數(shù)字信號(hào)處理第二章04預(yù)習(xí)

1、數(shù)字信號(hào)處理周治國(guó)2010.03第二章離散時(shí)間信號(hào)與系統(tǒng)分析基礎(chǔ)2-6一、幾個(gè)術(shù)語(yǔ)1.對(duì)任意實(shí)序列：1.x(n)為實(shí)序列，若x(n) x(n),則稱偶對(duì)稱，偶序列記為：xe (n) xe (n)2.x(n)為實(shí)序列，若x(n) x(n),則稱奇對(duì)稱，奇序列記為：xo (n) xo (n)3.x(n)為實(shí)序列，x (n) 1 x(n) x(n) 是偶序列e24.x(n)為實(shí)序列，x (n) 1 x(n) x(n) 是奇序列o2 x(n) xe (n) xo (n)結(jié)論：任一實(shí)序列可由偶序列和奇序列之和3 / 30。oddeven2-6一、幾個(gè)術(shù)語(yǔ)2.對(duì)任意復(fù)序列：1.x(n)為復(fù)序列，若x(n)

2、 x (n),則稱共軛對(duì)稱記為：x (n) x (n)ee2.x(n)為復(fù)序列，若x(n) x (n),則稱共軛稱記為：x (n) x (n)oo12x (n) x(n) x (n)是共軛對(duì)稱序列3.x(n)為復(fù)序列，e4.x(n)為復(fù)序列，x (n) 1 x(n) x (n) 是共軛稱序列o2 x(n) xe (n) xo (n)結(jié)論：任一復(fù)序列可由共軛對(duì)稱序列和共軛稱序列之和unconjugateconjugate2-63.DTFT的共軛對(duì)稱與共軛稱：DTFT離散時(shí)間變換X e j x(n)e jnn 1 2X e j e jndx nj1j jXe (e) X (e) X (e) 是共軛

3、對(duì)稱序列2j1j jXo (e) X (e) X (e) 是共軛稱序列2 X (e j ) X (e j ) X (e j )eo2-6DTFT x n X e j DTFT x n X e j 二、：變換DTFT離散時(shí)間X e j x(n)e jnDTFTxn Xejnx n X ej1X e j e jndx n x n X e j x n X e j 2jnj證明： 1.Xex(n)en X e j X e j DTFT x n x (n)e jn x(n)e jn nX e j e jndn 1 22.x nX e j e jnd 1 1 2X e j e jnd X e j xn 2

4、2-6x n X e j x n X e j DTFT離散時(shí)間變換X e j x(n)e jnnx n Xej1X e j e jndx n 2Rex n 1 x n x n 1 X (e j ) X (e j ) X (e j )e22j Imx n 1 x n x n 1 X (e j ) X (e j ) X (e j )o22x n 1 x n x n 1 X (e j ) X (e j ) ReX (e j )e22x n 1 x n x n 1 X (e j ) X (e j ) j ImX (e j )o222-6實(shí)序列:x n X (e j )1.x n x n X (e j ) X (e j )x n X e j x n X e j x n X e j X (e j ) ReX (e j ) j ImX (e j )2. j) Re X (e j) j Im X (e jX (e) ReX (e j ) ReX (e j ) ImX (e j ) ImX (e j )X (e j )實(shí)部是偶函數(shù)，虛部是奇函數(shù)j arg X (e j )jj3.極