DSPY2003Mid - November 4 2003 DSP Midterm 2:00pm ~...

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November 4, 2003 DSP Midterm 2:00pm ~ 4:00pm (Close Book) Note: If no indications are given, x [ n ], y [ n ], and h [ n ] as well as their associated z -transforms denote the input, the output, and the impulse response of the system, respectively. 1. For linear and time-invariant systems characterized by the following impulse responses, please identify them if the system is stable, causal, memory or not? (12%) (a) ] [ 4 ] [ 0 = δ = k k n n h ; (b) ] [ ] [ 100 0 = δ = k k n n h ; (c) ] [ 4 ] [ 100 0 = δ = k k k n n h ; (d) ] [ 4 ] [ 100 5 = δ = k k k n n h (e) ] [ 4 ] [ 100 = δ = k k k n n h ; (f) ] [ 4 ] [ 100 −∞ = δ = k k k n n h . 2. For linear and time-invariant systems characterized by the following z-transforms, please identify them if the system is stable, causal, memory or not? (12%) (a) H ( z ) = 1 3 1 3 + z z for 3 / 1 > z ; (b) H ( z ) = 1 3 1 3 1 + z z for 3 / 1 > z ; (c) H ( z ) = 1 3 1 3 + z z for 3 / 1 < z ; (d) H ( z ) = 1 3 1 3 1 + z z for 3 / 1 < z (e) H ( z ) = 1 1 3 1 3 + z z for 3 / 1 > z ; (f)
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DSPY2003Mid - November 4 2003 DSP Midterm 2:00pm ~...

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