Chapter-7-Structures-for-LTI-systems-Student

Chapter-7-Structures-for-LTI-systems-Student - Chapter 7:...

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ELEC 215: Tim Woo Spring 2009/10 Chapter 7 - 1 Chapter 7: Structures for LTI systems Spring 2009/010 Lecture: Tim Woo
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ELEC 215: Tim Woo Spring 2009/10 Chapter 7 - 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 7 - 3 Expected Outcome • In this chapter, you will be able to – Implement a system function with linear constant-coefficient differential or difference equation by structures with basic elements • Adders • Multipliers • Integrators / Delays – Construct the same system function with different structures for realization of causal continuous-time (or discrete-time) LTI system. – Compare the computational complexity of different structures – Compare the robustness design in different structures
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ELEC 215: Tim Woo Spring 2009/10 Chapter 7 - 4 Outline • Textbook – Section 9.8.2 Block Diagram Representations for Causal LTI systems Described by Differential Equations and Rational System Functions – Section 10.8.2 Block Diagram Representations for Causal LTI systems Described by Difference Equations and Rational System Functions • Reference book – A. V. Oppenheim, et. al., Discrete-time Signal Processing , 2nd edition, Prentice-Hall, 1999 – Section 6.1 Block Diagram representation of linear constant- coefficient difference equations – Section 6.3 Basic Structures for IIR systems – Section 6.7 The effects of coefficient quantization
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ELEC 215: Tim Woo Spring 2009/10 Chapter 7 - 5 Introduction As discussed in Chapter 4, a LTI system with a rational system function has the property that the input and output sequence satisfy a linear constant-coefficient differential (or difference) equation. When such systems are implemented with analog (or digital) hardware, the differential (or difference) equation must be converted to an algorithm or structure that can be realized in the desired technology. In this chapter, we will construct the system function by structures consisting of an interconnection of the basic operations of addition, multiplication by a scalar, and integrator (or delay).
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ELEC 215: Tim Woo Spring 2009/10 Chapter 7 - 6 Consider the difference equation, the output signal y [ n ] at time instant n requires y [ n -1 ], …., y [ n-N ] and x [ n ], x [ n -1 ], …., x [ n-M ]. Introduction
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Chapter-7-Structures-for-LTI-systems-Student - Chapter 7:...

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