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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

IIR


Iir

  • ButterworthChebyshev

  • IIR


Iir

6.1


Iir

1

1

a

b


Iir

2

LPHPBPBRF


Iir

3


Iir

2LP

LPHP


Lp bp

LPBP


Lp brf

LPBRF


Iir

3

  • 0.7073dB


Iir


Iir


Iir


Iir


Iir

4

  • :

    (1)

    (2)

    (3) DSP


Iir

5


Iir


Iir

3dB


Iir

6

H(z)


Iir


Iir

=


7 iir

7IIR

LSI

s

z


Iir

LSI

6.2


Iir


Iir

/2p

/ 0


Iir

mi

mo

pi

po


Iir

n < 0h(n) = 0

po = 0pi = N

1

2


Iir

n > 0h(n) = 0

po = Npi = 0

1

2


Iir

1

3

4

2n=0

5


Iir

w

6.3


Iir


Iir


Iir

  • N


Iir

H1(z)

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


Iir

H(z)

Hmin(z)

P231 66


Iir

2


Iir

3

Hap(z)


6 4 iir

s z

6.4 IIR

  • H(z) Ha(s)

    s z

  • Ha(s) H(z)

    s Re[s] < 0

    z |z| < 1


Iir

-

-

-


Iir

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


Iir


Iir

  • 2p/T


Iir

  • |W|>Ws/2

  • wc


Iir


Iir

  • s z

  • s

    z


Iir

T


Iir

IIR

T = 1s


Iir


Iir

  • h(n)ha(t)

  • w=WT


Iir

6.6

g(n)

ga(t)

T


Iir


Iir

Butterworth LPF

3dB50HzButterworth500Hz


Iir

T=1/500ZT

z-1


Iir

6.7


Iir

  • ,

  • ss1s1Z


Iir

  • c


Iir

c

1

2


Iir

z

s

z

s

1

2


Iir

s z


Iir

1

  • Ww

2


Iir

w1

W1w1


Iir


Iir


Iir

6.8

  • Butterworth

  • Chebyshev

  • Ellipse

  • Bessel


Iir

1

h(t)

Ha(s)

Ha(s)Ha(s)

Ha(s) Ha(-s)


Iir

  • s


Iir

K0


Iir

2

1 Butterworth

N

Wc

WcButterworth3


Iir

  • 3dB

1

WWstd1


Iir

2

Butterworth


Iir

  • sButtterworth2N

  • NN

Ha(s) Ha(-s)

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


Iir

3


Iir

4

  • N


Iir

N

Wc


Iir

  • Butterworth0.2p rad1dB0.3pp15dB

1

1

2T = 1 s


Iir

3Butterworth

a


Iir

b) N = 6

b)

c)

c)


Iir

4Ha(s):

Butterworth


Iir

Butterworth


Iir

1

2

2


Iir

3Butterworth

a


Iir

b)

c)


Iir

b) N = 6

c)


Iir

4Ha(s)Butterworth


2 chebyshev

2 Chebyshev

Type I Chebyshev

0<e<1e

Wc3dB

N

CN(x) NChebyshev


Iir

  • 1

  • 0

  • N

  • N


Iir

Chebyshev

  • Wc

  • e

  • N

Ws


Iir

Type II Chebyshev filter


Iir

  • Chebyshev0.2p rad1dB0.3pp15dB

1

2


Iir

3Chebyshev

a


Iir

b)


Iir

c)


Iir

b) N=4

c)


Iir

4 Chebyshev

Chebyshev


Elliptic filter

(Elliptic filter)


Bessel

Bessel

*


Iir

IIR


Iir

  • Butterworth

  • Chebyshev


6 9 iir

6.9 IIR


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