ELEC212 Chapter 6 Structures for Discrete-Time Systems

ELEC212 Chapter 6 Structures for Discrete-Time Systems -...

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1 The Hong Kong University of Science and Technology Department of Electronic and Computer Engineering ELEC 212 Chapter 6 Structures for Discrete-Time Systems 2 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Introduction ± An LTI system with a rational system function has the property that the input and output sequences satisfy a linear constant-coefficient difference equation (LCCDE). ± This lecture considers issues related to the implementation of LTI discrete-time systems. ± Will consider block diagram and signal flow graph representations of network structures for LTI causal systems described by LCCDE. ± Will also present a number of basic equivalent structures for implementing causal LTI systems. 3 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Block Diagram Representation of LCCDE 4 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Example: Second Order LCCDE
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5 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Higher Order LCCDE Direct Form I 6 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Higher Order LCCDE Direct Form II 7 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Example 8 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Signal Flow Graph Representation of LCC Equations ± A signal flow graph is another representation of LCCDE. ± A signal flow graph is a network of directed branches that connect at nodes . Associated with each node is a variable or node value. ± Two special types of nodes. Source nodes: nodes that have no entering branches Sink nodes: nodes that have only entering branches Example of nodes and branches in a signal flow graph Example of nodes and branches in a signal flow graph
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9 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Flow Graph Example 10 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Relationship Between Block Diagram and Signal Flow Graph 11 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Differences Between Block Diagram and Flow Graph Differences Between Block Diagram and Flow Graph ± Nodes in the flow graph represent both branching points and adders ± In the block diagram a special symbol is used for adders ± A branching point in the block diagram is represented by a node that has only one incoming branch and one or more outgoing branches in flow graph ± An adder in block diagram is represented by a node that has two or more incoming branches in flow graph 12 09-10 Fall ELEC 212 Structures for Discrete-Time Systems Example: Determination of the System Function from a Flow Graph Example: Determination of the System Function from a Flow Graph ± Apply z
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This note was uploaded on 03/27/2011 for the course ELEC 212 taught by Professor Prof.matthewmckay during the Spring '11 term at HKUST.

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ELEC212 Chapter 6 Structures for Discrete-Time Systems -...

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