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Appendix D: Sample Waveform Library
DĆ4
AWG2021 User Manual
Constants k0 indicates the half width (W50) for the pulse; k1 indicates the peak location
of the pulse.
Description The waveform generated when the pulse width is taken to be tW50 and the
peak location is taken to be 0 can be expressed as
Gaussian form in the frequency domain as well.
<Example> When t
w50
is 1 ms, the bandwidth will be 31.2 kHz.
V(t)Ă +Ă expĂ
NJ
ćIn(2)Ă @Ă
ǒ
2t
t
w50
Ǔ
2
Nj
Ă SubstitutingĂ sĂ +Ă
t
w50
22ĂIn(2)
Ǹ
Ăgives
f(t)Ă +Ă expĂ
ǒ
ćĂ
t
2
2s
2
Ǔ
, Ă andĂ takingĂ theĂ FourierĂ transformĂ gives
F(jw)Ă +Ă2p
Ǹ
sĂ @Ă expĂ
ǒ
ćĂ
w
2
s
2
2
Ǔ
.Ă ThisĂ showsĂ thatĂ thisĂ signalĂ hasĂ a
Settings Waveform points: 256
Clock frequency: 100 MHz
Output time: 2.56 ms