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SECTION
10.
PROCESSING INSTRUCTIONS
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
originaltime series data
and
the resulting 512 spectral bins are averaged
in groups of
8 (Parameter 3 =
3
= log base 2 of
B)
then
63
(=5724
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
willcontain the first resulting value.
PARAMETER
5
is
a scaling multiplier
that
is
applied to
the FFT results (i.e., after the FFT
cornputation 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 lntermediate
Memory Locations allocated must be greater
than or equal
to (N/8
+
2).
lf insutficient Input or
Intermediate Memory Locations have been
allocated, the datalogger will flag
an E60 or
E04,
respectively.
NOTE: The 21X
has 1 lntermediate
Location
that is not available for use
by Processing or
Output Instructions
so
the
number of
lntermediate
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
8.8.1.
DC COMPONENT
Before
the FFT
is
applied, the average
of
the
originaltime series data
is
subtracted
from each
value. This
is done
to maintain the resolution
the math
in
the rest of the FFT calculations.
lf
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.
lf 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
equalto
F/N
where
F is
the sample
frequency
in Hz (1/scan interval in seconds).
The
frequency
(f;)
of any given bin
iwhere
i
ranges
from
0
to (N/2)-1 is given
by
the
equation:
(i-1
.F)/N
<
fi< (i.F)/N
For
example, given that
the power spectra
resu
shows that the energy peak of a signal
falls
in
bin
'128
when it
is
sampled at
a
frequency
of
10
Hzlor
1024 samples, the frequency
of
the
sig
is:
127
"
10
I
1024< fi < 128 *
10
/
1024
1.24H2.
fi.
1
.25H2
REAL
AND IMAGINARY COMPONENTS
The result
of
the FFT when the real and
imaginary option is selected is N/2 input
locations containing
the realcomponents
(R;)
followed by N/2 input locations containing the
imaginary
components
(l;). There
is
a real
and
an imaginary component for each
bin.
The
value
of
ivaries from
1
to
N/2.
The
realand
imaginary results at each
frequency
i,
are
related to
the magnitude
(M;)
and phase
(P,)
as
shown below:
Ri
=Mi
*cosP;
li
=Mi
*sinPi
where
M; is
the magnitude and
P; is
the phase
the signal in
degrees.
Magnitude is half of the
10-8
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