Signals And Systems

Chapter 2 Signals and systems analysis in time domain

Part I Review

Systems Representation? Differential Equation LTI Systems representation? Linear Constant-coefficient Differential Equation

Example of second-order continuous-time systems C: capacitor L: inductor R: resistor

 general response zero-input response and zero-state response superposition theorem r(t) is the sum of

zero-input response Initial condition 0- state zero-state response Conditions: Initial state is “0” Conditions: 0- state 0+ state = 0- state(0)

Part II Zero-input Response

? A i : Initial condition zero-input Response Homogeneous equation Characteristic equation

Example1: Suppose that: determine r(t) and

Example2: Consider the differential equation of a second- order system determine r zi (t) if

Exercise Page 83 #2-6(zero-input response)