DSP 8 FIR Filter Design ?????????????????????????? FIR

1
DSP 8FIR Filter Design ?????????????????????????
? FIR
??. ?????? ????????????? ???????
??????????????????????
2
???????? FIR

• ???????????? (stable)
• ?????????????????????????????? ????????????
  (Linear phase) ???????

3
?????????????????? (linear phase)
??????
a????????
??????? FIR ?????? ???????????????
????????????????????????
4
?????????????????????????????

• ?????????????????????? h(n)

0
1
2
3
4
N ??????
?????? (symmetric)
0
1
2
3
4
5
N ??????
N ??????
0
1
2
3
4
?????? ?????????? (Anti-symmetric)
0
N ??????
1
2
3
4
5
5
???????????h(n) ???? ?????? ??? N ??????????
???? ??? n0,,N-1
????????
???????????
????
???
??????
???????? ???????? h(n) ??? ??????,N ??????
????????????? FIR
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FIR Filter Design

• ????????? FIR ????????????????????????????????????
  ??????????? (Linear phase) ???????????????????????
  ??????? ????????????????? (Magnitude) ????????
• ??????????? 2 ??????????????
• ??????????????????????? (Window Method)
• ????????? FIR ???????????????????? (Frequency
  Sampling Method)

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Low pass filter (LPF )
High pass filter (HPF)
Band pass filter (BPF)
Band stop filter (BSF)
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?????????????????????????????????? LPF
9
???????????????????????????????
????????????????????????? d(n) ??? ?????????
noncausal ?????????????????????? ???
(approximation)
10
????????????????????????
?????????? (Cut-off frequency)
11
?????????????????????????????????? ????????
?????? M ?????
12
???????????????? FIR ??????????????
????????(Windowing Techniques)

• ????????????????
• 1. ??????????? d(n) ???????? M ?????
• 2. ??????????? d(n) ??????????????????( infinite)
  ?????????? ????? (finite) ????????????????
  ???????? (window)

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?????????????????????

n
n
n
?????????????? h(n)
?????????????????????? w(n) ????
N ?????? (order) ?????????? M(N-1)/2
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????????????????? ???????????????????????
?????????
15
?????????????????????????????????
???????????????
???????? ???????
??????????????????????? ?????????????????? 1
???????? ????????????????????? 2
?????????????????
16
??????????????????????????(Filter specification)
???????
???????
??? ???????
17
????????????????????????????
???????(Main lobe)
??????? (sidelobe)
??????????????????????
18
???????? ??????????? 7.2 ??????? ? ?????
???????? As
?????????? 8.9 21 1
???????(Hanning) 0.63 44
??????? (Hamming) 0.22 53
???????? (Blackman) 0.02 74
19
???????????????????? FIR ??????????????

• ??? ????????????????????? ( ) ????
  ?????????????????? As ?????????????????????????
  (?????????????? ?????????????????????????)
• ??? ????????????????????????? ( ) ??
  ?????? (order) ?????????? (N) ??????????
• ?????? d(n) ?????????? M ??????? ????????
• h(n)d(n-M)w(n), n0,,N-1
• ?? h(n) ?????? ?? ??????? ??? ??? ???????

20
???????? 1

• ??????????????? FIR LPF ?????????????????? 500 Hz
  ?????? ?????????????????? ??? ???????????????????
  ???????? 90 Hz ?????????????????? (fs) 2 kHz

21
???????? 1 (???)
?????????? ???????
????????????????? ???????
??????????? 7.2
????????? ??????????
??????????????????????? ??????? 44.44 ???????
N45
22
???????? 1 (???)
23
?????????????????????????????????
500 Hz
ex_7_1.eps
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????????????????? h(n) ??????????
ex_7_2.eps
25
??????????????????
-21 dB
26
???????? ???????
-44 dB
27
???????? ????????
-74 dB
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???????????2
?????????????????????? ??????????????? 2 kHz
??????????
???? ???????????????????? ??? ????????????????????
?????
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1. ???????????????????
??????????? ???
?????????????? ???????? ???????????
???
???????????
??????????? ???????????
??????? ?????????????????????
30
2. ?????????????
??? ????????????????????? ????? ?????????????
???????? 7.2 ?????????? ??????????????????????????
??? 0.3 ??? ?????????????????? (8.9)
?????????????????? (0.63) ???????????
????????????????? ??? ???????????????
(0.22) ???????????????? (0.02)
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??????????????? (0.22)
?????????????????
????????????????? ???????
??????????? 7.2 ???????????????
??????????????????
?????? ???????????????????????????? 200 ???????
N201
32
???????????????? (0.02)
??????????? 7.2 ????????????????
???????? ??????????
?????? ???????????????????????????? 300 ???????
N301
33
window.m demonstrating of the window design
technique fc500 fs2000 N41 M(N-1)/2 wc2p
ifc/fs n0N-1 we can add a smallest
number 'eps' to avoid dividing by zero
dsin(wc(n-Meps))./(n-Meps)/pi uncomment
lines below for different windows wones(1,N)
Rectangular w.5-.5cos(2pin./(N-
1)) Hanning w.42-.5cos(2pin./(N-1)).08co
s(4pin./(N-1)) blackman hd.w figure(1)subp
lot(111)freqres(h,1,fs,'db') figure(2)subplot(11
1)stem(h) grid on xlabel('n') ylabel('h(n)')
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????????? FIR ???????????????????? (Frequency
Sampling Techniques)
????????????????????????? ??????????????????? ???
DFT ???????????????????????? ??????? 7
??????????????????????????????????????????????
1
35
??????????? ????????????????????????????????????
FIR Frequency Sampling ?? DSP 7
???????????????????????
??? ?????? h(n) ???????????????????????????? DFT
?????? ???????????????????
36
??????????????????????????????
???
??????
???????
???
37
????? N ?????????? ????????
1
10
1
3
0
2
20
38
???????????????????????? FIR ??????????
????????????? 2 kHz ??????????? (fs) 10 kHz
??????????????? 21 ???
????????
??????
?????????? ???????
?????????? ??? ???????????
??????????????? ??? ???????????
39
???????????????????????????????????
1
40
???????? 21 ???
ex_8_8.eps
41
????????????????????? 61 ???
?????????? ??? ???????????
??????????????? ??? ???????????
42
???????? 61 ???
??????????????
???????????????????? ???????? 21 ???
ex_8_9.eps
43
freq_sampl.m demonstrating low-pass design for
FIR fs10000 ??????????? 10 kHz wc
0.4pi ????????????????? N21
??????????????????????????? Mp
ceil(wcN/(2pi)) ?.?. ??? ?????????? 0ltwltpi
MppMp-1 ?.?. ??? ??????????
piltwlt2pi Ms N-Mp-Mpp ?.?. ???
?????????? 0ltwltpi Hones(1,Mp) zeros(1,Ms)
ones(1,Mpp) ?????????????? k01N-1
?? N ??????? HH.exp(-jpi(N-1)k/N)
?????????????? hreal(ifft(H))
???????????????????????????? figure(1) freqres(h,
1,fs)
44
????

• ???????????????? FIR ???????????
• ?????????????????????????? ??????????????
• ??????????????????????????? ??????????????????????
  ???????? ?????????????????????????
• ????????????????????????????????
  ?????????????????????????????????????