1. Signals and Systems
EE235
Lecture 14
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2. UNIX UNIX is basically a simple operating system
but you have to be a genius to understand the simplicity.
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3. Summary: Convolution Draw x() Draw h() Flip h() to get h(-)
Shift forward in time by t to get h(t-)
Multiply x() and h(t-) for all values of 
Integrate (add up) the product x()h(t-) over all  to get y(t) for this particular t value (you have to do this for every t that you are interested in) 3
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4. One more example For all t: x(t) t 4 2 1 -1 Flip Shift
Can you guess the “width” of y(t)? 4
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5. One more example For all t: x(t) t 5 2 1 -1 Multiply & integrate
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6. * Convolution examples 6 Approach? How to break it down?1 t
x(t) * 2
h(t) -1
y(t)=x(t)*h(t)
Approach? How to break it down?
System will start having non-zero output at time t = -1
The signal y(t) can be expressed in terms of 3 time regions:
t<-1 (where y(t)=0), -1<t<1, t>1 6
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7. * Convolution examples 7 Two non-zero regions:1 t
x(t) * 2
h(t) -1
y(t)=x(t)*h(t)
Two non-zero regions:
If you flip x(t), you’d get:
If you flip h(t), you’d get:
Identical? 7
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8. Another example (Mathematic method)
Approach?
What does each part “look” like?
y(t)=
= 1 if 3 - > 0
= 1 if t - > 0 8
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9. Another example (complicated)
y(t)=
= 1 if 3 - > 0
= 1 if t - > 0
Need to satisfy both:
That is &
Two cases to consider then: or 9
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10. Another example y(t)= 10 For = 1 if t - > 0 = 1 if 3 - > 0
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11. Another example 11 Combining two, with only one active at each t For
Then integrate… 11
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12. Summary
Convolution examples
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