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第六章 IIR 滤波器的设计 PowerPoint PPT Presentation


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第六章 IIR 滤波器的设计. 主要内容. 理解数字滤波器的基本概念 了解最小相位延时系统 理解全通系统的特点及应用 掌握冲激响应不变法 掌握双线性变换法 掌握 Butterworth 、 Chebyshev 低通滤波器的特点 了解利用模拟滤波器设计 IIR 数字滤波器的设计过程 了解利用频带变换法设计各种类型数字滤波器的方法. 6.1 引言. 数字滤波器:. 是指输入输出均为数字信号,通过一定运算关系改变输入信号所含频率成分的相对比例或者滤除某些频率成分的器件。. 优点:. 高精度、稳定、体积小、重量轻、灵活,不要求阻抗匹配,可实现特殊滤波功能.

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第六章 IIR 滤波器的设计

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IIR


  • ButterworthChebyshev

  • IIR


6.1


1

1

a

b


2

LPHPBPBRF


3


2LP

LPHP


LPBP


LPBRF


3

  • 0.7073dB






4

  • :

    (1)

    (2)

    (3) DSP


5



3dB


6

H(z)



=


7IIR

LSI

s

z


LSI

6.2



/2p

/ 0


mi

mo

pi

po


n < 0h(n) = 0

po = 0pi = N

1

2


n > 0h(n) = 0

po = Npi = 0

1

2


1

3

4

2n=0

5


w

6.3




  • N


H1(z)

1H(z)Hap(z)Hmin(z)


H(z)

Hmin(z)

P231 66


2


3

Hap(z)


s z

6.4 IIR

  • H(z) Ha(s)

    s z

  • Ha(s) H(z)

    s Re[s] < 0

    z |z| < 1


-

-

-


x

(

t

)

y

(

t

)

a

a

h

(

t

)

a

=

y

(

n

)

y

(

nT

)

a

=

x

(

n

)

x

(

nT

)

a

=

h

(

n

)

h

(

nT

)

a

6.5

h(n)

ha(t)

T



  • 2p/T


  • |W|>Ws/2

  • wc



  • s z

  • s

    z


T


IIR

T = 1s



  • h(n)ha(t)

  • w=WT


6.6

g(n)

ga(t)

T



Butterworth LPF

3dB50HzButterworth500Hz


T=1/500ZT

z-1


6.7


  • ,

  • ss1s1Z


  • c


c

1

2


z

s

z

s

1

2


s z


1

  • Ww

2


w1

W1w1




6.8

  • Butterworth

  • Chebyshev

  • Ellipse

  • Bessel


1

h(t)

Ha(s)

Ha(s)Ha(s)

Ha(s) Ha(-s)


  • s


K0


2

1 Butterworth

N

Wc

WcButterworth3


  • 3dB

1

WWstd1


2

Butterworth


  • sButtterworth2N

  • NN

Ha(s) Ha(-s)

(a) N=4 ( (b)N=4


3


4

  • N


N

Wc


  • Butterworth0.2p rad1dB0.3pp15dB

1

1

2T = 1 s


3Butterworth

a


b) N = 6

b)

c)

c)


4Ha(s):

Butterworth


Butterworth


1

2

2


3Butterworth

a


b)

c)


b) N = 6

c)


4Ha(s)Butterworth


2 Chebyshev

Type I Chebyshev

0<e<1e

Wc3dB

N

CN(x) NChebyshev


  • 1

  • 0

  • N

  • N


Chebyshev

  • Wc

  • e

  • N

Ws


Type II Chebyshev filter


  • Chebyshev0.2p rad1dB0.3pp15dB

1

2


3Chebyshev

a


b)


c)


b) N=4

c)


4 Chebyshev

Chebyshev


(Elliptic filter)


Bessel

*


IIR


  • Butterworth

  • Chebyshev


6.9 IIR


  • Login