CHAPTER 6 Digital Filter Structures

1. CHAPTER 6 Digital Filter Structures Wang Weilian wlwang@ynu.edu.cn School of Information Science and Technology Yunnan University 2005-09 ~ 2006-01

2. Outline • Block Diagram Representation • Equivalent Structures • Basic FIR Digital Filter Structures • Basic IIR Digital Filter Structures • FIR Cascaded Lattice Structures • Summary 云南大学课程：数字信号处理

3. Block Diagram Representation • Digital filters • The difference equation • A first-order causal LTI IIR digital filter: • Knowing the initial condition y[-1] and the input x[n] for , we can computer y[n] for 云南大学课程：数字信号处理

4. Block Diagram Representation • An LTI digital filter can be conveniently represented in block diagram form using the basic building blocks representing theunit delay, the multiplier, the adder and the pick-off nods. • e.g. : A first-order LTI digital filter 云南大学课程：数字信号处理

5. Equivalent Structures • Two digital filter structures is equivalent if they have the same transfer function. • There are a number of methods for the generation of equivalent structures: • ( i ) Reverse all paths, • ( ii ) Replace pick-off nodes by adders, and vice versa, • ( iii ) Interchange the input and the output nodes. 云南大学课程：数字信号处理

6. Basic FIR Digital Filter Structures • Direct forms • In the time-domain: • The transfer function: • An FIR filter of order N requires N+1 multipliers and N two-input adders for implementation in general. 云南大学课程：数字信号处理

7. Basic FIR Digital Filter Structures • Direct Forms Direct form FIR structures 云南大学课程：数字信号处理

8. Basic FIR Digital Filter Structures • Cascade Form • 2L=N unit delays，2L+1=N+1multipliers，2L=Nadders Cascade form FIR structure 云南大学课程：数字信号处理

9. Basic FIR Digital Filter Structures • Linear-Phase FIR Structures • A linear-phase FIR filter of order N • The symmetric impulse response: • The antisymmetric impulse response: Linear-phase FIR structure 云南大学课程：数字信号处理

10. Basic IIR Digital Filter Structures • Direct Forms • An Nth-order IIR digital filter transfer function requires 2N+1 multipliers and 2N two-input adders for implementation in general. 云南大学课程：数字信号处理

11. Basic IIR Digital Filter Structures • Direct Forms Direct form I Direct form It 云南大学课程：数字信号处理

12. Basic IIR Digital Filter Structures • Cascade Realizations • Various different cascade realizations of H(z) can be obtained by different pole-zero polynomial pairings. • Usually, the polynomials are factored into a product of first-order and second-order polynomials. • e.g. : 云南大学课程：数字信号处理

13. Basic IIR Digital Filter Structures • Cascade Realizations Cascade realization of a IIR transfer function 云南大学课程：数字信号处理

14. Basic IIR Digital Filter Structures • Parallel Realizations • Making use of the partial-fraction expansion of the transfer function: • The parallel form I: • The parallel form II: 云南大学课程：数字信号处理

15. Basic IIR Digital Filter Structures • Parallel Realizations Parallel realization of a IIR transfer function 云南大学课程：数字信号处理

16. FIR Cascaded Lattice Structures • Realization of Arbitrary FIR Transfer Functions • All-Zeros filter: • From fig 6.39: 云南大学课程：数字信号处理

17. Summary • The realization of a causal digital transfer function, called structures, are usually represented in block diagram forms that are formed by interconnecting adders, multipliers, and unit delays. • The structure can be analyzed to develop its input-output relationship either in the time-domain or in the transform-domain. 云南大学课程：数字信号处理