Operator`s manual

SECTION 10. PROCESSING INSTRUCTIONS
10-8
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 21X 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
8.8.1.
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
REAL AND IMAGINARY COMPONENTS
The result of the FFT when the real and
imaginary option is selected is N/2 input
locations containing the real components (R
i
)
followed by N/2 input locations containing the
imaginary components (I
i
). There is a real and
an imaginary component for each bin. The
value of i varies from 1 to N/2. The real and
imaginary results at each frequency i, are
related to the magnitude (M
i
) and phase (P
i
) as
shown below:
R
i
= M
i
* cos P
i
[2]
I
i
= M
i
* sin P
i
[3]
where M
i
is the magnitude and P
i
is the phase of
the signal in degrees. Magnitude is half of the