Signals and Systems EE235 Leo Lam © 2010-2011

Working with computers Leo Lam © 2010-2011

Today’s menu Homework 3 due today Supplemental material online tonight Review (Hossein) Thursday 5:30 pm @ EEB105 Review session (me) Wednesday 5:30 pm @ Sieg 232 (Lab) Midterm Friday! A hard Convolution example Leo Lam © 2010-2011

Hardest example (mathematically) Approach? What does each part “look” like? y(t)= = 1 if 3 - > 0 = 1 if t - > 0 4 Leo Lam © 2010-2011

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 Leo Lam © 2010-2011

Another example y(t)= 6 For = 1 if t - > 0 = 1 if 3 - > 0 Leo Lam © 2010-2011

Another example 7 Combining two, with only one active at each t For Then integrate… 7 Leo Lam © 2010-2011

Convolution Properties 8 Leo Lam © 2010-2011

Commutative Commutative: Doesn’t matter which signal to flip, it’s the same Pick the easier one! 9 Leo Lam © 2010-2011

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 Leo Lam © 2010-2011

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 Leo Lam © 2010-2011

Summary Finished Convolution Some Convolution properties Leo Lam © 2010-2011