# HW5 (S 2007) - { , , 3 , } (d) x [ n ] = { 1 , (0 . 5) , (0...

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ELCT 321 Digital Signal Processing Homework Assignment # 5 (Chapter 5: FIR Filters) by Dr. Yong-June Shin Assigned: March 22, 2007 Due: March 29, 2007 1. (30 Points) For each of the following systems, determine whether or nor the system is (1) linear and (2) time-invariant. In order to get full credit, show your proof based on the deﬁnitions. (a) y [ n ] = cos( x [ n ]) (b) y [ n ] = Ax [ n ] + B ( A and B are constants) (c) y [ n ] = e - x [ n ] (d) y [ n ] = x [2 n ] (e) y [ n ] = x [ n 2 ] 2. (40 Points) Compute the convolution, y [ n ] = x [ n ] * h [ n ], of the fol- lowing signals and systems. (a) x [ n ] = { 1 , 2 , 4 } ,h [ n ] = { 1 , 1 , 1 , 1 } (b) x [ n ] = { 1 , 2 , - 1 } ,h [ n ] = x [ n ] (c) x [ n ] = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } ,h [ n ] =

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Unformatted text preview: { , , 3 , } (d) x [ n ] = { 1 , (0 . 5) , (0 . 5) 2 , (0 . 5) 3 , (0 . 5) 4 , (0 . 5) 5 } ,h [ n ] = { 1 ,-. 5 } 1 3. (10 Points) A linear time-invariant system has impulse response h [ n ] = 3 δ [ n ] + 2 δ [ n-1]-δ [ n-3] + 5 δ [ n-4] (a) Draw the implementation of this systems as block diagram in direct form (b) Draw the implementation of this systems as block diagram in transposed form 4. (20 Points) Problem 5.12 in textbook on page 156. 2...
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## This note was uploaded on 04/28/2008 for the course EE ELCT 321 taught by Professor J.shin during the Spring '08 term at University of South Carolina Beaufort.

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HW5 (S 2007) - { , , 3 , } (d) x [ n ] = { 1 , (0 . 5) , (0...

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