Appendix F: Miscellaneous
AWG610 Arbitrary Waveform Generator User Manual F-3

Integration

The integ() function integrates numerically based on a trapezoidal formula. The
trapezoidal formula is expressed with the following equation:
ŕ() +ȍ
+1
(1))()
2@D
+D
2{(1))2(2))2(3)) AAA ) 2(1))()}
Here, n is the number of waveform points and i is an integer in the range
i = 1, 2, ..., n.
x
i
f(x
i–1
)
f(x
i
)
f(x
i+1
)
x
i
x
n
n
x
x
i+1
x
i–1
Figure F-2: Equation integration
The integration is actually calculated with the following formula:
ŕ() +1ń2NJ(1))2(2))2(3)) AAA ) 2(1))()Nj
However, the imaginary initial value f(x0) always takes a value of 0.