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
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 He (jo2) ∫Hm)pl兀, CID H(ejo) DIC xa(t x yIn y T continuous-time specifications are converted to discrete time specifications by: w=T, H(e/)=Hor(G ").b V<丌 5
5 ◆If input is bandlimited and sampling frequency is high enough to avoid aliasing, then overall system behaves as an LTI 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 =
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 L 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) W<w 0,1。<lw<兀 SIn w n 0<n<O 元- 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 W<<兀 h(n)=8[n 0<1<00 H 2丌 2丌 8
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) ww<w H 0. others H -
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 H,(en) <1 others H -
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 lHer(in)l tolerance scheme discrete-time 1+6 容限图 H(e°) 1-61 continuous-time 1+1 Passband i Transition Stopband Passband i Transition W=QT 6 he/=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 =
