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Unformatted text preview: ECE 320 Networks and Systems Exam 1 Tuesday, February 19, 2008 Closed Book. Closed Notes. No Calculator. 100 Points Total. No credit without explaining your work. 1. (33 pts.=11+11+11) A staircase quantizer Q is defined by two strictly increasing sequences { q j : j = , 1 , . . . , n } and { τ j : j = 0 , 1 , . . . , n, n + 1 } , with τ =∞ and τ n +1 = + ∞ , by ( ∀ x ∈ IR) Q ( x ) = q j if τ j ≤ x < τ j +1 . (1) Suppose n = 3, τ =∞ , τ 1 = 0, τ 2 = T , τ 3 = 2 T , and τ 4 = + ∞ (where T is a constant), and q = 0, q 1 = v , q 2 = 2 v , q 3 = 3 v (where v is a constant). Suppose the input to Q is a random variable denoted by X . Then the output of Q is also a random variable, which is denoted by Y . Define the quadratic error, a random variable denoted by Z , by Z = ( X Y ) 2 . Suppose X is a continuous random variable with a pdf that is uniform on the interval [ T, 3 T ] ( T here and T in the definition of τ i are the same T ). (a) Plot the graph of Q ....
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This note was uploaded on 03/10/2008 for the course ECE 3200 taught by Professor Fine during the Spring '06 term at Cornell.
 Spring '06
 FINE

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