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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)

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]

Networks and Communication Department

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.

Networks and Communication Department

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)

Networks and Communication Department

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.

Networks and Communication Department

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?

Networks and Communication Department

Answer

a) Is the system memoryless?

The system is not memoryless because y[n] depends on past values of x[n].

Networks and Communication Department

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?

Networks and Communication Department

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.

Networks and Communication Department

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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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

Networks and Communication Department

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.

Networks and Communication Department

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)

Networks and Communication Department

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]

Networks and Communication Department

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