1、 1 n n n 2.1 2.1.1 ) (n x - = - = n n j j e n x e X w w ) ( ) ( w f s f 2 s f f p w 2 = ) (n x ) ( w j e X ) ( w j e X w w ) (n x ) ( w j e X w ) (n x ) ( w j e X ) ( w j e X ) ( ) ( ) ( Im ) ( Re ) ( w w w w w j i j r j j j e jX e X e X j e X e X + = + = ) ( | ) ( | ) ( w q w w X j j j e e X e X =
2、) ( ) ( | ) ( | 2 2 w w w + = j i j r j e X e X e X ) ( ) ( tan ) ( 1 w w w q j r j i X e X e X - = | ) ( | w j e X ) (n x ) (w q X p p ) (n x = 0 0 0 5 . 0 ) ( n n n x n p p ) ( w j e X ) sin( 5 . 0 ) cos( 5 . 0 1 ( 1 5 . 0 1 1 ) 5 . 0 ( 5 . 0 ) ( 0 0 w w w w w w j e e e e X j n n j n j n n j + - =
3、 - = = = - = - - = ) cos( 25 . 1 1 ) sin( 5 . 0 ( ) cos( 5 . 0 1 ( 1 | ) ( | 2 2 w - = w + w - = w j e X 3 1 ) cos( 5 . 0 ) sin( 5 . 0 tan ) ( 1 - = - w w w q X w 2.1 2.2 2.1.2 ) ( w j e X ) (n x w p w p p w d e e X n x n j j ) ( 2 1 ) ( - = - = - - - - = - = r r n j n j r r j d e r x d e e r x w p
4、w p p p w w p p w ) ( ) ( 2 1 ) ) ( ( 2 1 r n 4 0 ) ( ) ) sin( 2 | | ) ( 1 ) ( ) ( ) ( = - - = - - = - = - = - - - r n r n e e r n j d e r n j r n j r n j p w p w w p w w p p w r n = p ) ( ) ( 2 1 ) ( 2 1 ) ( n x d n x d e r x r r n j = = - - = - - p p p p w w p w p c c c j e X - = 0 1 ) ( w w w w )
5、 (n x w w - w p w = w p = c c n n d e n x c n j ) sin( 2 1 ) ( 0 = n c w ) (n x 2.1.3 Z Z w = w = j e Z j Z X e X | ) ( ) ( 2-17 Z Z - = n n x | ) ( | 2-18 2.2 2-1 DTFT w f DTFT 1 2 3 4 5 2.2.1 ) ( w j e X | ) ( | | ) ( | ) ( ) ( w - w w - w = = j j j r j r e X e X e X e X 2-19 ) ( ) ( ) ( ) ( w - q
6、 - = w q - = w - w X X j i j i e X e X 2-20 2-21 - = - = w w - w = n n j n n x j n n x e X ) sin( ) ( ) cos( ) ( ) ( 2-21 2-1 2-22 ) ( ) ( * w - w = j j e X e X 2-22 2.2.2 ) ( w j e X w p ,. 2 , 1 , 0 ) ( ) ( ) 2 ( = = p w w k e X e X k j j 2-23 ) ( w j e X 2-1 w p w p f s f ) (n x ) (t x 2.2.3 ) (
7、) ( ) ( ) ( 2 1 2 1 w w + + j j e bX e aX n bx n ax 2-24 ) ( 1 n x ) ( 2 n x DTFT ) ( 1 w j e X ) ( 2 w j e X DTFT ) ( ) ( 2 1 n bx n ax + 6 ) ( ) ( ) ( ) ( ) ( ) ( ( 2 1 2 1 2 1 w w w w w j j n n j n n j n n j e bX e aX e n bx e n ax e n bx n ax + = + = + - = - - = - - - -2-25 2-24 2.2.4 ) ( ) ( )
8、( ) ( 2 1 2 1 w w j j e X e X n x n x * 2-26 ) ( * ) ( 2 1 ) ( ) ( 2 1 2 1 w w p j j e X e X n x n x 2-27 2-26 2-27 ) ( ) ( ) ( 2 1 n x n x n x * = ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( 2 1 2 1 2 1 - = w - - = - = - = - = w - w - w - = - = * = n n j k n n k n j n j j e k n x k x e k n x k x e n x n x e X2-2
9、8 m k n = - ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 1 2 1 w w - = w - - = w - w - - = w - - = w = = = j j m m j k k j k j m m j k j e X e X e m x e k x e e m x k x e X2-29 2-26 2.3 2-26 | ) ( | ) ( | | ) ( | w w w j j j e X e H e Y = 2-30 ) ( ) ( ) ( w q w q w q X H Y + = 2-31 2-30 2.3 | ) ( | w j e H c w
