???????

1
?????????

• 2002.5.28

2
???????

• ????????
• ??????
• ???????
• ????????
• ????????
• ?????????????????
• ?????????????????????
• ?????????????
• ???????????
• ?????????????????
• ?????????
• ?????????????(????????)
• ???????? (DFT, FFT)
• DFT?????????????
• MATLAB(?????????)????????????

?
?
3
?????

• ??????????
• ?????????????????????????????
• ???FFT?????
• ????????
• ??????
• ??????(????)
• Z??(????)
• Z????????????????????

4
???????(???)????????????????
(?)????????
?????????????
???????? (????????? Laplace??,Z?????)
???(??????????? ???????????????)
??????(?????)
?????????????????
??????????
5
FFT?????????????? FFT (DFT)????
A/D??
???????? ?????
???? N?
??????
??????
FFT????????????????
FFT
??????
(??????2????)
???????? (????????????)
Hz???????
???????????
6
FFT?????????????? ??????????????
?????3.2s ????

• -0.0433
• 0.3991
• 0.0010
• 0.0836
• -0.1682
• -0.1237
• -0.3928
• 0.6362
• 0.1327
• 0.1031
• -0.1061
• 0.0594
• -0.7124
• 0.5028
• 0.3991
• 0.0227
• 0.1067
• -0.0054
• -0.4223

0.2865 -0.4039 - 0.2695i -0.3387
0.0922i -0.2183 - 0.3678i 0.3589 0.5210i
0.0980 - 4.2816i -0.0829 0.0915i -0.2634
0.2688i -0.5076 - 0.1058i -0.4996 0.0068i
0.7744 - 4.7456i 0.2837 0.9688i 0.2713
0.4669i -0.1144 - 0.4914i 0.0467 0.5260i
-0.0816 - 3.4903i -0.3160 -0.0816
3.4903i 0.0467 - 0.5260i -0.1144
0.4914i 0.2713 - 0.4669i 0.2837 - 0.9688i
0.7744 4.7456i -0.4996 - 0.0068i -0.5076
0.1058i -0.2634 - 0.2688i -0.0829 - 0.0915i
0.0980 4.2816i 0.3589 - 0.5210i -0.2183
0.3678i -0.3387 - 0.0922i -0.4039 0.2695i
0 Hz 0.3125Hz 0.625Hz 0.9375Hz
1.25Hz 1.5625Hz 1.875Hz 2.1875Hz 4.
375Hz 4.6875Hz 5Hz
FFT
????(1-16)? ???????? ???????
f(n)
F(n)
32?
32?
(??)?????f(n)?????? 1???(N/21)??????????? ???????
?????????1???17???
7
FFT?????????????? ???????????????????????
?????
????
????
FFT
IFFT
??(???) ???????
??(???) ???????
??????? ???
????????? ???
?????
8
FFT?????????????? ???
6Hz
5.5Hz
??????????? ????????
?????? ?????
9
FFT?????????????? ???
??????? ??????? ?????????
?????????? ????????
????????? ????????? ?????????
????????
10
FFT?????????????????
???????? ???????
11
FFT??????????????????????
???
?????
?????
???????
??????? ??????
12
FFT?????????????? ?????????????

• ???????????????????????
• ???????????????????????
• A/D?????
• ???????????(????????????2????????????)
• ????0???
• ?????0?????
• ???????
• FFT?????
• ?????????????????????
• ??????????????????????????s(?????????????????????)

13
Z?????????
14
?????????????
L
x(t)
y(t)

• ??????????????????????????????????????????????????
  ?????????????????????????

(?)???2?????????2?????????????????
???2?????????4?????????????????????
15
??????????????

• ????????????????(??????)????????????????
• ????????????????????????????(linear time
  invariant)?????

