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HW_2_assignment

# HW_2_assignment - ACS 513 DIGITAL SIGNAL PROCESSING Fall...

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ACS 513 - DIGITAL SIGNAL PROCESSING Fall 2010 Homework #2 Assigned: 9/7/2009 Due: 9/16/2009 1. Consider the sequence { x [ n ]} = {1, -2, 3,-2, 1}. a. Assume the sequence starts at n = 0, and write an expression for x [ n ] as a sum of scaled and delayed discrete delta functions (i.e. a m [ n-m ] ). b. Assume the sequence starts at n = 0, and write an expression for x [ n ] as a sum of scaled and delayed unit step functions (i.e. a m u [ n-m ] ). c. Assume the sequence starts at n = -2, and write an expression for x [ n ] as a sum of scaled and delayed discrete delta functions (i.e. a m [ n-m ] ). d. Assume the sequence starts at n =+2, and write an expression for x [ n ] as a sum of scaled and delayed unit step functions (i.e. a m u [ n-m ] ). 2. For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time-invariant, and (5) memoryless: a. ] [ ) cos( ]} [ { n x n n x T , b. ] 1 [ ] [ ] 1 [ ]} [ { n x n x n x n x T c. ] [ ]} [ { n x e n x T d. b n ax n x T ] [ ]} [ {, a and b constants Please justify your answer for each property and each example.

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HW_2_assignment - ACS 513 DIGITAL SIGNAL PROCESSING Fall...

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