Chapter-5-Transient-and-Frequency-responses-of-LTI-systems

Chapter-5-Transient-and-Frequency-responses-of-LTI-systems...

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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 1 Chapter 5: Transient and Frequency responses of LTI systems Spring 2009/10 Lecture: Tim Woo
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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 2 Laplace Transform Where we are Differential equations State-space model CTFT Hardware Implementation System Characteristics System Responses Closed-loop Systems Continuous-time z-Transform Difference equations State-space model DTFT Hardware Implementation System Characteristics System Responses Closed-loop Systems Discrete-time Mapping Done in 211 To be covered In progress Done Will be covered if available Open-loop Systems Open-loop Systems
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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 3 Expected Outcome • In this chapter, you will be able to – Analysis the system performance with the use of transient and frequency response tools • Impulse response • Step response • Ramp response • Bode plot – Evaluate the transient and frequency responses of the first- and second-order continuous-time and discrete-time LTI systems – Understand the specification of filter in the filter design – Categories different linear-phase digital filters
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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 4 Outline Textbook: – Section 6.2 The Magnitude-phase representation of the frequency response of LTI systems – Section 6.3 Time-domain properties of an ideal frequency selective filters – Section 6.4 Time-domain and frequency-domain aspects of non-ideal filters – Section 6.5 First-order and Second-order Continuous-time systems – Section 6.6 First-order and Second-order Discrete-time systems – Section 6.7 Examples of time- and frequency domain analysis of systems Reference book – A. V. Oppenheim, et. al., Discrete-time Signal Processing , 2nd edition, Prentice-Hall, 1999 – Section 5.7.3 Causal FIR generalized linear phase system
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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 5 Introduction Basically, any LTI system can be regarded as filtering system. Some signals are being suppressed or amplified. Meanwhile, they are also suffered from different amount of delays. Typically, we can analysis the system performance either in time- domain and/or frequency domain analytical tools. Time-domain analysis Frequency domain analysis Transient responses: -Impulse response -Step response -Ramp response Frequency responses: -Magnitude and phase spectrum -Bode plot x ( t ) y ( t ) x [ n ] y [ n ] System Output Input System Output Input
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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 6 Time-domain analysis: Transient response We refer to the output response as ‘Transient Response’, the process generated in going from the initial state to the final state. These responses will allow us to investigate the time domain characteristics of dynamic systems. Common test signals to produce the response include – Unit Impulse function Impulse response – Unit Step function Step response – Unit Ramp function Ramp response System System System time time time
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ELEC 215: Tim Woo Spring 2009/10 Chapter 5 - 7 Time-domain analysis: Transient response
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This note was uploaded on 03/27/2011 for the course ELEC 215 taught by Professor Prof.kamtimwo during the Spring '11 term at HKUST.

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Chapter-5-Transient-and-Frequency-responses-of-LTI-systems...

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