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Unformatted text preview: Problem (1) (a). Use phasors to simplify the sum ) 4 . cos( ) 3 / 2 4 . cos( 2 ) 3 / 4 . cos( ] [ + = + + + = n A n n n x The values of A and are obtained as )] 3 2 sin( 2 ) 3 [sin( ) 3 2 cos( 2 ) 3 cos( 2 3 / 2 3 / + + + = + = j e e Ae j j j 761 . 1 6457 . 2 598 . 2 5 . ] 732 . 1 866 . [ 1 5 . j e j j = + = + + = Therefore ) 761 . 1 4 . cos( 6457 . 2 ] [ + = n n x (b) 5 , 24 , 2 12 5 3 , 16 , 2 8 3 2 2 1 1 = = = = = = r A n r n r n r n The period is the LCM of {16, 24}=48. Power: 625 . 1 2 / 25 . 2 / 1 1 ) 3 / 12 / 5 cos( 5 . * ) 8 / 3 cos( * 2 ) 3 / 12 / 5 cos( 5 . * 2 ) 8 / 3 cos( 2 ) 3 / 12 / 5 ( cos 25 . ) 8 / 3 ( cos 1 ( 48 1  ) 3 / 12 / 5 cos( 5 . ) 8 / 3 cos( 1  48 1  ] [  48 1 ) 2 2 47 2 47 2 47 2 = + + = + + + + + + + + = + + + = = = = = n n n n n n n n n x P n n n (c) ] 2 [ 5 . ] 1 [ ] [ 5 . ] 1 [ 2 ] 2 [ ] [ + + + + = n n n n n n z Since ] 1 [ ] [ ] [ = n u n u n ] 2 [ 5 . ] 1 [ ] [ 5 . ] 1 [ 2 ] 2 [ ] [ + + + + = n n n n n n z ]) 3 [ ] 2 [ ( 5 . ]) 2 [ ] 1 [ ( ]) 1 [ ] [ ( 5 . ]) [ ] 1 [ ( 2 ] 1...
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This note was uploaded on 01/11/2011 for the course EE 4015 taught by Professor Shuhungleung during the Fall '10 term at City University of Hong Kong.
 Fall '10
 ShuHungLeung
 Digital Signal Processing, Signal Processing

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