實(shí)驗(yàn)7-窗函數(shù)法設(shè)計(jì)FIR濾波器

實(shí)7-窗函數(shù)法設(shè)器

dccdsin[dccdsin[ωα)]實(shí)驗(yàn)窗函數(shù)法計(jì)數(shù)字濾器一、實(shí)驗(yàn)?zāi)康恼拼皵?shù)設(shè)字波的理具方。二、實(shí)驗(yàn)設(shè)備環(huán)境計(jì)機(jī)MATLAB件境三、實(shí)驗(yàn)基礎(chǔ)論1基原窗數(shù)計(jì)的本想，先擇個(gè)當(dāng)理的Hj然用函截它單脈響h，到性位dd和果FIR波這種法重是擇個(gè)適窗數(shù)理想濾器設(shè)的波的位沖應(yīng)近想波的位脈響。2設(shè)步(1)給理濾器頻響H

jω

，通上有位益線相，阻上有響。個(gè)寬ω(ω通波由式定

<π)的低H

jω

1?eαω){0ω

|ω|ωc<|ω|πc

(7-1)其α為樣遲其用為得因的統(tǒng)(2)定個(gè)波的位沖應(yīng)h

d

()cα)

(7-2)為得一(n)長(zhǎng)度為N因的性位波，們

????????????令α=

N2

(7-3)(3)窗數(shù)取h

d

()到設(shè)計(jì)FIR數(shù)字濾波nhn=h

d

n)

(7-4)3.函的擇常的函有形）窗、寧）窗海（窗布克窗凱（Kaiser窗提供一函用產(chǎn)窗數(shù)如7-1示表7-1MATLAB中生函的令MATLAB函數(shù)boxcarhanninghannming

窗函數(shù)MATLAB函數(shù)矩形窗函blackman漢寧窗函kaiser海明窗函

窗函數(shù)布萊克曼函數(shù)凱瑟窗函在計(jì)程我需根給的波技指選濾器長(zhǎng)和窗函數(shù)（n表7-2列出了常窗數(shù)一特，可供設(shè)時(shí)考表7-2常窗數(shù)特窗函數(shù)

窗函數(shù)頻率特性

加窗后濾波器指標(biāo)矩形窗

旁瓣峰值-13

主瓣寬度4πN

過(guò)渡帶寬

最小阻帶衰減（dB）1.8-21N漢寧窗-31海明窗-41

8π8π

NN

6.26.6π

NN

-44-53

??I00pssβ=??I00pssβ={布萊克曼-57

12π

N

11π

N

-74凱窗一在際用廣應(yīng)的函，由式定W(n)=

0

[β√1I[β]

2nN

]

0≤n≤N-1（7-5）其I

[x]是正零貝函參β制小阻衰這窗數(shù)于同N可以供同過(guò)帶由貝爾數(shù)較雜，這種窗函數(shù)設(shè)方很推，然而幸的是有些驗(yàn)計(jì)程以接用已給的標(biāo)，ω，R，波長(zhǎng)凱窗ps數(shù)可按下瑟設(shè)方給：過(guò)帶：ω=ω

ωstp

N≈

A?7.95

+1

0.1102)≥50ssA(A21)A<50sss）四、實(shí)驗(yàn)內(nèi)容1設(shè)一數(shù)低濾波器其術(shù)標(biāo)下ω

p

=π,R=0.25dBp

ω

st

=0.3π,=s分采矩窗漢窗海窗布克窗凱窗計(jì)濾器結(jié)實(shí)結(jié)，分別討采上方設(shè)的字波是否能足定標(biāo)求實(shí)代及果矩窗===N+1n===h'fill');tight;xlabel('n'ylabel('hd(n)'w1]=tight;xlabel('\omega/\pi'ylabel('H(\omega)''fill');tight;xlabel('n'

)()()()()()(ylabel('h(n)'=1);xlabel('\omega/\pi'ylabel('dB'on;10.2ndh

0.10

0.5H005

1015

00.20.40.60.8n

00.2nh

0.1

Bd

-50005

1015

-10000.5

1n

：

)()()()()()()()()()()()(10.2ndh

0.1

H

0.50020

4060

0

00.20.40.60.8n

nh

0.20.150.10.050

Bd

0-50-100-150020

4060

-20000.5

1n

：10.2ndh

0.1

H

0.50020

4060

0

00.20.40.60.8nh

n00.20.15-50B0.1d0.05-100

0020

4060

-15000.5

1n

)()()()()()(：1ndh

H

00n

0

0

0nh

Bd0

0n

0

1窗：===N+1=n===h'fill');

)()()()()()(tight;xlabel('n'ylabel('hd(n)'w1]=tight;xlabel('\omega/\pi'ylabel('H(\omega)''fill');tight;xlabel('n'ylabel('h(n)'=1);xlabel('\omega/\pi'ylabel('dB'on;1ndh

H

00

40

0

00.20.40.60.8nh

n00.15-50Bd0.05-100

00

40

-150

00.5

1n

st1sp2pst2sst1sp2pst2s2設(shè)一數(shù)帶濾波器其術(shù)標(biāo)下下帶緣=0.2下帶緣

p1

=0.35R=1dBp上帶緣=0.65R=1dB上帶緣=0.8實(shí)代及果矩窗====+====+NN2)n======h'fill');tight;

)(h)()()(h)()(xlabel('n'ylabel('hd(n)'w1]=tight;xlabel('\omega/\pi'ylabel('H(\omega)''fill');tight;xlabel('n'ylabel('h(n)'=1);xlabel('\omega/\pi'ylabel('dB'on;nd

0-0.2

H

1005

10

00.20.8n

nh

0

Bd

0-0.205

10

0

1n

)()()()()()()()()()()()(ndh

：0.40.20

H

10.5-0.201020n

0

00.20.40.60.8nh

0.40.20

Bd

0-50-0.201020

-100

00.5

1n

Hamming窗0.40.2

1ndh

0

H

0.5-0.201020n

3040

0

00.20.40.60.8nh

0.40.20

Bd

0-50-0.201020n

3040

-10000.5

1

)()()()()()(Blackman窗0.40.2

1ndh

0

H

0.5-0.202040n

60

0

00.20.40.60.8nh

0.40.20

Bd

0-50-100-0.202040n

60

-15000.5

1Kaiser窗====1====1NN2)=n

======h'fill');tight;xlabel('n'ylabel('hd(n)'w1]=tight;xlabel('\omega/\pi'ylabel('H(\omega)''fill');tight;xlabel('n'ylabel('h(n)'=1);xlabel('\omega/\pi'ylabel('dB'on;

)()()()()()(10.2ndh

0

H

0.5-0.201020

3040

0

00.20.40.6