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. Another example 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. Another example At all t 0≤t<0.5 5 h(t) moving right Shift Multiply
Integrate
h(t) moving right 5
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6. Another example At all t 0.5≤t<1 6 h(t) moving right Shift Multiply
Integrate
h(t) moving right 6
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7. Another example At all t 1≤t<1.5 7 h(t) moving right Shift Multiply
Integrate
h(t) moving right 7
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8. Another example At all t 1.5≤t? 8
Shift
Multiply
Integrate
y(t)=0 because there is no more overlapping 8
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9. Another example At all t Combining Can you plot and formulate it? 9
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10. Another example
At all t 10
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11. Few things to note Three things: Stretching the thinking 11
Width of y(t) = Width of x(t)+Width of h(t)
Start time adds
End time adds
y(t) is smoother than x(t) and h(t) (mostly)
Stretching the thinking
What if one signal has infinite width? 11
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12. From yesterday Stretching the thinking
What if one signal has infinite width?
Width = infinite (infinite overlapping)
Start time and end time all infinite 12
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13. One more example For all t: x(t) t 13 2 1 -1 Flip Shift
Can you guess the “width” of y(t)? 13
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14. One more example For all t: x(t) t 14 2 1 -1 Multiply & integrate
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15. Summary
Convolution examples
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