Signals and Systems 2022 Question Paper — Government College of Engin…

Instructions

• Attempt five questions selecting atleast two questions from each section.
• Use of calculator is allowed.
• Assume missing data,if any.
• Each question carries equal marks.

Questions

Section - A

• Q1. 1.a. Explain in detail classification of signals. b. A continuous time signal x(t) is shown in fig below: [Signal Waveform] Sketch the waveform of x(2-3t). [15 marks]
• Q2. 2.a. Determine energy and power of following signals i. $x(t) = e^{j(3t+(\pi/6))}$ ii. $x(t) = 3\cos 5\Omega_0 t$ b. Verify whether the following continuous time signals are periodic. If periodic,find the fundamental period and fundamental frequency. i. $x(t) = 2\cos(t/4)$ ii. $x(t) = 3\cos(\sqrt{2}t) + 7 \cos 5\pi t$ [15 marks]
• Q3. 3.a. Define unit step response. Derive an expression to obtain unit step response using convolution. b. Perform convolution of following casual signals. i. $x_1(t) = tu(t)$ , $x_2(t) = e^{-5t}u(t)$ ii. $x_1(t) = e^{-2t}u(t)$ , $x_2(t) = e^{-5t}u(t)$ [15 marks]
• Q4. 4.a. Test the stability of LTI systems,whose impulse responses are given below: i. $h(t) = e^{-3tu}(t)$ ii. $h(t) = e^{-t} \sin t \; u(t)$ b. Determine complete response of first order discrete time system described by difference equation, $y(n) = -0.5y(n-1) + x(n)$ When input is unit step, and width initial condition i. $y(-1) = 0$ ii. $y(-1) = 1/3$ [15 marks]

Section - B

• Q5. What are the various conditions for existence of Fourier series. Find the trignometric Fourier series of the waveform as shown in the fig: [Signal Waveform] [15 marks]
• Q6. 6.a. Write down various properties of Fourier transform. b. Find the Fourier transform of triangular pulse shown in Fig: [Signal Waveform] [15 marks]
• Q7. 7.a. Draw pole zero diagram of following z domain signal: $X(z) = \frac{1.25 - 1.25 z^{-1} + 0.2 z^{-2}}{2 + 2z^{-1} + z^{-2}}$ b. Find the one sided z transform of discrete time signals generated by mathematically sampling the following continuous time signal. $X(t) = \sin \Omega_0 t$ c. Determine z transform and ROC of $x(n) = 0.2^n u(-n-1)$ [15 marks]
• Q8. 8.a. Explain frequency domain analysis of sampled signal. What are the various methods to reconstruct a sampled signal? b. Explain filtering system in detail. [15 marks]

Related pages

• Signals and Systems syllabus
• All Signals and Systems papers from 2022

Other years

• Signals and Systems 2022 question paper — end-term
• Signals and Systems 2022 question paper — end-term