ecen314-fall11-hw2

# ecen314-fall11-hw2 - n(d x n = u n-u n-5 h n = u n-2-u n-8...

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ECEN 314: Signals and Systems, Fall ‘11 Homework #2 Homework Assignment #2 Due date – Sep. 22, 2011 (Thu), 3:55PM in class. Problem 1. System properties (10 points) Determine whether the following systems are (1) memoryless, (2) causal, (3) stable, (4) linear, (5) time- invariant. Justify your answer. (a) y ( t ) = x ( t - 2) + x (2 - t ) (b) y ( t ) = [ cos (3 t )] x ( t ) (c) y ( t ) = R 2 t x ( τ ) (d) y ( t ) = ± 0 , t < 0 x ( t ) + x ( t - 2) , t 0 (e) y ( t ) = x ( t/ 3) Problem 2. System properties (10 points) Determine whether the following systems are (1) memoryless, (2) causal, (3) stable, (4) linear, (5) time- invariant. Justify your answer. (a) y [ n ] = x [ - n ] (b) y [ n ] = nx [ n ] (c) y [ n ] = E v { x [ n - 1] } (d) y [ n ] = x [ n ] , n 1 0 , n = 0 x [ n + 1] , n ≤ - 1 (e) y [ n ] = x [4 n + 1]

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Problem 3. Convolution (10 points) Compute the convolution y [ n ] = x [ n ] * h [ n ] . Also plot the signal y [ n ] . (a) x [ n ] = (1 / 2) n u [ n ] , h [ n ] = (1 / 3) n u [ n ] . (b) x [ n ] = h [ n ] = (1 / 2) n u [ n ] . (c) x [ n ] = ( - 1 / 2) n u [ n - 4] , h [ n ] = 4 n u [2 -
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Unformatted text preview: n ] . (d) x [ n ] = u [ n ]-u [ n-5] , h [ n ] = u [ n-2]-u [ n-8] + u [ n-11]-u [ n-17] . (e) x [ n ] = u [ n ]-u [ n-5] , h [ n ] = δ [ n + 4] + δ [ n + 2] + δ [ n ] . Problem 4. Convolution (10 points) Compute the convolution y ( t ) = x ( t ) * h ( t ) . Also plot the signal y ( t ) . (a) x ( t ) = e-t u ( t ) , h ( t ) = e-2 t u ( t ) . (b) x ( t ) = e-t u ( t ) , h ( t ) = e-t u ( t ) . (c) x ( t ) = u ( t )-2 u ( t-2) + u ( t-5) , h ( t ) = e 2 t u (1-t ) . (d) x ( t ) = u ( t ) , h ( t ) = δ ( t )-2 δ ( t-2) + δ ( t-5) . (e) x ( t ) = δ ( t + 1) + δ ( t-1) , h ( t ) = δ ( t + 1) + δ ( t ) + δ ( t-1) ....
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ecen314-fall11-hw2 - n(d x n = u n-u n-5 h n = u n-2-u n-8...

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