JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year SIGNALS AND SYSTEMS Previous Question Paper (April/May - 2023 - R13)
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 trigonometric Fourier series.
Answer
A periodic signal x(t) with fundamental period T and fundamental frequency ω0 = 2π/T can be represented as a sum of harmonically related sinusoids: x(t) = a0 + Σ [an cos(nω0t) + bn sin(nω0t)], where the summation runs from n=1 to infinity.
What is the criterion for choosing error function?
Answer
The error function is chosen to minimize the mean square error (MSE) between the original signal and its approximation. The criterion requires that the error signal be orthogonal to the basis functions used for the approximation, ensuring the best possible fit in the least-squares sense.
What is anti-aliasing filter?
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Define Hilbert transform of a signal.
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What is signal bandwidth?
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State paley-Wiener criterion.
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Define spectral density.
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When the convolution and correlation equivalent?
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Define inverse Z – transform.
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State and prove the initial and final value theorems.
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Part B
Define a Signal. What are the different types of signals?
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Derive the expression for component vector C12 of approximating the function f1(t) over f2(t) and also prove that the component vector becomes zero if the f1(t) and f2(t) are orthogonal.
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Discuss the cosine form representation of Fourier series.
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Find the complex exponential Fourier series representation of x(t) = cos2t.
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State the properties of Fourier transform.
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Find the Fourier transform of x(t) = sin(8t + 0.1π).
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Find Fourier transform of e-2|t| sgn(t).
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Explain about effects of under sampling.
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Obtain the conditions for distortionless transmission through a system.
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Consider a stable LTI system characterized by the differential equation. Find its impulse response.
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Let the system function of an LTI system be 1/(jω + 3). What is the output of the system y(t) for an input (0.5)tu(t)?
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Write the ideal characteristics of LPF.
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Explain the detection of periodic signal in the presence of noise by autocorrelation.
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State and explain Parseval’s theorem.
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Write the properties of convolution.
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Find the convolution of the following signals by graphical method: x1(t) = u(t + 1) and x2(t) = u(t - 2).
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Prove that the signals x(t) = e-atu(t) and x(t) = e-atu(-t) have the same X(s) and differ only in ROC.
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Explain the distribution between Laplace, Fourier and Z-Transforms.
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Find Laplace Transform of x(t) = e-atsinh(ωt)u(t).
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