Title: DSP 8 FIR Filter Design ?????????????????????????? FIR
1DSP 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
6FIR Filter Design
- ????????? FIR ????????????????????????????????????
??????????? (Linear phase) ???????????????????????
??????? ????????????????? (Magnitude) ???????? - ??????????? 2 ??????????????
- ??????????????????????? (Window Method)
- ????????? FIR ???????????????????? (Frequency
Sampling Method)
7Low pass filter (LPF )
High pass filter (HPF)
Band pass filter (BPF)
Band stop filter (BSF)
8?????????????????????????????????? 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)
13?????????????????????
n
n
n
?????????????? h(n)
?????????????????????? w(n) ????
N ?????? (order) ?????????? M(N-1)/2
14????????????????? ???????????????????????
?????????
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
24????????????????? h(n) ??????????
ex_7_2.eps
25??????????????????
-21 dB
26???????? ???????
-44 dB
27???????? ????????
-74 dB
28???????????2
?????????????????????? ??????????????? 2 kHz
??????????
???? ???????????????????? ??? ????????????????????
?????
291. ???????????????????
??????????? ???
?????????????? ???????? ???????????
???
???????????
??????????? ???????????
??????? ?????????????????????
302. ?????????????
??? ????????????????????? ????? ?????????????
???????? 7.2 ?????????? ??????????????????????????
??? 0.3 ??? ?????????????????? (8.9)
?????????????????? (0.63) ???????????
????????????????? ??? ???????????????
(0.22) ???????????????? (0.02)
31??????????????? (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)')
34????????? 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 ???????????
- ?????????????????????????? ??????????????
- ??????????????????????????? ??????????????????????
???????? ????????????????????????? - ????????????????????????????????
?????????????????????????????????????