Signals and Systems EE235 Leo Lam © 2010-2013

UNIX UNIX is basically a simple operating system but you have to be a genius to understand the simplicity. Leo Lam © 2010-2013

One more example For all t: x(t) t 3 2 1 -1 Flip Shift Can you guess the “width” of y(t)? 3 Leo Lam © 2010-2013

One more example For all t: x(t) t 4 2 1 -1 Multiply & integrate Leo Lam © 2010-2013

* Convolution examples 5 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 5 Leo Lam © 2010-2013

* Convolution examples 6 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? 6 Leo Lam © 2010-2013

Another example (Mathematic method) Approach? What does each part “look” like? y(t)= = 1 if 3 - > 0 = 1 if t - > 0 7 Leo Lam © 2010-2013

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 8 Leo Lam © 2010-2013

Another example y(t)= 9 For = 1 if t - > 0 = 1 if 3 - > 0 Leo Lam © 2010-2013

Another example 10 Combining two, with only one active at each t For Then integrate… 10 Leo Lam © 2010-2013