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 97.2 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 97.5 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 causal 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

Linear time-invariant discrete-time system If input is bandlimited and sampling frequency is high enough to avoid aliasing then overall system behaves as an Lti continuous-time system Hel iQT 丌 CID H(e/) D/C xa(t) yIn ya(t) effective T continuous-time specifications are converted to discrete time specifications by: a=5l,lejo\= T/ a i

5 ◆If input is bandlimited and sampling frequency is high enough to avoid aliasing, Linear time-invariant discrete-time system continuous-time specifications are converted to discrete time specifications by: ( ) , eff j H H j T e       =       = T, then overall system behaves as an LTI continuous-time system ( ) ( ) ( ), 0, j T c eff H e T H j H j T        =  =      effective

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

6 Stages of Filter Design ◆Determine the specification of the desired properties of the system. ◆The approximation of the specifications using(designing) 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(discrete-time system) l(e") < 0.w<w<兀 sn w n <n<0 2丌 2丌

7 Frequency-Selective Filters ◆Ideal lowpass filter (discrete-time system) ( )       = 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 Ideal highpass filter(discrete-time system) 0 Hh(en) <1 1,w<w<丌 m()=-51 0<n<O 丌n 2丌 2丌

8 Frequency-Selective Filters ◆Ideal highpass filter(discrete-time system) ( ) 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 discrete-time system) <w P 0. others

9 Frequency-Selective Filters ◆Ideal bandpass filter(discrete-time system) ( )     = 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 discrete-time system) < J l1, others 10

10 Frequency-Selective Filters ◆Ideal bandstop filter(discrete-time system) ( )     = 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

tolerance scheme容限图 Figure depicts the typical representation of the tolerance limits associated with approximating an ideal lowpass filter ler(n)l tolerance scheme discrete-time 1+a1 容限图 IH(ejm) 1-6 continuous-time 1+a1 Passband transition Stopband Passband i Transition W=OT Hle ow H 0

11 tolerance scheme 容限图 tolerance scheme 容限图 ◆Figure depicts the typical representation of the tolerance limits associated with approximating an ideal lowpass filter. w T =  continuous -time discrete-time ( ) eff jw w H H j T e   =    