Tektronix AWG710, AWG710B Convolution

Appendix F: Miscellaneous
F-4 AWG710&AWG710B Arbitrary Waveform Generator User Manual
Convolution
The operation expressed by the following equation is called convolution. With
respect to a discrete system, convolution y(n) of a certain waveform x(n) and a
second one h(i) is expressed by the following equation. N is the number of it ems of
data.
Periodic. The Periodic enables you to specify whether the two–wa vefor ms must be
regarded as periodic during calculation. Below is an example showing differenc es
between non–periodic and periodic waveforms.
Waveform A = a0, a1, a2, a3, a4 (5 points)
Waveform B = b0, b1, b2 (3 points)
For nonperiodic case:
A*B = a0b0,
a0b1+a1b0,
a0b2+a1b1+a2b0,
a1b2+a2b1+a3b0,
a2b2+a3b1+a4b0,
a3b2+a4b1,
a4b2,
0, (8 points)
The data length of the waveform c re ate d is the total of the number of points of t he
two–waveform files.
For periodic case:
A*B = a0b2+a1b1+a2b0,
a1b2+a2b1+a3b0,
a2b2+a3b1+a4b0,
a3b2+a4b1+a0b0,
a4b2+a0b1+a1b0, (5 points)
Waveforms A and B are regarded as periodic during calculation. The count of the
operation of sum of products is equivalent to the length of the shorter waveform.
The resulting waveform’s c ycle equals the same as th e longer wav eform. The actual
output segment of the waveform correspo nds to one c ycle. The starting po int va lue
of the waveform equals the sum of products that is obtaine d with the sta rting point
values of waveforms A and B added.
y
n() xi()hn i–()
t0=
N1–
∑
=