Appendix F: Miscellaneous
F-6 AWG710&AWG710B Arbitrary Waveform Generator User Manual
Unlike convolution, the result of A ×B and B×A are different in correlation. B×A is
calculated as follows (B and A are those from the example on page F-5):
For nonperiodic case:
A×B = b0a4,
b0a3+b1a4,
b0a2+b1a3+b2a4,
b0a1+b1a2+b2a3,
b0a0+b1a1+b2a2,
b1a0+b2a1,
b2a0,
0, (8 points)
For periodic case:
A×B = b0a0+b1a1+b2a2,
b0a4+b1a0+b2a1,
b0a3+b1a4+b2a0,
b0a2+b1a3+b2a4,
b0a1+b1a2+b2a3, (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 the products that is obtained with the starting
point values of waveforms A and B added.