16
??????d??????????
?????????????????????????? ??????(??)(Convolution)
???????
?????????????????d(n)???????
0
T
2T
3T
17
?????? d??????????
???????0??????(??d(t))?????? ??????????????
d(t)
h(t)
??????
?????
???????
18
?????????????
???? ???
x
1.0
0.8
0.7
x(t)
y(t)
0.5
0.3
y
????????????
2
0
3
1
4
?????
19
???????????????????
???????????????????????t0????????????h(t)???
???????
???????? ??????(Convolution) ????
x???????????? d????????????
20
?????????????????
????????????????????? t0????????????????h(n)??? ?
????????x(n)???????????y(n)?? ????????????????????
????????
?????
?????
(??????????? ???????)
21
???????????????
??????????????????? ??????????????? ???????h(t)???
???? ??????x(t)?????? ??y(t)???????????
22
????????????????
?????????????(??)???????????????????s(sj?)?????
???????????????????????????????????????????
?????????
j????? sj????
23
????????????????
??????????
????
s
t(????)
1
?????
h(t)??????????????????? x(t)???????????H(s)???????
??????
24
????????????
??????????????
??????
??????
25
Z???Z?????
??????????(??)???????????? ???????s(sj?)???????
???????? ????????????????????????? ???????? Z???
???????????????Z??????? (zexp(sT)
????????z??H(z)???????? ??????
???? x(n) ax(n)by(n) x(n-m) x(n)y(n)
z??(?????) X(z) aX(z)bY(z) X(z)z X(z)Y(z)
-m
26
Z?????????Laplace??Z??
??????
????????????? ?????????????T ???????
???
??????
27
Z???Z?????
Z?????
??????????? ???????
(T??????????)
n?0,1,2,3??????? ?????
28
Z???Z??????
29
Z???Z????????????????

• ?????????????????????
• Z???? ??????????????? ??????????n????????
• ?????????z??????????????????????
• ?????1?????????????(?????)????

30
Z?????????Laplace??Z??
Z??
z????????????? ??????
s????????????? ??????
31
Z???Z?????
???
????
32
Z???Z?????(?????)
??????????????????????? ?Z???????????
??????
??????
Z??
33
Z??????????????????????????

• ?????????????????????????????????????

2??????????
34
MATLAB?????????

• Fs10000 10kHz?????????
• tlinspace(0,1,Fs) 10kHz?1s?????????
• y10.7sin(2pi100t) 100Hz???
• y20.2sin(2pi4000t) 4kHz???
• yy1y2 ???????
• y_mave(1)0 ????????????0??????
• for n2Fs, ????????
• y_mave(n)(y(n)y(n-1))/2 ????????
• end
  ????????
• hold off
• plot(t,y,LineWidth,2.0)
  ????????????
• hold on
  ????????????
• plot(t,y_mave,r,LineWidth,2.0)
  ?????????????
• axis(0 0.05 -1 1) ?????????????

35
Z??????????????????????????
?????????????????Z??????? ??????
Y(z)
-1
X(z)
Z??

Z
1/2

??????
36
Z??????????????????????????
????????????
Z??
?????????
37
Z??????????????????????????
??????? ???????
?????? ????? ??????
T????????
?,?????????fs1/T10kHz???f?/2p? ???????????5k
Hz?????????? ?????
38
Z??????????????????????????
??????? ?????
100Hz
??????? ?????
4kHz
39
MATLAB?????????

• hold off ?????????
• flinspace(0,Fs,Fs) ?????????
• Hcos(pif/Fs) ???????
• fft_yfft(y) ????FFT
• plot(f,abs(fft_y)/Fs2,LineWidth,2.0) ????
• hold on ?????????
• plot(f,H,r,LineWidth,2.0) ???????
• axis(0 5000 0 1) ???????

40
??????????????
41
FFT??????????????Matlab??????
?????????

• y4real(ifft(fft_y2)) ?FFT?????????????
• sound(y4,Fs)

??????????? ????????????FFT?? ?FFT??????????????
???????????????FFT???FFT????????f(x)??????????????
???????????????????????? 1)???????????????????????
???????????? ????????????????????????????????? 2
)?????????????????????????????????????(???????????
?????????) ?????????????????????????????
42
?????

• ??????????
• ?????????????????????????????
• ???FFT?????
• ????????
• ??????
• ??????(????)
• Z??(????)
• Z????????????????????

43
?????

• ????????
• ???????
• FIR????