signal and system lecture 14
TRANSCRIPT
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Signals and SystemsFall 2003
Lecture #14
23 October 2003
1. Review/Examples of Sampling/Aliasing
2. DT Processing of CT Signals
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Sampling Review
Demo: Effect of aliasing on music.
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Strobe Demo
> 0, strobed image moves forward, but at a slower pace
= 0, strobed image still
< 0, strobed image moves backward.
Applications of the strobe effect (aliasingcan be useful sometimes):
E.g., Sampling oscilloscope
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DT Processing ofBand-LimitedCT Signals
Why do this?
Inexpensive, versatile, and higher noise margin.
How do we analyze this system?
We will need to do it in the frequency domain in both CT andDT
In order to avoid confusion about notations, specify
CT frequency variable
DT frequency variable ( = )
Step 1: Find the relation betweenxc(t) andxd[n], orXc(j) andXd(ej)
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Time-Domain Interpretation of C/D Conversion
Note: Not fullanalog/digital
(A/D) conversion
not quantizing
the x[n] values
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Illustration of C/D Conversion in the Frequency-Domain
)(eX
j
d
)(eX jd
1T = 2T =
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D/C Conversion yd[n] yc(t)Reverse of the process of C/D conversion
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Now the whole picture
Overall system is time-varying if sampling theorem is notsatisfied
It is LTI if the sampling theorem is satisfied, i.e. for bandlimited
inputsxc(t), with
When the inputxc(t) is band-limited (X(j) = 0 at || > ) and the
sampling theorem is satisfied (s > 2M), then
M