10、 c w 2.3 2-31 7 ) ( w j e H 2.3 2.2.5 Parseval Parseval Z 2-32 + - - - - p = x x c n R z R dv v v z X v X j Z n x n x | | , ) ( ) ( 2 1 ) ( ) ( 1 * * *2-32 Z=1 dv v v X v X j n x n x c - - p = 1 * * * ) 1 ( ) ( 2 1 ) ( ) ( 2-33 w = j e v - - - = = p p w p p w w w p w p d e X d e X e X n x n x j j j
11、2 * * | ) ( | 2 1 ) ( ) ( 2 1 ) ( ) ( 2-34 ) (n x w p p p w d e X n x j - - = 2 2 | ) ( | 2 1 ) ( 2-35 2 ) ( w j e X 2-35 Parseval 2.3 ) (n h ) ( w j e H - = w - w = n n j j e n h e H ) ( ) ( n j e w ) (n h ) ( w j e H ) (n x ) (n h ) ( * ) ( ) ( n x n h n y = ) ( w j e X ) ( w j e H ) ( ) ( ) ( w w
12、 w = j j j e X e H e Y w w w LSI w cw c 8 n j e n x w = ) ( ) (n h ) (n y ) ( ) ( ) ( ) ) ( ( ) ( ) ( ) ( ) ( ) ( n x e H e e H e e k h e k h k n x k h n y j n j j n j k k k j k n j k w w w w - = - = w - - w - = = = = = - = 2-37 ) (n x ) (n y ) ( w j e H 2-3 n j e p 5 . 0 3 ) (n h ) (n y 2-37 ) ( 3
13、) 3 )( ( ) ( 5 . 0 5 . 0 5 . 0 5 . 0 p p p p = = j n j n j j e H e e e H n y 2-38 2-37 2-39 ) ( ( | ) ( | ) ( w q + w w = H n j j e e H n y 2-39 ) cos( ) ( n n x w = Euler 2 ) cos( ) ( n j n j e e n n x w - w + = w = 2-40 ) ) ( ) ( ( 2 1 ) ( n j j n j j e e H e e H n y w - w - w w + = 2-41 ) ( cos(
14、| ) ( | ) ( 2 | ) ( | ) ( ( ) ( ( w q + w = + = w w q + w - w q + w w H j H n j H n j j n e H e e e H2-42 w w w | ) ( | w j e H w ) (w q H 2-4 ) 5 . 0 cos( ) ( n n x p = ) (n y ) ( ) 1 ( 5 . 0 ) ( n x n y n y = - - 2-43 Z ) (Z H 1 5 . 0 1 1 ) ( - - = Z Z H , |Z|0.5 2-44 9 ) (Z H ) sin( 5 . 0 ) cos(
15、5 . 0 1 1 5 . 0 1 1 ) ( w + w - = - = w - w j e e H j j2-45 ) 5 . 0 cos( ) ( n n x p = ) ( 5 . 0 p j e H 894 . 0 5 . 0 1 1 | 5 . 0 1 1 | | ) ( | 2 5 . 0 = + = + = p j e H j2-46 4636 . 0 5 . 0 tan ) ( 1 - = - = w q - H2-47 ) (n y ) 4636 . 0 5 . 0 cos( 894 . 0 ) ( - p = n n y 2-48 2.4 Z ) (Z H ) ( w j
16、 e H = - = - - l - = N k k M k k Z p Z G Z H 1 1 1 1 ) 1 ( ) 1 ( ) ( 2-49 k k p , l Z ReZ ImZ 1 -1 +j -j p 1 p 2 l1 2.4 Z 10 2.4 4 / 2 4 / 1 8 . 0 , 8 . 0 p - p = = j j e p e p 5 . 0 1 - = l (2-49) = w - = w - w - l - = N k j k M k j k j e p e G e H 1 1 ) 1 ( ) 1 ( ) ( 2-50 = w - = w - w - l - = N k
17、 j k M k j k j e p e G e H 1 1 | 1 | | 1 | | | | ) ( | 2-51 | 1 | w - l - j k e | 1 | w - - j k e p w j e | | | 1 | k j j k e e l - = l - w w -2-52 | | | 1 | k j j k p e e p - = - w w -2-53 k DZ k l w j e k DP k p w j e 2.5 2-51 = = w = N k k M k k j DP DZ G e H 1 1 | | | | | | | ) ( | 2-54 ReZ ImZ 1 -1 +j w j e k p k DP k DZ k l 2.5 w 2-54 2.5 k DZ k DP w k l w j e 2.5 k DZ | | k DZ k p w j e 2.5 11 k DP | | k DP
