JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year SIGNALS, SYSTEMS AND SIGNAL PROCESSING Previous Question Paper (April/May - 2023 - R18)
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 Energy and power signals. Give examples.
Answer
An energy signal is a signal that has finite total energy and zero average power. Its energy is defined as E = ∫|x(t)|² dt from -∞ to ∞. An example is a single rectangular pulse. A power signal is a signal that has finite non-zero average power and infinite total energy. Its power is defined as P = lim(T→∞) (1/2T) ∫|x(t)|² dt from -T to T. An example is a continuous sinusoidal signal.
Give the relationship between unit impulse and unit step functions.
Answer
The unit impulse function, denoted by δ(t), and the unit step function, denoted by u(t), are related through differentiation and integration. The unit impulse is the derivative of the unit step function:
Conversely, the unit step function is the integral of the unit impulse function:
This relationship implies that the unit step function represents the accumulation of the unit impulse, effectively acting as a switch that turns on at t = 0.
What are Dirichlet’s conditions?
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State and prove time shifting property of Fourier transform.
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Determine whether the LTI system with impulse response h(t) = etu(-t-1) is BIBO stable or not?
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Draw the frequency response of ideal high pass and band stop filters.
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Find the Z- transform of a signal x(n) = δ(n-1) + δ(n+1).
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State the properties of ROC of Laplace transform.
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What are the applications of FFT?
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What are the advantages of Chebyshev filters over Butterworth filters?
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Part B
Determine whether the following system is linear, time-invariant, causal and stable with appropriate test conditions y(t) = 2x(t) + u(t+1).
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Show that the two complex functions ejnω0t and ejmω0t are orthogonal over an interval [t0, t0 + 2π/ω0] for integral values of m and n.
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A rectangular function defined as f(t) = A ; 0 ≤ t ≤ π, f(t) = -A; π ≤ t ≤ 2π. Approximate the above function by cos(t) over an interval (0, 2π) such that the mean square error is minimum.
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Explain about classification of signals with examples.
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Determine the exponential Fourier series representation of the periodic signal x(t) = t2; 0 < t < 2 with fundamental period T = 2 sec.
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Compute the Fourier transform of a signal x(t) = 1 + cos(πt); -1 ≤ t ≤ 1, = 0; otherwise.
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State and prove any four properties of Fourier series.
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Find the Fourier transform of a signal x(t) = e-3|t|.
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Draw the circuit diagram of a physically realizable LPF and also sketch its impulse response.
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Determine the convolution of the following signals x(t) = e2tu(-t) and h(t) = u(-t) using graphical method.
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Write short notes on distortion less transmission through a system.
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Derive the relation between Bandwidth and rise time.
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Find the inverse Laplace transform of a function X(s).
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State and prove multiplication property of Z-transform.
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State and prove any two properties of Laplace transform.
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Determine the inverse Z transform of a function X(Z) with ROC |Z| > 2.
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Compute the convolution of sequences x1(n) = (1, 2, 1, 2) and x2(n) = (1, 3, 4, 2).
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Convert an analog filter with transfer function H(s) into equivalent digital filter using impulse invariant method.
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Find the DFT of the following sequence using radix-2 decimation-in-time FFT algorithm. x(n) = (1, 2, 3, 4, 4, 3, 2, 1).
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Determine the transfer function of a second order normalized low pass Butterworth Filter.
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