山东大学：《生物医学信号处理 Biomedical Signal Processing》精品课程教学资源（PPT课件讲稿）Chapter 07 Filter Design Techniques

Chapter 7 Filter Design Techniques ◆7.0 Introduction 7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters 7.2 Design of FIR Filters by windowing 7.3 Examples of FIR Filters design by the Kaiser window method 7.4 Optimum Approximations of FIR Filters 7. 5 Examples of FIR Equiripple Approximation 7.6 Comments on Iir and FIr Discrete-Time Filters

2 Chapter 7 Filter Design Techniques ◆7.0 Introduction ◆7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters ◆7.2 Design of FIR Filters by Windowing ◆7.3 Examples of FIR Filters Design by the Kaiser Window Method ◆7.4 Optimum Approximations of FIR Filters ◆7.5 Examples of FIR Equiripple Approximation ◆7.6 Comments on IIR and FIR Discrete-Time Filters

Filter Design Techniques 7.0 Introduction

3 Filter Design Techniques 7.0 Introduction

7.0 Introduction Frequency-selective filters pass only certain frequencies Any discrete-time system that modifies certain frequencies is called a filter We concentrate on design of causa Frequency-selective filters

4 7.0 Introduction ◆Frequency-selective filters pass only certain frequencies ◆Any discrete-time system that modifies certain frequencies is called a filter. ◆We concentrate on design of causal Frequency-selective filters

Stages of Filter Design Determine the specification of the desired properties of the system The approximation of the specifications using a causal discrete-time system The realization of the system Our focus is on second step A Specifications are typically given in the requency domain

5 Stages of Filter Design ◆Determine the specification of the desired properties of the system. ◆The approximation of the specifications using a causal discrete-time system. ◆The realization of the system. ◆Our focus is on second step ◆Specifications are typically given in the frequency domain

Frequency-Selective Filters ◆ Ideal lowpass filter W<w 0,1。<lw<兀 SIn w n 0<n<O 元- 2丌

6 Frequency-Selective Filters ◆Ideal lowpass filter ( )       = w w  w w H e c j w c l p 0, 1, 0 wc − 2 − − wc  2 ( ) jw H e 1 ( ) = −   n   n w n h n c l p , sin 

Frequency-Selective Filters ◆ [deal highpass filter 0 W<<兀 h(n)=8[n 0<1<00 H 2丌 2丌

7 Frequency-Selective Filters ◆Ideal highpass filter ( ) 0, 1, jw c hp c w w H e w w     =      0 wc − 2 − − wc  2 ( ) jw H e 1 ( )   sin , c hp w n h n n n n   = − −    

Frequency-Selective Filters Ideal bandpass filter ww<w H 0. others H - 8

8 Frequency-Selective Filters ◆Ideal bandpass filter ( )     = others w w w H e j w c c bp 0, 1, 1 2 0 1 wc 1 − − wc  ( ) jw H e 1 2 wc 2 − wc

Frequency-Selective Filters ◆ Ideal bandstop filter H,(en) <1 others H -

9 Frequency-Selective Filters ◆Ideal bandstop filter ( )     = others w w w H e j w c c bs 1, 0, 1 2 0 1 wc 1 − − wc  ( ) jw H e 1 2 wc 2 − wc

Linear time-invariant discrete-time system If input is bandlimited and sampling frequency is high enough to avoid aliasing then overall system behave as a continuous-time system H T Ωm/T7 H(ejo) DIC xa(t x yIn ya(o) continuous-time specifications are converted to discrete time specifications by H H f <丌

10 ◆If input is bandlimited and sampling frequency is high enough to avoid aliasing, then overall system behave as a continuous-time system: ( ) ( )         =  T H e T H j j T eff   0, , Linear time-invariant discrete-time system ( ) , eff jw w H H j w T e    =      continuous-time specifications are converted to discrete time specifications by: w= T

Example 7.1 Determining Specifications for a Discrete-Time Filter H(e? Known Specifications of the continuous-time filter ◆1. passband1-001-()/T maX 2T T CD H(e/) D/C yIn ya(t) For bandlimited input aliasing avoided when sampling frequency s high enough

11 Example 7.1 ◆Specifications of the continuous-time filter: ◆1. passband ◆2. stopband 1− 0.01 H ( j) 1+ 0.01 for 0    2 (2000) eff Heff ( j)  0.001 for 2 (3000)   4 T s 10− = max ( ) 2 2 2 5000 2 f T T   ( )   = = = ( ), , 0, j T eff H e T H j T        =      For bandlimited input, aliasing avoided when sampling frequency is high enough Example 7.1 Determining Specifications for a Discrete-Time Filter H(ejw) ? Known: