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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

Net 222: Communications and networks fundamentals (Practical Part)

Tutorial 1 : Chapter 1 problems (Signals & Systems)

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Chapter 1 problems page 57
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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Question
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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Answer
Answer

  • 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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Question1
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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Answer1
Answer

  • 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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Question2
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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Answer2
Answer

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
Answer (Cont.)

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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Answer cont1
Answer (Cont.)

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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Question3
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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Answer3
Answer

  • 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 cont2
Answer (Cont.)

Therefore, the system is linear.

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Answer cont3
Answer (Cont.)

  • 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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Question4
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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Answer4
Answer

  • a) x(t-1)

  • b) x(2-t)

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Question5
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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Answer5
Answer

  • a)x[n-4]

  • c)x[3n]

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The end
The End

Any Questions ?

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