Assignment5
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ECSE-303 SIGNALS AND SYSTEMS I Assignment 5
ECSE-303 Problem Assignment 5 Problem 1 (25 marks) Find the output y(t) of the system h ( t ) = e
−2t
u ( t ) for the anti-causal input x ( t ) = e − t u ( −t ) by
using the Laplace transforms.
Problem 2 (30 marks) Compute the Laplace transform of the following signal. Find its Fourier transform if it exists.
(
)
x(t ) = 1 − e− t u (t ) − et u (−t )
Problem 3 (45 marks) Consider an LTI system with transfer function
H (s) =
s2 − s − 2 . s 2 + 5s + 6
Sketch all possible regions of convergence (ROC's) of H ( s ) on a pole-zero plot and compute the associated impulse responses h(t ) . Indicate for each impulse response whether it corresponds to a system that is causal/stable.
1/1
Rev. 2/27/2007
ECSE-303 Problem Assignment 5 Problem 1 (25 marks) Find the output y(t) of the system h ( t ) = e
−2t
u ( t ) for the anti-causal input x ( t ) = e − t u ( −t ) by
using the Laplace transforms.
Problem 2 (30 marks) Compute the Laplace transform of the following signal. Find its Fourier transform if it exists.
(
)
x(t ) = 1 − e− t u (t ) − et u (−t )
Problem 3 (45 marks) Consider an LTI system with transfer function
H (s) =
s2 − s − 2 . s 2 + 5s + 6
Sketch all possible regions of convergence (ROC's) of H ( s ) on a pole-zero plot and compute the associated impulse responses h(t ) . Indicate for each impulse response whether it corresponds to a system that is causal/stable.
1/1
Rev. 2/27/2007
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