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Chapter 5
Signal Generation Fundamentals
NI PXIe-5450 User Manual
5-4
ni.com
The following figure shows a desired 5 MHz sine wave generated by a 6
MS/s DAC. The solid line represents the desired waveform, and the arrows
represent the digitized samples that are available to recreate the continuous
time 5 MHz sine wave. The dotted line indicates the signal that would be
seen, for example, with an oscilloscope at the output of a DAC.
In this case, the high–frequency sine wave is the desired signal, but was
severely undersampled by only being generated by a 6 MS/s DAC; the
actual resulting waveform is a 1 MHz signal.
In systems where you want to generate accurate signals using sampled data,
the sampling rate must be set high enough to prevent aliasing.
Aliased Images
An aliased image is a frequency component that appears in continuous time
waveforms being recreated from discrete-time, digital waveforms. The
frequencies where these extra components appear are related to both the
frequency of the signals being recreated as well as the frequency of the
sample rate. Looking only at positive frequencies, the two frequencies are
related by the following equation:
f
ai
= |
f
o
+ nf
s
|
where
f
ai
= the aliased images
f
o
= the desired waveform frequency
f
s
= the sample rate
n
= an integer (either positive or negative)
As the equation indicates, there are an infinite number of these aliased
images that occur. As
n
gets larger, however, the power content of these
extra frequencies “falls off.”
t