,
January 1978. When the taper is used, the
CR10X applies a correction by multiplying the
results by the ratio of the variance before the
taper to the variance after the taper.
The variance ratio is saved only when the power
spectra option is selected. The variance ratio is
saved in input location (N/2)+B, where B is the
location (Parameter 4) that contained the first
value of the original time series data.
PARAMETER 3 specifies how many of the
resulting spectral bins (if any) are to be
averaged. Bin averaging is only allowed when
power spectral is output. Parameter 3 is equal
to the log base 2 of A where A is the number of
bins to be averaged. For example, if there are
1024 samples in the original time series data
and the resulting 512 spectral bins are averaged
in groups of 8 (Parameter 3 = 3 = log base 2 of
8) then 63 (=N/2A 1) averaged bins will be
produced.
PARAMETER 4 defines which input location will
contain the first value at the original time series
data. Once the FFT program has executed, this
location will contain the first resulting value.
PARAMETER 5 is a scaling multiplier that is
applied to the FFT results (i.e., after the FFT
computation has been done). The multiplier is
not applied to the DC component.
MEMORY REQUIREMENTS
The number of Input Memory Locations
allocated must be enough to accommodate the
N sampled values, where N is defined under
Parameter 1. The number of Intermediate
Memory Locations allocated must be greater
than or equal to (N/8 + 2). If insufficient Input or
Intermediate Memory Locations have been
allocated, the datalogger will flag an E60 or E04,
respectively.
NOTE: The CR10X has 1
Intermediate Location that is not
available for use by Processing or
Output Instructions so the number of
Intermediate Locations allocated
must exceed the indicated total
requirement by at least 1.
FFT RESULTS WITHOUT BIN AVERAGING
When no bin averaging is specified, the FFT
results may be calculated in terms of the
real/imaginary components, the
magnitude/phase components, or the power
spectra. The rest of this section deals with the
DC component, bin frequency, and the FFT
results just mentioned. An example showing
each of the possible results is given in Section
8.11.1.
DC COMPONENT
Before the FFT is applied, the average of the
original time series data is subtracted from each
value. This is done to maintain the resolution of
the math in the rest of the FFT calculations.
If the real and imaginary or the magnitude and
phase results are specified by Parameter 2 the
DC component is the average of the original
time series data. If power spectra results are
specified, the DC component is equal to the
square of the average of the original time series
data times 2N.
The DC component is stored in the first input
location specified by Parameter 4 which
corresponds with the frequency at 0 Hz (bin 0).
BIN FREQUENCY
The band width or the frequency covered by
each bin is equal to F/N where F is the sample
frequency in Hz (1/scan interval in seconds).
The frequency (f
i
) of any given bin i where i
ranges from 0 to (N/2)-1 is given by the following
equation:
(i-1 * F) / N < f
i
< (i * F) / N [1]
For example, given that the power spectra result
shows that the energy peak of a signal falls in
bin 128 when it is sampled at a frequency of 10
Hz for 1024 samples, the frequency of the signal
is:
127 * 10 / 1024 < f
i
< 128 * 10 / 1024
1.24 Hz < f
i
< 1.25 Hz