JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II SIGNALS AND STOCHASTIC PROCESS Previous Question Paper (November/December - 2017 - R16)
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.
Part A
Write about unit step function and unit impulse function.
Answer
The unit step function u(t) is defined as 1 for t ≥ 0 and 0 for t < 0. The unit impulse function δ(t) is defined as 0 for t ≠ 0, with an area of 1, such that the integral from -∞ to +∞ of δ(t)dt = 1.
Define signal bandwidth and system bandwidth.
Answer
Signal bandwidth is the range of frequencies over which the signal's spectral density is non-zero or significant. System bandwidth is the range of frequencies over which a system (such as a filter or channel) provides a specified level of performance, typically defined by the 3-dB cutoff points.
Determine the complex exponential Fourier series representation for
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Find the Fourier transform of
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Find the Laplace transform of
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Write the differences between the continuous-time signal
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Explain about second order stationary process.
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Explain about Cross-Covariance function.
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Define Cross-Power Spectrum function.
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Find auto correlation function for
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Part B
Define orthogonal signal space and orthogonal vector space. Bring out clearly its applications in representing a signal and vector respectively.
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Explain how functions can be approximated using orthogonal functions.
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Derive the relationship between rise time and bandwidth.
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State and Prove the Convolution property of Fourier transform.
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Expand following function f(t) by trigonometric Fourier series over the interval (0,1). In this interval f(t) is expressed as f(t) = At
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State and prove multiplication property of continuous time Fourier series.
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Find the Fourier transform of symmetrical gate pulse and sketch the spectrum.
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State and prove sampling theorem for band limited signals using analytical approach.
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State and prove the properties of ROC of Laplace transform.
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Find the inverse Laplace transform of
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Find X(z) and sketch the zero-pole plot and the ROC for a < 1 and a > 1 for the signal
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Determine the inverse Z transform of
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Explain briefly about Gaussian and Poisson Random Process.
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Show that the random process
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Explain about Auto-correlation function with their properties.
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Show that mean square value of output response is independent of time t.
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Explain about cross power spectrum density and its properties with proofs.
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Derive the relationship between cross-power spectrum and cross correlation function.
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