soln7 - EECS 451 SOLUTIONS TO PROBLEM SET #7 1a. Reverse...

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Unformatted text preview: EECS 451 SOLUTIONS TO PROBLEM SET #7 1a. Reverse the second sequence: { 4 , 3 , 2 , 2 } { 2 , 2 , 3 , 4 } , repeat the cycle, and shift: y(0): { 1 , 2 , 3 , 1 , 1 , 2 , 3 , 1 } { 4 , 2 , 2 , 3 , 4 , 2 , 2 , 3 } (1)(4) + (2)(2) + (3)(2) + (1)(3) = 17. y(1): { 1 , 2 , 3 , 1 , 1 , 2 , 3 , 1 } { 3 , 4 , 2 , 2 , 3 , 4 , 2 , 2 } (1)(3) + (2)(4) + (3)(2) + (1)(2) = 19. y(2): { 1 , 2 , 3 , 1 , 1 , 2 , 3 , 1 } { 2 , 3 , 4 , 2 , 2 , 3 , 4 , 2 } (1)(2) + (2)(3) + (3)(4) + (1)(2) = 22. y(3): { 1 , 2 , 3 , 1 , 1 , 2 , 3 , 1 } { 2 , 2 , 3 , 4 , 2 , 2 , 3 , 4 } (1)(2) + (2)(2) + (3)(3) + (1)(4) = 19 . { 17 , 19 , 22 , 19 } . 1b. X 1 (0) = 1 + 2 + 3 + 1 = 07 . X 1 (1) = 1 + 2(- j ) + 3(- 1) + 1( j ) =- 2- j . X 1 (2) = 1- 2 + 3- 1 = 01 . X 1 (3) = 1 + 2( j ) + 3(- 1) + 1(- j ) =- 2 + j . X 2 (0) = 4 + 3 + 2 + 2 = 11 . X 2 (1) = 4 + 3(- j ) + 2(- 1) + 2( j ) = +2- j . X 2 (2) = 4- 3 + 2- 2 = 01 . X 2 (3) = 4 + 3( j ) + 2(- 1) + 2(- j ) = +2 + j ....
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This note was uploaded on 12/10/2009 for the course EECS 451 taught by Professor Andrewyagle during the Spring '08 term at University of Michigan.

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soln7 - EECS 451 SOLUTIONS TO PROBLEM SET #7 1a. Reverse...

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