JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III LINEAR SYSTEMS ANALYSIS Previous Question Paper (July - 2023 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
Define state variable.
Answer
A state variable is a set of variables that represent the minimum amount of information about a system at a given time t0, which, along with the knowledge of input for t ≥ t0, is sufficient to determine the state of the system at any future time t > t0.
Write the general form of state space representation.
Answer
The general state space representation is given by the state equation and the output equation:
Where x(t) is the state vector, u(t) is the input vector, y(t) is the output vector, and A, B, C, and D are the system, input, output, and direct transmission matrices respectively.
What is a periodic function?
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What is a Fourier series?
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How do we calculate Laplace transform?
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What is the Laplace transform of sin t?
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Explain the difference between natural and flat sampling.
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List the properties of correlation function.
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State the differences between Laplace and Fourier transform.
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State the properties of region of convergence in Z transform.
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Part B
How do we identify state variables of a circuit?
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What are the advantages of state variable analysis?
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Explain network topology method with suitable example.
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Find the Fourier series of the function f(x) = x2, –𝜋 < x < 𝜋.
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Find the value of the real number a0 of the Fourier series if f(x) = x2 for 0 ≤ x ≤ 2𝜋.
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For f(x) = x2 (1 – x4), find the bn of the Fourier series x ∈ (–l,l).
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Explain different properties of Fourier Transform.
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Consider y' - 2y = e3x and y(0) = -5. Find the value of L(y).
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An electric circuit consisting of a resistance (R) and an inductor (L), connected in series. Consider the switch (S) is closed at time t=0, find the step response.
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Find the step response and impulse response of the series RL circuit.
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What is the Convolution Theorem? Explain with example.
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State and explain sampling theorem with example.
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Derive the graphical and analytical proof for Band Limited Signal.
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Explain the relation between auto correlation function and Energy spectral density function.
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Explain cross correlation in signal sampling.
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Write the Z-transform for a finite sequence given below: x = {-2, -1, 1, 2, 3, 4, 5}.
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What is Z-transform of a discrete sequence? Explain with example.
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What are discrete time complex exponentials?
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What are the properties of Z-transforms?
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