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Appendix F: Miscellaneous
AWG2021 User Manual
FĆ5
Integration
The integ() function integrates numerically based on a trapezoidal formula. The
trapezoidal formula is expressed with the following equation.
ŕ
f (x)dx [
ȍ
n
i+1
f (x
i–1
) ) f (x
i
)
2
@ Dx
+ D
x
2
{
f (x
1
) ) 2f (x
2
) ) 2f (x
3
) ) AAA ) 2f (x
n–1
) ) f (x
n
)
}
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
nx
x
i+1
x
i-1
Figure FĆ5: Equation Integration
The integration is actually calculated with the following formula.
ŕ
f (x)dx [ 1ń2
{
f (x
1
) ) 2f (x
2
) ) 2f(x
3
) ) AAA ) 2f(x
n–1
) ) f(x
n
)
}
However, the imaginary initial value f(x0) always takes a value of 0.