Ex,6,2 draw Direct Form i and direct Form II implementation of an LTI system Solution xn 1.5 yn-1 x[n-1] 0.9 wIn y[n-2 1O-y[n 1.5 1+2z H(z)= 0.9 n2] 1-1.5z1+0.9z2
23 Ex. 6.2 draw Direct Form I and Direct Form II implementation of an LTI system 1 1 2 1.5 1 2 ( ) 1 0.9 z H z z z − − − + + = − x[n] + z −1 z −1 + 1.5 − 0.9 y[n] w[n-1] w[n-2] + 1 2 w[n] + z −1 1 2 x[n] x[n-1] + z −1 z −1 + 1.5 − 0.9 y[n] y[n-1] y[n-2] v[n] Solution:
Structures for Discrete-Time Systems 62 Signal Flow Graph(信号流图) Representation of Linear Constant Coefficient Difference equations
24 Structures for Discrete-Time Systems 6.2 Signal Flow Graph(信号流图) Representation of Linear ConstantCoefficient Difference Equations
6.2 Signal Flow Graph Representation of linear Constant-Coefficient Difference Equations LA Signal Flow Graph is a network of directed branches(有向支路) that connect at nodes(节点) associated with each node is a variable or node value, being denoted win 梅森( Mason) 信号流图 Wun N ode Node k 25
25 6.2 Signal Flow Graph Representation of Linear Constant-Coefficient Difference Equations Associated with each node is a variable or node value, being denoted wj [n]. ◆A Signal Flow Graph is a network of directed branches (有向支路)that connect at nodes(节点). wj [n] wk [n] Node j Node k 梅森(Mason) 信号流图
Nodes and branches We will only consider linear Signal Flow Graph Input w;n Output A linear transformation of input such as constant gain and unit delay if omitted, it indicates unity In a or zA/wk[n] Node Node k Brach (, k) Each branch has an input signal and an output signal An internal node serves as a summer. i. e. its value is the sum of outputs of all branches entering the node
26 Nodes And Branches wj [n] wk a or z-1 [n] Brach (j, k) Each branch has an input signal and an output signal. Input wj [n] Output: A linear transformation of input, such as constant gain and unit delay. We will only consider linear Signal Flow Graph An internal node serves as a summer, i.e., its value is the sum of outputs of all branches entering the node. Node j Node k if omitted, it indicates unity
Source nodes(源点) Nodes that have no entering branches Source node j wkn o Sink node k Sink nodes(汇点) Nodes that have only entering branches
27 Source Nodes (源点 ) ◆Nodes that have no entering branches xj [n] wk [n] Source node j Sink Nodes (汇点 ) ◆Nodes that have only entering branches yk w [n] j [n] Sink node k