Net 222: Communications and networks fundamentals ( Practical Part)

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Net 222: Communications and networks fundamentals ( Practical Part). Tutorial 1 : Chapter 1 problems (Signals & Systems) . Chapter 1 problems page 57. 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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### Net 222: Communications and networks fundamentals (Practical Part)

Tutorial 1 : Chapter 1 problems (Signals & Systems)

Networks and Communication Department

Chapter 1 problems page 57
• 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).

Networks and Communication Department

Question
• 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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• 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
• 1.5Let x(t) be a signal with x(t) =0 for t<3 , for each signal given below, determine the values if tfor which it is guaranteed to be zero.
• d)x(3t)
• e)x(t/3)

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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.
• 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
• 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 Awhere A is any real number or complex number ?

c) Is the invertible?

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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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b) Determine the output of the system when the input Awhere A is any real number or complex number ?

The output of the system will be

c) Is the invertible?

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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 Therefore, the system is not invertible.

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Question
• 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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• 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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Therefore, the system is linear.

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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
• 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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• a) x(t-1)
• b) x(2-t)

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Question
• 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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