Transcript Slide 1

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NET 222: COMMUNICATIONS AND
NETWORKS FUNDAMENTALS
(PRACTICAL PART)
Networks and
Communication
Department
Tutorial 1 : Chapter 1 problems (Signals & Systems)
Chapter 1 problems page 57
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Chapter 1 problems page 57 (Signals & systems
book).
1.4 (a,b).
1.5 (d,c).
1.16.
1.19 (a).
1.21 (a,b).
1.22 (a,c).
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Question
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1.4 Let x[n] be a signal with x[n] =0 for n<-2 and
n>4 , for each signal given below, determine the
values if n for which it is guaranteed to be zero.
a) x[n-3]
b) x[n+4]
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Answer
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a) x[n-3]
The signal x[n] is shifted by 3 to the right. The
shifted signal will be zero for n <1 & n>7.
b) x[n+4]
The signal x[n] is shifted by 4 to the left. The
shifted signal will be zero for n <-6 & n>0.
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Question
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1.5 Let x(t) be a signal with x(t) =0 for t<3 , for
each signal given below, determine the values if t
for which it is guaranteed to be zero.
d)x(3t)
e)x(t/3)
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Answer
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d)x(3t)
x(3t) is obtained by linearly compressing x(t) by
a factor of 3. there for, x(3t) will by zero for t<1.
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e)x(t/3)
x(t/3) is obtained by linearly stretching x(t) by a
factor of 3 . Therefore, x(t/3) will be zero for t<9.
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Question
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1.16 consider a discrete – time system with input
x[n] and output y[n]. The input output
relationship for this system is
y[n]=x[n]x[n-2]
a) Is the system memoryless ?
b) Determine the output of the system when the
input A 𝜹 𝐧 , where A is any real number or
complex number ?
c) Is the invertible?
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Answer
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a) Is the system memoryless ?
The system is not memoryless because y[n]
depends on past values of x[n].
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Answer (Cont.)
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b) Determine the output of the system when the
input A 𝜹 𝐧 , where A is any real number or
complex number ?
The output of the system will be
y=𝜹 𝐧 𝜹 𝐧−𝟐 =𝟎
c) Is the invertible?
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Answer (Cont.)
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c) Is the invertible?
From the result of part (b), we may conclude that
the system output is always zero for inputs of the
form 𝜹 𝐧 − 𝒌 , 𝒌 ∈ 𝑳. Therefore, the system is not
invertible.
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Question
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1.19 for each of the following input-output
relationships, determine whether the
corresponding system is linear, time invariant or
both.
a) y(t)=t2x(t-1)
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Answer
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1- consider two arbitrary inputs
and
Let
be a linear combination of
That is
Where a and b are arbitrary scalars. If
is the
input to the given system, then the corresponding
output
is
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Answer (Cont.)
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Therefore, the system is linear.
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Answer (Cont.)
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2- consider an arbitrary input
let
be the corresponding output. Consider a second input
obtained by shifting
in time:
The output corresponding to this input is
Also note that
Therefore, the system is not time-invariant.
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Question
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1.21 a continuous-time signal x(t) is shown in
figure P1.21. sketch and label carefully each of
the following signals:
a) x(t-1)
b) x(2-t)
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Answer
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a) x(t-1)
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b) x(2-t)
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Question
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1.22 a discrete signal x[n] is shown in figure
P1.22. sketch and label carefully each of the
following signals:
a)x[n-4]
c)x[3n]
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Answer
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a)x[n-4]
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c)x[3n]
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The End
Any Questions ?
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