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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
f (x)dx +
ȍ
n
i+1
f (x
ić1
) ) f (x
i
)
2
@ Dx
+ D
x
2
{
f(x
1
) ) 2f(x
2
) ) 2f(x
3
) ) AAA ) 2f(x
nć1
) ) 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
n
x
x
i+1
x
i–1
Figure F-2: Equation integration
The integration is actually calculated with the following formula:
ŕ
f (x)dx + 1ń2
NJ
f (x
1
) ) 2f (x
2
) ) 2f (x
3
) ) AAA ) 2f(x
nć1
) ) f (x
n
)
Nj
However, the imaginary initial value f(x
0) always takes a value of 0.