Signals and Systems
(40242)
Department of Computer Engineering
Instructor: Dr Manzuri
Sharif University
of Technology
Deadline: 23 Mehr
HW 1 – Theory
Notes:
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Deliver your answers to Dr Manzuri at the end of class session at 23 Mehr.
Each day delay in delivering will result into 25% decreasing of grade.
If there is any question about this homework, just contact Ms. Ebrahimi or Ms. Salimi .
1. Calculate the energy of signals below. (6 point)
I. [ ]
II. [ ]
[ ]
{
III.
2. Determine if each of the following systems is time-invariant, memory less, linear, stable
and causal. Justify your answers. (20 point)
[ ]
I.
II.
∑
x(t)= (cos
[ ]
x(t)
∫
III.
[ ]
IV.
∑
[ ]
3. Determine whether or not each of the following signals is periodic. If a signal is periodic,
specify its fundamental period. (20 point)
I.
[ ]
( )
( )
II.
III.
IV.
V.
1
[
(
)
4. Consider the system which multiply the input signal with u[n], after transmission by LTI
system with
[ ]
[
]. Justify your answer about questions about total
system. (9 point)
I. Is it LTI?
II. Is it stable?
III. Is it causal?
5. Consider a causal LTI system related by the difference equation below: (9 point)
y[n]- y[n-1] = x[n]
I. Find the impulse response of system (h[n]).
II. Find the unit step response of system (u[n]).
III. Is the system causal? Justify your answer.
6. Consider a LTI and causal system with given impulse response below. (10 point)
I. Find unit step response of
for
II. Compute
when
and input signal is
(Initial energy of system is zero when
.
)
7. Consider the continues-time system with following input x[n] and output y[n]. the
input output relationship is: (10 point)
∫
I.
II.
III.
IV.
V.
Is the system memory less?
Is it causal?
Is it stable?
Is it linear?
Is it time invariant?
For each part justify your answer.
8. Problem number 2.43 from the Oppenheim’s book. (8 point)
9. Problem number 2.24 from the Oppenheim’s book. (8 point)
Good luck
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