1. Convolution sum & Integral
Lecture #03
Convolution sum & Integral

2. Convolution Integral :
Linear system
Convolution Integral :
LTI system
LTI system …
meiling chen
signals & systems

3. Transfer function of the system
Linear system
LTI system
I.C.=0
Impulse response
Transfer function of the system
LTI system
I.C.=0
Any input
Zero state response
meiling chen
signals & systems

4. Example : Graphical convolution
Linear system
Example : Graphical convolution
(1)
meiling chen
signals & systems

5. Linear system
(2)
(3)
meiling chen
signals & systems

6. Linear system
(4)
(5)
meiling chen
signals & systems

7. Linear system
Ans:
meiling chen
signals & systems

8. Convolution sum
meiling chen
signals & systems

9. LTI system Only true for linear system (linearity property)
x[k] is a constant with respect to H
(linearity property)
Let
Only true for time invariant system
Convolution sum
meiling chen
signals & systems

10. convolution
meiling chen
signals & systems

11. meiling chen
signals & systems

12. Example 2.1
Impulse
response
meiling chen
signals & systems

13. Example 2.2 The input and impulse response are of infinite duration
Consider a system with impulse response
Find y[n] when the input is x[n]=u[n]
meiling chen
signals & systems

14. meiling chen
signals & systems

15. meiling chen
signals & systems

16. meiling chen
signals & systems