第七章作业答&ael

第七章作业答&ael

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Unformatted text preview: (P288-291) 7.11-7.22 7.11 ] 1 [ ] 2 [ ] 1 [ ] [ − + − + − = n x n y n y n y 1 ) ( ) ( ) ( z X z Y z H = H(z) 2 3 1 Z Y ) ( ) ( ) ( ) ( 1 2 1 z X z z Y z z Y z z − − − + + = 2 1 1 1 ) ( ) ( ) ( − − − − − = = z z z z X z Y z H 2 5 1 | :| + > z ROC 2 } 1 { )} ( { ] [ 2 1 1 1 1 − − − − − − − = = z z z Z z H Z n h ) 2 5 1 ( 1 5 1 ) 2 5 1 ( 1 5 1 1 1 ) ( 2 − − − + − = − − = z z z z z z H ] [ ) 2 5 1 ( 5 1 ] [ ) 2 5 1 ( 5 1 )} ( { ] [ 1 n u n u z H Z n h n n − − + = = − 3 2 5 1 2 , 1 ± = p 618 . , 618 . 1 2 , 1 = p ROC h[n] 618 . 1 | | 618 . : 2 1 = < < = p z p ROC , ] [ ) 2 5 1 ( 5 1 ] 1 [ ) 2 5 1 ( 5 1 )} ( { ] [ 1 n u n u z H Z n h n n − − − − + = = − 7.12 ] 1 [ ] 2 [ 2 1 ] 1 [ ] [ − = − + − − n x n y n y n y 1 H(z) 2 h[n] 3 ) cos( 5 ] [ π = n n x 1 Z ) ( ) ( 2 1 ) ( ) ( 1 2 1 z X z z Y z z Y z z − − − = + − Y 2 1 1 2 1 1 ) ( ) ( ) ( − − − + − = = z z z z X z Y z H-0.5 0.5 Im Re 1 0.5 2 2 2 1 | :| = + > j z ROC 2 H(z) 1 4 2 , 1 2 2 π ϑ j j e re p ± ± = = P272 7-2 2 1 1 2 1 1 ) ( ) ( ) ( − − − + − = = z z z z X z Y z H 2 2 1 1 ] cos 2 [ 1 ] sin [ ] [ ] sin − − − + − ⋅ ←→ z r z r z r n u n r Z n ω ω ω [ 4 , 2 1 π ω = = r ] [ ) 4 sin( ) 2 1 ( ] [ ] sin [ )} ( { ] [ 1 n u n n u n r z H Z n h n n π ω ⋅ = = = − P99 100 ) 2 2 1 )( 2 2 1 ( 2 1 1 ) ( 1 4 1 4 1 2 1 1 − − − − − − − − − = + − = z e z e z z z z z H j j π π } 2 2 1 1 2 2 1 1 { ) 2 2 1 )( 2 2 1 ( ) ( 1 4 1 4 1 4 1 4 1 − − − − − − − − − − − = − − = z e z e j z e z e z z H j j j j π π π π H(z) ] [ ) 4 sin( ) 2 1 ( ] [ ) 2 2 ( ] [ ) 2 2 {( )} ( { ] [ 4 4 1 n u n n u e n u e j z H Z n h n n j n j π π π ⋅ = − − = = − − H(z) Z h[n] 3 ) cos( 5 ] [ π = n n x 2 1 1 2 1 1 2 1 ) 1 ( 5 ] cos 2 [ 1 ] [cos 1 5 ] cos 5 [ ) ( − − − − − − + + + = + π − π − ⋅ = π = z z z z z z n Z z X ) 1 )( 2 1 ( 5 2 1 ) 1 ( 5 2 1 1 ) ( ) ( ) ( 2 2 2 1 1 2 1 1 + + − = + + + ⋅ + − = = − − − − − − z z z z z z z z z z z X z H z Y Y(z) Z ) 2 1 ( 2 1 3 ) 2 1 ( 2 1 2 1 2 ) 1 )( 2 1 ( 5 ) ( 2 2 2 2 2 + − ⋅ − + − − ⋅ − + =...
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第七章作业答&ael

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