DSPY2004Mid

# DSPY2004Mid - Midterm Close Book Exam 17:30pm 19:30pm Note...

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Midterm November 11, 2004 Close Book Exam 17:30pm – 19:30pm 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. Multiple Answers and Multiple Choices (25%) . (1) ( ) Which systems are linear? (a) y [ n ]= x [3 n ]; (b) y [ n ] = max{ x [ n 1], x [ n ]}; (c) y [n] = 3 y [ n 1] + x [ n ] with y [ 1] = 0; (d) y [ n ]= 5 x [ n 1] + 3 x [ n + 2] + 5; (e) h [ n ] = 5 n u [ n 1]. (2) ( ) Which systems are time-invariant? (a) y [ n ] = ; (b) y [ n ] = 3 x [ n ] + 2 x [ n 1]+2; k n k n n x 3 if 3 if 0 ] 3 / [ 3 = (c) y [ n ] = x 2 [ n ]; (d) y [ n ] = min{ x [ n 1], x [ n ]}; (e) h [ n ] = 2 n n u [ n 1]. (3) ( ) Which systems are time-invariant? (a) y [ n ] = 2 x [ n ] + 3 u [ n 3]; (b) y [ n ] = x [ n /2] for n =even and y [ n ] = 0 for n =odd; (c) y [ n ] = sin( x [ n ]); (d) h [ n ] = 3( n 2 +2)( n 2) δ [ n ]; (e) H (z) = 2 3 2 z z . (4) ( ) Which systems are stable? (a) y [ n ] = 4 y [ n 1] x [ n 2]; (b) H ( z ) = 5 . 0 2 1 + z z z for z < 0.5; y [ n ] = x 2 [ n ]; (d) h [ n ] = sin[ n ] [ n 4]; (e) h [ n ] = n [ n 2]. (5) ( ) Which systems are causal? (a) h [ n ] = 2 [ n 1] + 3 [ n +5]; (b) y [ n ] 0.5 y [ n 1] = 2 x [ n ]; h [ n ] = 4 n [ n 1] + 2 [ n ]; (d) H ( z ) = 2 1 z for z > 2; (e) H ( z ) = 5 . 0 1 z for z < 0.5 2. For linear and time-invariant systems characterized by the following z-transforms, (a) Identify them if the system is stable or not? (12%)

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DSPY2004Mid - Midterm Close Book Exam 17:30pm 19:30pm Note...

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