86 structures for discrete-time system 6.0 Introduction 6. 1 Block Diagram Representation of Linear Constant-Coefficient Difference Equations 6.2 Signal Flow Graph Representation of Linear constant-Coefficient difference Equations 6. 3 Basic structures for iir Systems 6. 4 Transposed Forms 6.5 Basic Network structures for Fir Systems
2 6.0 Introduction 6.1 Block Diagram Representation of Linear Constant-Coefficient Difference Equations 6.2 Signal Flow Graph Representation of Linear Constant-Coefficient Difference Equations 6.3 Basic Structures for IIR Systems 6.4 Transposed Forms 6.5 Basic Network Structures for FIR Systems §6 structures for discrete-time system
Structures for discrete-time Systems 6.0 Introduction
3 Structures for Discrete-Time Systems 6.0 Introduction
6.0 Introduction haracterization of an LTI System: ◆ Impulse Response→ Frequency response Z-Transform: system function ◆ Difference equation converted to a algorithm or structure that can be realized in the desired technology when implemented with hardware Structure consists of an interconnection of basic operations of addition, multiplication by a constant and delay
4 Characterization of an LTI System: ◆Impulse Response ◆z-Transform: system function ◆Difference Equation ◆converted to a algorithm or structure that can be realized in the desired technology, when implemented with hardware. ◆Structure consists of an interconnection of basic operations of addition, multiplication by a constant and delay 6.0 Introduction →Frequency response
xample: find the output of the system h()=+h zab with input x[nI Solution 1 I -az IIR Impulse n=bauIntba-uln Response {m]=xp]*小]=∑x[l]h[n-1]=∑小]x[n- k=0 even if we only wanted to compute the output over a finite interval. it would not be efficient h(n-k k 5 Illustration for the iir case by convolution
even if we only wanted to compute the output over a finite interval, it would not be efficient to do so by discrete convolution since the amount of computation required to compute y[n] would grow with n . 5 Example: find the output of the system 1 0 1 1 ( ) , | | | |, 1 b b z H z z a az − − + = − 1 0 1 1 − = + − n n h n b a u n b a u n 0 n k k y n x n h n x k h n k h k x n k =− = = = − = − Illustration for the IIR case by convolution IIR Impulse Response with input x[n]. Solution1:
Example: find the output of the system bo+bE Y() H(E)1-a2(),|=plal, with input x[n] Solution2: yn n-avln =bx{小]+bx1[n-1] y[n]=ay[n-1]+box[n]+bjx[n-1] computable recursively The algorithm suggested by the equation is not the only computational algorithm, there are unlimited variety of computational structures(shown later)
6 Example: find the output of the system 1 0 1 1 ( ) , | | | |, 1 ( ) ( ) b b z H z z a az Y z X z − − = + = − y n ay n b x n b x n − − = + − 1 1 0 1 y n ay n b x n b x n = − + + − 1 1 0 1 computable recursively The algorithm suggested by the equation is not the only computational algorithm, there are unlimited variety of computational structures (shown later). with input x[n]. Solution2: