Appendix B: Algorithms
B–12
TDS 684A, TDS 744A, & TDS 784A User Manual
The integration algorithm used by the oscilloscope is as follows:
ŕ
B
A
W(t)dt
is approximated by
ŕ
B
A
W
^
(t)dt
where:
W(t) is the sampled waveform
W
^
(t)
is the continuous function obtained by linear interpolation of W(t)
A and B are numbers between 0.0 and RecordLength–1.0
If A and B are integers, then:
ŕ
B
A
W
^
(t)dt + s
ȍ
B*1
i+A
W(i) ) W(i ) 1)
2
where s is the sample interval.
Similarly,
ŕ
B
A
(
W(t)
)
2
dt
is approximated by
ŕ
B
A
ǒ
W
^
(t)
Ǔ
2
dt
where:
W(t) is the sampled waveform
W
^
(t)
is the continuous function obtained by linear interpolation of W(t)
A and B are numbers between 0.0 and RecordLength–1.0
If A and B are integers, then:
ŕ
B
A
ǒ
W
^
(t)
Ǔ
2
dt + s
ȍ
B*1
i+A
(
W(i)
)
2
) W(i) W(i ) 1) )
(
W(i ) 1)
)
2
3
where s is the sample interval.
Measurements on Envelope Waveforms
Time measurements on envelope waveforms must be treated differently from
time measurements on other waveforms, because envelope waveforms contain so
many apparent crossings. Unless otherwise noted, envelope waveforms use either
the minima or the maxima (but not both), determined in the following manner:
1. Step through the waveform from Start to End until the sample min and max
pair DO NOT straddle MidRef.
2. If the pair > MidRef, use the minima, else use maxima.
Integration Algorithm
