{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

&ccedil;&not;&not;08&ccedil;&laquo;&nbsp; DFT(&auml;&cedil;‹)

# ç¬¬08ç«  DFT(ä¸‹)

This preview shows pages 1–13. Sign up to view the full content.

11 2 2 [] , [] DFT x n X kx n X n Xk ↔↔ 8.6 properties of the Discrete Fourier transform 12 1 2 ax n bx n aX k bX k +↔ + 2. circular shift （循环或圆周移位） of a sequence [(( )) ] [ ] km NN N xn m R n WX k −↔ [ ( ( ) )] [] nl N Wx n l R k ↔− Assume: 1. linearity

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Figure 8.12 EXAMPLE. 图示循 环移位 ] [ ] ))) ( [(( ] [ ] )) [(( ] [ 1 n R m N n x n R m n x n x N N N N + = = Definition of circular shift of a sequence
8.42 EXAMPLE. ] [ 1 n h ] [ 2 n h 8points DFT | ] [ | 1 k H | ] [ | 2 k H 1024 points DFT | ) ( | 1 ω j e H | ) ( | 2 j e H 当成 8 点信号是循环 移位关系，当成 1024 点则不是。

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
) 2 . 0 cos( ] [ n n n x π = | ]} [ { | | ] [ | n x DFT k X = ]} [ { n X DFT EXAMPLE. [ ], 1,. ., 1 [ ] [(( )) ] [ ] [(( )) ] [ ] [0], 0 DFT NN Nx N k k N Xn N x k R k N x N k Nx k =− ↔− = = = 3. Duality （对偶性）
] [ ] [ ] )) [(( ] [ ] )) [(( k N X k R k N X k R k X N N N N = = ] [ k X '[ ] [ ] Xk X N k =− 近似写法

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
** * * [ ] [(( )) ] [ ] [ ] [ ] DFT NN x nX k R k X N k R k X N k −= * [(( )) ] [ ] [ ] [ ] DFT x nR n x N n X k 11 [ ] ( [ ] *[ ]) ( [ ] *[ ]) Re{ [ ]} 22 DFT ep xn x n x Nn X k X k X k =+ + = Re{ [ ]} ( [ ] *[ ]) ( [ ] ]) [ ] DFT ep x nx n x n X k X N k X k =+↔ + = Im{ [ ]} ( [ ] *[ ]) ( [ ] ]) [ ] DFT op jx n x n x n X k X N k X k =− = [] ([] * [ ] ) ( [] * ) Im { [] } DFT op x n x N n X k X k j X k = 4. Symmetry properties
Here, we define: : the periodic conjugate-symmetric components （圆周（周期）共轭对称分量） : the periodic conjugate-antisymmetric components （圆周（周期）共轭反对称分量） ] [ k X ep ] [ k X op ] [ ]) [ ] [ ( ] [ ] [ ]) [ ] [ ( ] [ ] [ ] [ ] [ k N X k N X k X 2 1 k X k N X k N X k X 2 1 k X where, k X k X k X * op * op * ep * ep op ep = = = + = + = Any finite-length sequence can be decomposed as: The length of the three sequences are all N.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
] [ * ] [ k N X k X = | [ ]| | [ ]| [] [ ] Xk XN k = = −− (( ]} [ Im{ ]} [ Im{ ]} [ Re{ ]} [ Re{ k N X k X k N X k X = = ] [ * ] [ n x n x = 5. for a real sequence 圆周（周期）共轭对称：周期延拓后共轭对称
N=10 EXAMPLE. 实序列 DFT 9 ... 0 ), 5 . 0 cos( 5 . 0 ] [ = + = n n n x n π Real{X[k]} Imag{X[k]} |X[k]| arg{X[k]}

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
N=9 （奇数点） |X[k]| Arg{X[k]}

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This is the end of the preview. Sign up to access the rest of the document.