1. Linear Time-Invariant Systems (LTI) Superposition Convolution

2. Linear Time-Invariant Systems (LTI) Superposition Convolution Causal System

3. Linear Time-Invariant Systems (LTI) Superposition Convolution Causal System Causal

4. Linear Time-Invariant Systems (LTI) Superposition Convolution Causal System Causal

5. Matched Filter Signal plus noise, recover the signal Can we choose h(t) to make y(t)=s(t)?

6. Matched Filter Signal plus noise, recover the signal Can we choose h(t) to make y(t)=s(t)? Assume s(t)=0, t t 0. Let h(t)=s(t 0 -t)

7. Matched Filter Signal plus noise, recover the signal Can we choose h(t) to make y(t)=s(t)? Assume s(t)=0, t t 0. Let h(t)=s(t 0 -t)

8. Matched Filter Signal plus noise, recover the signal h(t)=s(t 0 -t)

9. Matched Filter Signal plus noise, recover the signal Assume s(t)=0, t t 0 Let h(t)=s(t 0 -t)

10. s(t)s(t 0 -t)

11. http://www.eas.asu.edu/~eee407/labs03/node3.html#SECTION 00021000000000000000 MATLAB simulation of Convolution

12. Example 1 1 1 1 h(t) By inspection, y(t)=0, t<0 y(t)=0, t>2 t-1 t

13. Example 1 1 1 1 h(t) By inspection, y(t)=0, t<0 y(t)=0, t>2 t-1 t for Maximum @ t=1,

14. Example 1 1 1 1 h(t) By inspection, y(t)=0, t<0 y(t)=0, t>2 t-1 t