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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
( ) + 1 ń 2
NJ
(
1
) ) 2 (
2
) ) 2 (
3
) ) AAA ) 2 (
1
) ) ( )
Nj
However, the imaginary initial value f(x
0
) always takes a value of 0.