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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