第三章 DFT 离散傅里叶变换
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Transcript of 第三章 DFT 离散傅里叶变换
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.DFT
1.
2.
3. DFT
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.---
0t0
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:
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.---
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*Tp, 2/Tp
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. ---0------
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.--DFTx(nT)=x(n)t0T2T1 2 N nNT
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3-1 DFS
.DFS DFS
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N
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k=0,1,..., N-1k=N,...,2N-1
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. k 1.
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p
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n=0N-1
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DFS
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1/N
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3.
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4. Z
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,Z
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Z Nk=0
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a,b 3-1-2DFS.
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.
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i=m+n, n=i-mn=0 i=m; n=N-1i=N-1+m * N
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.
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( )mm,
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. 1.
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2. 1 2 ,
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3
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4
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5
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31
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3.
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3-2 DFT--
. 1. m
nNmN
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(1)
(2)
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;
2.
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.x(n) x(n)x(n)
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N-1nx(n)00N-1n=0 N-1
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. X(k) X(k) X(k)
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.DFSDFT DFS,IDFSn=0n=N-1,k=0N-1 (DFT):
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,
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N.
_1062360455.unknown
_1062360530.unknown
_1062360558.unknown
_1062360406.unknown
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(N=12)NDFT.
_1061217888.unknown
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()
_1061390482.unknown
_1061390859.unknown
_1061390318.unknown
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NDFT
EMBED Equation.3 (
)
_1061390611.unknown
_1061390893.unknown
_1159826954.unknown
_1061390824.unknown
_1061218017.unknown
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.
,
_1061808042.unknown
_1061808275.unknown
_1061808306.unknown
_1061808349.unknown
_1061808072.unknown
_1055493283.unknown
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3-2-2 DFT.1.N
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2. N1N2
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N
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.1.
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2.
n=0N-1 N :
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12345n=0N=6
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.1. N
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0m0m0m0m
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.1.
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. :1012n1012n3
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mn210314523321
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2. . , ,L, ;
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,,L ,L: ,,
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N
:
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3.4
.1. : ,,,, : ()DFTX(k)DFT
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2. x(n)Z
x(n),,Z,X(z)N,
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, ,
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, x(n) ,1 , m=n+rN , 0 , m
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3. x(n) x(n)M,NM,,
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1.X(k)X(z) x(n),0nN-1Z
.X(k) X(z)
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X(k)X(z),
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2. :
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,
N,
, Z=0(N-1)
(N-1),
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,(N-1)
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3. Z, 4.
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, k,
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,
,
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N=5,
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N=5
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ik,i k , ,
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5. X(k)
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1, X(k)
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,
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DFT
.DFT 1. , , ;
,T
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2.
,, ,,,,,.
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0n0nn
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3. DFT , F
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DFT 1.
2.
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3.DFT:
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4.DFT DFTT IDFT ,,
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DFTT
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IDFT
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5.DFT
DFT 1/N
IDFTN
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FST
_1159050881.unknown
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_1160252136.unknown
_1160251967.unknown
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