1. Signals and Systems
EE235
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2. Working with computers
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3. Today’s menu Homework 3 due today Supplemental material online tonight
Review (Hossein) Thursday 5:30 EEB105
Review session (me) Wednesday 5:30 Sieg 232 (Lab)
Midterm Friday!
A hard Convolution example
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4. Hardest example (mathematically)
Approach?
What does each part “look” like?
y(t)=
= 1 if 3 - > 0
= 1 if t - > 0 4
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5. Another example y(t)= 5 Need to satisfy both: That is &
= 1 if 3 - > 0
= 1 if t - > 0
Need to satisfy both:
That is &
Two cases to consider then: or 5
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6. Another example y(t)= 6 For = 1 if t - > 0 = 1 if 3 - > 0
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7. Another example 7 Combining two, with only one active at each t For
Then integrate… 7
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8. Convolution Properties8
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9. Commutative
Commutative: Doesn’t matter which signal to flip, it’s the same
Pick the easier one! 9
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10. Associative Associative: Order doesn’t matter 10 h1(t) h2(t) x(t) y(t)
The overall response of two LTI systems in series is given by 10
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11. Distributive + + Distributive: Two types
h1(t)
h2(t)
x(t)
y(t) +
h(t)
x1(t)
y(t) +
x2(t)
“Divide and conquer” for input signals
The overall response of two systems in parallel is 11
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12. Summary Finished Convolution Some Convolution properties
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