EE4150_2003_quiz1sol

EE4150_2003_quiz1sol - EE4150 Digital Signal Processing...

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EE4150 Digital Signal Processing Quiz One Solution Dr. Hsiao-Chun Wu 1. Compute the system response y ( n ), n , for a LTI system, through the discrete-time convolution of x ( n ) and h ( n ). Input sequence is } 3 , 2 , 1 { ) ( = n x . The impulse response of the LTI system is } 1 , 2 , 1 { ) ( = n h . Answer: 1 , 1 = = = = h x h x U U L L . Hence = elsewhere n n y , 0 2 2 , 0 ) (. n =-2, = = = = = = = 1 1 } , min{ } , max{ 1 ) 1 ( ) 1 ( ) ( ) ( ) ( ) ( ) 2 ( k L n U k U n L k h x k n h k x k n h k x y h x h x n =-1, 4 2 2 ) 1 ( ) 0 ( ) 0 ( ) 1 ( ) ( ) ( ) ( ) ( ) 1 ( 0 1 } , min{ } , max{ = + = + = = = = = = k L n U k U n L k h x h x k n h k x k n h k x y h x h x n =0, 8 3 4 1 ) 1 ( ) 1 ( ) 0 ( ) 0 ( ) 1 ( ) 1 ( ) ( ) ( ) ( ) ( ) 0 ( 1 1 } , min{ } , max{ = + + = + + = = = = = = h x h x h x k n h k x k n h k x y k L n U k U n L k h x h x n =1, ) 0 ( )
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