第08章 DFT(中)

第08章 DFT(中)

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
8.4 Fourier representation of finite-duration sequences: Discrete Fourier Transform (离散傅立叶变换) ] )) [(( ] mod [ ] [ ] [ ~ N r n x N n x rN n x n x = = = −∞ = ] [ ] [ ~ ] [ n R n x n x N = Figure 8.8 EXAMPLE. To each sequence x[n] with finite length N, we can always associate a period sequence is a rectangular sequence. ] [ n R N 后两种只适于无混迭
Background image of page 1

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

View Full DocumentRight Arrow Icon
11 00 1 0 [ ] [(( )) ] [] ([] ) [ ] [ ] [ ] [ ] , 0,1,. ... 1 N NN kn kn nn N kn n xn x n Xk DFSxn xnW XkR k xnW k N −− == = = = = ∑∑ ± ± ±± ± Let’s consider a sequence with finite-length N and a period sequence , We define a finite-length sequence as discrete Fourier transform (DFT) of x[n] which is a period of DFS . The procedure can be illustrate by the steps followed: ] [ n x ] [ ~ n x ] [ k X ] [ ~ k X We can reconstruct by get a period of . ] [ n x ] [ ~ n x 1 0 [ ] [ ] ( [ ]) [ ] [(( )) ] 1 [] [] , 0 , 1 , . . . 1 kn kn N kk N kn k XkW IDFSXk xn x n xnR n X kW n N N = = = = ± ± ] [ ] [ ~ ] [ n R n x n x N =
Background image of page 2
1 0 1 0 [ ] [ ] , 0,1,. ... 1 1 [ ] [ ] , .. 1 N kn N n N kn N k Xk xnW k N xn X kW n N N = = == = = = = 1 0 1 0 ] [ 1 ] 0 [ ] [ ] 0 [ N k N n k X N x n x X So, for a sequence with duration N, it’s DFT and reverse transform are defined as: DFT IDFT 具有固有的周期性 信号的长度 , 求和项数 , 频域取样点数相等
Background image of page 3

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

View Full DocumentRight Arrow Icon
k N j e z k N j N n n j j N n N kn j N n kn N z X e X k X e n x e X N k e n x W n x k X π ω 2 | ) ( | ) ( ] [ , ] [ ) ( 1 ,.... 1 , 0 , ] [ ] [ ] [ 2 1 0 1 0 / 2 1 0 = = = = = = = = = = = DFT is the sample of Fourier transform at equally spaced frequency 2/ , 0 , 1 , . . . 1 k kN k N = =− 所以 DFT 可以与 FT 独立 1 0 1 [] 1 ( ) 2 N kn N k jj n xn X kW N x nX e e d ωω = = =
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/29/2012 for the course EE 325 taught by Professor Lilili during the Fall '11 term at BYU.

Page1 / 16

第08章 DFT(中)

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online