User's Manual

AWG710&AWG710B Arbitrary Waveform Generator User Manual F-1
Appendix F: Miscellaneous
This appendix covers the following items.
 Sampling theorem
 Differentiation
 Integration
 Convolution
 Correlation
 Code Conversion
Sampling Theorem
When the signal is continuous and the highest frequency component of the signal
is f
0
, sampling with T≤ 1/2f
0
loses none of the data contained in the signal. T is the
sampling interval. This theorem is well known as the sampling theorem. If data is
created to meet this theorem, the necessary signal can be obtained.
A continuous analog signal x(t) can be reproduced from the digital data with the
above equation. In the Waveform Generator, this is realized using a D/A converter.
Differentiation
The diff() function calculates the central deviation as the differential value. The
equation below expresses the central deviation when the function f(x) is given at
even intervals of nx.
Xt() Xnt()
2π T⁄()tnT2⁄–(){}sin
2π T⁄()tnT2⁄–()
-------------------------------------------------------------
n ∞–=
∞
∑
=
f′ x()
f
xx∆+()
f
xx∆–()–
2 x∆()
-------------------------------------------------=