Signals & Systems Fundamentals: Chapter 1 Problems and Solutions
Explore Chapter 1 problems related to Signals & Systems in the field of Communications and Networks. Understand how signals shift and compress based on given conditions to determine when they are guaranteed to be zero.
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1 NET 222: COMMUNICATIONS AND NETWORKS FUNDAMENTALS (PRACTICAL PART) Networks and Communication Department Tutorial 1 : Chapter 1 problems (Signals & Systems)
Chapter 1 problems page 57 2 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 3 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 4 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 5 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) Networks and Communication Department
Answer 6 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 7 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 ? ? , where A is any real number or complex number ? c) Is the invertible? Networks and Communication Department
Answer 8 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.) 9 b) Determine the output of the system when the input A ? ? , where A is any real number or complex number ? The output of the system will be y = ? ? ? ? ? = ? c) Is the invertible? Networks and Communication Department
Answer (Cont.) 10 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 11 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
Answer 12 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.) 13 Therefore, the system is linear. Networks and Communication Department
Answer (Cont.) 14 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 15 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
Answer 16 a) x(t-1) b) x(2-t) Networks and Communication Department
Question 17 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
Answer 18 a)x[n-4] c)x[3n] Networks and Communication Department
The End 19 Any Questions ? Networks and Communication Department
