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# KTU B.Tech S4 Model Questions Signals & Systems

#### EC202 Signals and Systems

Time: 3 Hrs                                                                                            Marks: 100
PART A
( Answer any One from 1 and 2. Q.No: 3 is Compulsory )
1. a)Define the following continuous functions.
(i) Signum function (ii) Sync function (3 mark)
b) Plot the signals

OR
2. a) Determine the odd and even part of the signal, x(t) = (1+t3 ) cos3 10t( 2 marks)
b) Check whether the following signals are Energy signals or power, Also determine energy / power.
(i) x(t) = A cos ( ω0t +θ)
(ii) x(t) = u(t+1)     (8 Marks)

3. (a) Determine the convolution of signals x1(t) = cost u(t), x2(t) = tu(t).(4 Marks)
(b)Plot the signals (6 marks)
(c) Graphically determine the convolution of signals (10 Marks)

PART B
(Answer any One from 4 and 5. Q.No: 6 is Compulsory)
4        i) Find LT of x(t) = e2t ( u(t) – u(t-4) ) (4 Marks)
ii)Find the complex exponential Fourier series representation of the signal given by x(t) = cos ω0t.
(6 marks)
OR
5        i)  Plot Magnitude spectrum and Phase spectrum of the signal x(t) = e –at   u(t) . (6 marks)
ii) Write down the time convolution property of Fourier Transform  (4  marks)
6        i) Verify initial value theorem for the function x(t) = 2- e 5t (5  marks)
ii) State and prove convolution theorem of Fourier series. (5 marks)
iii) Write down the time convolution property of Fourier Transform (5 marks)
iv) Expand the function x(t) shown, by trigonometric Fourier series over interval (0,1)(5 Marks)
PART C
(Answer any One from 7 and 8. Q.No: 9 is Compulsory)
7   i) What are the different sampling techniques? Explain in detail. (7 marks)
ii)Write a note on Discrete Hilbert Transform. (3 marks)
OR
8    i) Determine Z transform and ROC of the signal x(n) = u(n) – u (n-8)(6 Marks)
ii) Find DTFT of the sequence x(n) = -a n u(-n-1) (4Marks)
9      i) A band limited signal x(t) is sampled by a train of pulses of width τ and period T. Determine the spectrum of           sampled signal and sketch it. Also find expression for sampled signal (10 marks)
ii) Find the Inverse Z transform of the signals (10 marks)