JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II SIGNALS AND SYSTEMS Previous Question Paper (November/December - 2017 - R16)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
Part A
Discuss the concepts of impulse function.
Answer
The unit impulse function, denoted by δ(t), is defined as a signal that is zero everywhere except at t = 0, where it has an infinite amplitude such that its total area equals unity. It serves as the fundamental building block for representing any arbitrary signal through the sifting property, x(t) = ∫ x(τ)δ(t-τ) dτ.
Explain about the convergence of the Fourier series.
Answer
Fourier series convergence refers to the conditions under which the infinite sum of trigonometric terms accurately represents a periodic signal. For a signal to be representable by a Fourier series, it must satisfy the Dirichlet conditions: the signal must be absolutely integrable over one period, have a finite number of maxima and minima, and have a finite number of discontinuities within any finite interval.
What is aliasing?
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Derive the Fourier transform of unit step signal.
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Distinguish between LTI and LTV systems.
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Define Rise time.
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Write any two properties of Correlation function.
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Write relation between convolution and correlation.
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Find the Laplace transform X(s) and sketch the pole-zero plot with the ROC for the signal x(t) = e-2tu(t) + e-3tu(t).
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State and Prove final value theorem in z-transform.
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Part B
Define orthogonal signal space and orthogonal vector space. Bring out early its applications in representing a signal and vector respectively.
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Define the following elementary signals: (i) Real exponential signal. (ii) Continuous time version of a sinusoidal signal and bring out the relation between sinusoidal and complex exponential signals.
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Let x1(t) be the continuous time periodic signal with frequency ω1 and FS coefficients ak. Let x2(t) = x1(1 - t) + x1(t - 1). How is ω2 of x2(t) related to ω1? Also find the relationship between the Fourier Series coefficients of x2(t), bk and coefficients ak.
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State the properties of Fourier series.
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Find the Fourier transform of i) x(t) = e-2|t-1| u(t-1) ii) e-2|t-1|
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Show that the signal m(t) and its Hilbert transform m^(t) are orthogonal over the entire time.
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State and prove sampling theorem for band limited signals using analytical approach.
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Give introduction to band pass sampling.
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The transfer function of an LTI system H(ω) is 16 / (4 + jω). Find the response y(t) for an input x(t) = u(t).
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Derive the relationship between Bandwidth and Rise Time.
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Explain causality and physical reliability of a system and hence give poly-wiener criterion.
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Sketch the frequency response of ideal LPF, HPF and BPF.
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Prove that the correlation and convolution functions are identical for even signals.
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Explain about graphical procedure to perform convolution.
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Explain the extraction of signal from noise by filtering.
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Derive the convolution property of Fourier transform.
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State and prove the properties of ROC of Laplace transform.
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Find the inverse Laplace transform of X(s) = s / ((s2+2s+5)(s+3)(s+5)2), Re(s) > -3.
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Distinguish between Laplace, Fourier and z-transforms.
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State and prove time shifting and convolution properties of z-transform.
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