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6.1 signal flow graph representation of linear constant- coefficient difference equations 6.2 basic structures for IIR system 6.2.1 direct forms 6.2.2 cascade forms 6.2.3 parallel forms 6.2.4 lattice structure 6.2.4 lattice structure 6.2.4 lattice structure 6.3 basic structures for FIR system 6.3.1 direct forms 6.3.2 cascade forms 6.3.3 structures for linear-phase FIR system 6.2.4 lattice structure 6.2.4 lattice structure 6.2.4 lattice structure CHAPTER6 Structures for discrete- time system

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6.1 signal flow graph （信号流图） representation of linear constant-coefficient difference equations When a linear time-invariant discrete-time system is implemented with discrete-time analog or digital hardware, the difference equation or the system function representation must be converted to an algorithm or structure that can be realized in the desired technology . The basic elements required for implementation of a linear time- invariant discrete-time system are adders , multipliers , and memory for storing delayed sequence values . The interconnection of these basic elements is conveniently depicted by signal flow graph.
Figure 6.8 Formally, a signal flow graph is a network of directed branches that connect at nodes （节点） . Associated with each node is a variable or node value. We often indicate the value of node k with the notation w k [n]. Branch (j,k) （支路） denotes a branch originating at node j and terminating at node k, with the direction from j to k being indicated by an arrowhead on the branch. If the output of the branch is a constant multiple or delay of the input to the branch, the constant or z -1 is shown next to the arrowhead. z -1 3

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Figure 6.9 节点：源、阱、网络 支路：常数、 z -1 1 -1 节点值 = 所有输入支路之和
w 2 [n] w 1 w 3 [n] - w 4 6 w 5 3 2 z -1 y[n] x[n] z z EXAMPLE 12 1 25 4 31 1 43 54 1 13 5 () () 6 () 3 () () 2 () Wz Xz Wz Wz z Wz Wz z Yz zWz W z W z =+ =− = = = + 2 1 1 18 1 ) 4 2 ( ) ( ) ( + + = z z z z X z Y 2 1 1 18 1 ) 4 2 ( ) ( ) ( ) ( + + = = z z z z X z Y z H ] 1 [ 4 ] [ 2 ] 2 [ 18 ] 1 [ ] [ + = + n x n x n y n y n y

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6.2 basic structures for IIR system

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## This note was uploaded on 02/29/2012 for the course EE 325 taught by Professor Lilili during the Fall '11 term at BYU.

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