Subject Code: 2141005
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER-IV (NEW) EXAMINATION - WINTER 2018
Subject Name: Signals and Systems
Time: 02:30 PM TO 05:00 PM
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1
(a) Explain Energy and power signal [03]
(b) Explain time shifting and periodicity property of laplace transform. [04]
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(c) Write the properties of convolution and explain them with suitable example. [07]
Q.2
(a) Define system and explain the classification of system. [03]
(b) Consider the following signal X(t)= de-atu(t), a>0 Is X(t) an energy signal or power signal as a->0 what is the nature of signal? [04]
(c) Compute convolution: [07]
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- y(n)=x(n)*h(n), x(n)={1,1,0,1,1}, h(n)={1,2,3,3,4}
- y(n)=x(n)*h(n), x(n)= h(n)={1,2,-1,3}
OR
Q.3
(a) Explain the properties of continuous time and discrete time systems. [03]
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(b) Prove that a DT LTI system is causal if and only if h(n)=0 for n<0. [04]
(c) Impulse response of DT LTI system is given by h(n)=n (1/2)n u(n). Determine whether the system is stable or not. [07]
Q.3
(a) Obtain the convolution integral of X(t)=1 for -1<t<1 H(t)=1 for 0<t<2 [03]
(b) State and prove a condition for a discrete time LTI system to be stable. [04]
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(c) Find and sketch even and odd component of following: f(x)={ t, 0<t<1 2—t 1<t<2 [07]
Q.4
(a) Find the convolution of two signals X1(t) and X2(t) X1(t)= e-tu(t) X2(t)=u(t —4) [03]
(b) State and prove the initial value theorem. [04]
(c) Find the fourier series representation for the saw tooth wave depicted in the following figure. [07]
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OR
Q.4
(a) Write the time scaling property of fourier transform and find the fourier transform of x(t)= e -atu(t) [03]
(b) Prove that when a periodic signal is time shifted, then the magnitude of its fourier series coefficient remains unchanged. (|an|=|bn|) [04]
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(c) Find the fourier transform of the periodic signal x(t)=cos(2pft) u(t) [07]
Q.5
(a) Obtain the DFT of unit impulse d(n) [03]
(b) Determine the z-transform of following finite duration sequence X(n)={1,2,4,5,0, 7} [04]
(c) Find the Z-transform of the signal X(n)=(1/3)n u(n) + 5 (1/2)n u(-n—1) [07]
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OR
Q.5
(a) Explain discrete fourier transform and enlist its features. [03]
(b) Define the region of convergence with respect to z-transform. [04]
(c) Find the inverse z-transform of X(z)=z/(z-1) |z| >1 [07]
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Date: 14/12/2018
Total Marks: 70
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