1. Signals and Systems
EE235
Lecture 13
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2. 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) 2
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3. Flip Shift Multiply Integrate y(t) at specific time t0 3 y(t0=3/4)= ?
Here t0=3/4
y(t0=3/4)= ?
3/4
Multiply (at all tau)
Integrate from –inf to inf. 3
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4. y(t) at all t At all t t<0 4
Shift
Multiply
Integrate
The product of these two signals is zero where they don’t overlap 4
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5. y(t) at all t At all t 0≤t<1 5 Shift Multiply Integrate
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6. y(t) at all t At all t 1≤t<2 y(t)=2-t for 1≤t<2 6 Shift Multiply
Integrate 6
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7. y(t) at all t At all t t≥2 y(t)=0 for t≥2 (same as t<0, no overlap)
Shift
Multiply
Integrate 7
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8. y(t) at all t Combine it all 8 y(t)=0 for t<0 and t>2
y(t)=t for 0≤t<1
y(t)=2-t for 1≤t<2 8
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