Operator`s manual

SECTION 10. PROCESSING INSTRUCTIONS
10-13
The Input Processing phase is where new input
values are received, the necessary squares or
cross products formed, and the appropriate
summations calculated as required by the
desired final output. The rate at which the
measurements can be made, the input values
ordered, and the input processing phase
completed without interruption determines the
maximum rate of execution (see Execution
Time).
The Averaging Period Processing occurs
whenever the number of input samples entered
in Parameter 7 is satisfied or whenever an
Output Interval occurs (i.e., whenever the
Output Flag is set). Results from these
calculations are stored sequentially in Input
Storage locations starting with the location
specified in Parameter 9. The calculations
performed are shown below, where N is the
number of input samples in the averaging
period:
1. Means:
M(X) = ΣX/N
2. Variances:
V(X) = ΣX
2
/N - (ΣX/N)
2
3. Standard Deviations:
SD(X) = V(X)
1/2
4. Covariances:
CV(X,Y) = ΣXY/N - ΣX ΣY/N
2
5. Correlations:
CR(X) = CV(X,Y)/(SD(X)SD(Y))
NOTES: 1. The square root
algorithm in the 21X returns a result
of 0 for negative arguments.
2. The divide algorithm returns the
largest floating point number possible
(±10
18
displayed as ±99999) for a
divide by 0.
3. When computing the variance of a
constant signal, round off error
produces a small negative result.
The 21X returns a 0 for the square
root of a negative number; therefore,
the standard deviation is set to 0. If
the signal is also used in a
correlation calculation, division by 0
returns an overrange value for the
correlation result.
If a fast execution interval is specified, it is
possible that the combined execution times of
the input and averaging period processing may
exceed the program table execution interval.
The occurrence of an execution interval Overrun
(see Section 2.1 of 21X Operator's Manual) is
noted by decimal points on either side of the G
in LOG (*0 MODE). This results in the omission
of one input sample. The calculations are not
affected, however, since the number of input
samples is incremented only when valid input
processing occurs. Averaging period processing
occurs only when the number of input samples
specified in Parameter 7 is accumulated.
Regardless of whether all of the input samples
for the averaging period (specified in Parameter
7) have occurred or not, averaging period
processing occurs whenever the Output Flag is
set. This accommodates situations where the
Output Interval may not be an integer multiple of
the averaging period. If for example a 30 minute
Output Interval is set by Instruction 92 and an 8
minute averaging period is specified by
Parameter 7, then three 8 minute and one 6
minute calculations will occur. The proper
weighting of these values in producing the final
output is described below.
The Output Processing occurs only at the
Output Interval and involves averaging the
statistical results obtained at the averaging
periods. These final results are then stored
sequentially in Input Storage beginning with the
location specified in Parameter 9. The Sample
Instruction 70 must be used to transfer the data
to Final Storage. All but the last averaging
period in the Output Interval will contain the
same number of input scans as specified by
Parameter 7. To insure that results from the
averaging periods contribute to the final result
proportional to their averaging periods, the
output processing uses the following equation:
RF = (NR1 + NR2 + .... + N'RL)/NT
RF is the final result
R1 R2, etc., are the results from the averaging
period processing
RL is the result from the last averaging period
in the Output Interval
N is the number of input samples in the
specified averaging period (Parameter 7)