PS1-2010

# PS1-2010 - 5 Problem 2.38 of the textbook 6 Problems 2.85...

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ECE161A March 30, 2010 Discrete Time Signal Processing Professor T. Javidi Problem Set #1 Due: Tuesday April 6, 2010 I encourage you to work together on your homework but what you hand in must be written up on your own. 1. Consider the system y [ n ] = - 4 | x [ n ] | 3 . Determine whether this system is (a) memoryless? (b) invertible? (c) causal? (d) stable? (e) time invariant? (f) linear? 2. Repeat Problem 1 for y 1 [ n ] = ± x [ n ] /a 2 for x [ n ] > 0 2 otherwise and y 1 [ n ] = ± x [ n ] /a 2 for n > 0 2 otherwise 3. consider two signals, x [ n ] and y [ n ] , and their even and odd components, x e [ n ] , x o [ n ] , y e [ n ] , y o [ n ] . Deter- mine which one of the following are odd or even: (a) x e [ n ] * y e [ n ] (a) x o [ n ] * y e [ n ] (a) x o [ n ] * y o [ n ] 4. Show that any periodic signal with period N is a power signal. Calculate its power.
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Unformatted text preview: 5. Problem 2.38 of the textbook 6. Problems 2.85 and 2.87 of the textbook. 7. Given x [ n ] = a n u [ n ] , ﬁnd the Z-transform and ROC of b 2( n +1) x [ n/ 5] . Answer to an extra problem (for your own use, not to be turned; not to be graded): 1. The commutative property of the convolution is only valid when the convolution does exist in the ﬁrst place. Consider the following three signals: x [ n ] = 2 ,y [ n ] = u [ n ] , and z [ n ] = δ [ n ]-δ [ n-1] . Show that z * ( y * x ) 6 = ( y * z ) * x ....
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