JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year SIGNALS AND SYSTEMS Previous Question Paper (May/June - 2019 - R13)
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.
Part A
Plot unit Impulse signal and clearly indicate all the values.
Answer
The unit impulse signal, denoted by δ(t), is defined as a signal that has an infinite amplitude at t = 0 and zero amplitude elsewhere, while maintaining an area of unity. Graphically, it is represented by an arrow pointing upwards at the origin (t = 0) on the horizontal axis.
The vertical arrow is labeled with the value 1 to indicate its area (strength). The horizontal axis represents time (t), and the vertical axis represents the amplitude δ(t). The signal is zero for all t ≠ 0.
Find whether the signal given by x(n) = 5cos(6n) is periodic or not.
Answer
A discrete-time sinusoidal signal of the form x(n) = A cos(Ωn) is periodic if and only if the frequency Ω/2π is a rational number. For the given signal x(n) = 5 cos(6n), the angular frequency is Ω = 6 radians/sample.
To check for periodicity, we evaluate the ratio:
Since π is an irrational number, the ratio 3/π is also irrational. Because the ratio is not a rational number, the signal x(n) = 5 cos(6n) is aperiodic.
Find the Fourier transform of x(t)=sin(wt).
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List any three properties of Fourier transform.
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Define time invariant and time varying systems.
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Define impulse response of a linear time invariant system.
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Write the convolution equation representing its operation.
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State the Properties of Auto correlation.
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What are the two types of Z transform?
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What is the time shifting property of Z transform?
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Part B
Explain the analogy of vectors and signals in terms of orthogonality and evaluation of constant.
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List the properties of Fourier series.
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State the dirichilet’s conditions for existence of Fourier series.
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Derive the expression for Exponential Fourier series co-efficients.
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What is the Fourier transform of a Rectangular pulse existing between t = -T/2 to t = T/2.
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Find the Fourier transforms of signal x(t) = e-At sin(At).
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What are all the blocks are used to represent the CT signals by its samples?
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Find the Fourier transform of a signal x(t) = e-At sin(wt) u(t).
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Determine whether the following input-output equations are linear or non linear: i) y(t)=x2(t) ii) y(t)=x(t2) iii) y(t)=t2x(t-1) iv) y(t)=x(t) cos 50πt
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What are the three elementary operations in block diagram representation of CT system?
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Define system impulse response h(t). State the conditions for physical realizability in both time and frequency domains.
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Derive the conditions for distortion less transmission through a system.
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Determine the convolution of two functions x(t)=a e-at; y(t)= u(t).
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State and prove Parseval’s Theorem?
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Determine the convolution of two same Rectangular pulses x(t) shown in figure and also find its Auto correlation. Prove that both results are same.
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Find the z-transform of the following sequences: i) x[n]= cos nw u[n] ii) x[n]= an sin nw u[n] iii) x[n]= an u[-n]
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Find the Laplace transform of the following function, x(t)= (1/t) sin2 wt.
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Find the Laplace Transform of cos ωt and sin ωt using frequency shifting property.
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Compare and contrast Laplace and Fourier Transforms with examples.
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