Net 222: Communications and networks fundamentals ( Practical Part)

1. Net 222: Communications and networks fundamentals (Practical Part) Tutorial 1 : Chapter 1 problems (Signals & Systems) Networks and Communication Department

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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) Networks and Communication Department

12. 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

13. Answer (Cont.) Therefore, the system is linear. Networks and Communication Department

14. 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

15. 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

16. Answer • a) x(t-1) • b) x(2-t) Networks and Communication Department

17. 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

18. Answer • a)x[n-4] • c)x[3n] Networks and Communication Department

19. The End Any Questions ? Networks and Communication Department