Subject 2018 Question Paper — Government College of Engineering and T…

Instructions

• Attempt five questions in all selecting at least two questions from each Section.
• Each question carries 20 marks.

Questions

Section - A

• Q1. (a) Explain the concept of probability and derive for Baye's theorem. (b) Two factories produce identical clocks. The production of the first factory consists of 10000 clocks of which 100 are defective. The second factory produces 20000 clocks of which 300 are defective. What is the probability that a particular clock was produced in the first factory? . ( 10, 10 ) [20 marks]
• Q2. (a) Prove that the energy of the Gaussian pulse is given by $1/26 \pi$ where $6$ is the standard deviation of the pulse. (b) Which of the following functions satisfy the properties of PDF and why? (i) $f_x (x) = \frac{1}{x (1+x^2)}$ (ii) $f_x (x) = x \text{ for } x < 1$ (iii) $f_x (x) = (8-x)/6$ . ( 10, 10 ) [20 marks]
• Q3. (a) Discuss the Autocorrelation function for Energy signals and derive for the properties. ( 10 ) (b) Find the magnitude and the phase spectrum of the following signals in Figure 1. ( 10 ) $X(t) = A \text{ for } -T \le t \le 0$ $-A \text{ for } 0 \le t \le T$ $0, \text{ otherwise.}$ [20 marks]
• Q4. (a) Find the exponential Fourier series of the following wave formin Figure 2 and final Parseval's power. (b) Consider a pulse given as: $F(t) = \cos (\pi/T) \text{ for } -T/2 \le t \le T/2$ $0, \text{ otherwise.}$ Find (i) Autocorrelation function (ii) Energy spectral density. ( 10, 10 ) [20 marks]

Section - B

• Q5. (a) Discuss the following noises: (i) Atmospheric noise (ii) Industrial Noise (iii) Low frequency & High frequency noise. (b) For the circuit shown in the Figure 3, calculate the equivalent input noise resistance. ( 10, 10 ) [20 marks]
• Q6. Determine the concept of linear filtering in case of RC low pas filter, ideal low pass filter and the ideal band pass filter. Also find the noise B. W for the RC filter. [20 marks]
• Q7. (a) Explain the concept of information and its sources. Discuss entropy and the information Rate. (b) For a lossless channel with m input symbols and m output symbols prove that $H(X) = H(Y) \text{ and } H(X|Y) = 0$ ( 10, 10 ) [20 marks]
• Q8. (a) Given the BSC in Figure 4, with $P(x_1) = \alpha$. Show that (i) $I(X; Y) = H(Y) + p \log_2(p) = (1-p) \log_2(1-p)$ (ii) $I(X; Y) \text{ when } \alpha = 0.5 \text{ and } p = 0.1$ (b) A DMS X with five symbols $x_1, x_2, x_3, x_4 \text{ and } x_5$ having probabilities $0.2, 0.15, 0.05, 0.1, 0.5$. (i) Construct a Shannon - Fano coding for x and calculate code efficiency. (ii) Repeat for Huffman coding. ( 10, 10 ) [20 marks]