1. Chapter 2 linear time invariant systems continuous time systems Prepared by Dr. Taha MAhdy

2. What is a system? A system is a mathematical model that represents the transformation of some input signal x(t) into an output signal y(t).

3. Systems In digital domain, the system may be a digital filter

4. Systems For our purposes, we aren't going to worry about the particulars of how the system is implemented. It will be a black box and our only concern will be the mathematical properties of the system.

5. Systems Mathematically, we represent the system by a transformation or operator that we will denote by T. Then we can write the action of a system on an input signal as Y(t) = T{x(t)} A system is known as a continuous time system if x = x(t) and y = y(t) are continuous time signals.

6. System properties: Memoryless Systems If the output y(t) of a given system depends only on the input x(t) at the same time, then the system is called memoryless. A simple example of a memoryless system is an output that depends on a constant multiple of the input y(t) = ax(t) where a is some real constant.

7. Memory system A system with memory is one where the output depends on the values of the input at previous times. An example of such a system is one where we add up

8. Example

9. Causal and Noncausal Systems If a system output y(t) depends only on the input at present or earlier times, we say that the system is causal. Another way to say this is that the output does not anticipate future values of the input. All memoryless systems are causal.

10. Non causal system

11. Linear Systems

12. Example Check the linearity (soln. a,c linear) (soln. a,c linear)

13. Time (Shift) Invariance

14. System Stability

15. Example cosh

16. The Unit Impulse Function

19. Properties of unit impulse

20. More properties

21. Very important

22. The Unit Step Function

26. Square pulse using unit step

27. Relationship between unit impulse and unit step

28. Assignment Solve the problems of the chapter