JNTU
JNTU B.Tech II SIGNALS AND SYSTEMS Previous Question Paper (April/May - 2018 - R15)
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
Write any two requirements for orthonormality.
Answer
Two requirements for orthonormality of a set of functions {φn(t)} are:
- Orthogonality: The integral of the product of any two distinct functions in the set over a specified interval is zero. Mathematically, ∫-∞∞ φm(t) φn*(t) dt = 0 for m ≠ n.
- Normality (or Unit Energy): The integral of the squared magnitude of each function in the set over the specified interval is one. Mathematically, ∫-∞∞ |φn(t)|2 dt = 1 for all n.
Correlate the relationship between Unit Step and Unit Impulse Functions.
Answer
The Unit Step function, u(t), and the Unit Impulse function, δ(t), are closely related through differentiation and integration.
The Unit Step function is defined as:
u(t) = { 1, for t ≥ 0
0, for t < 0 }
The Unit Impulse function is the derivative of the Unit Step function:
δ(t) = du(t)/dt
Conversely, the Unit Step function is the integral of the Unit Impulse function:
u(t) = ∫-∞t δ(τ) dτ
This means that the Unit Impulse function represents a sudden change or a spike at t=0, and integrating this spike results in the rise of the Unit Step function from 0 to 1 at t=0.
What is Hilbert Transform?
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Determine x(t) whose Fourier Transform is given by X(jω) = 1 for |ω| < W and 0 otherwise.
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Define bandwidth of a signal.
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What is the Paley-Wiener criterions for physical realization?
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State Parseval’s Theorem for Fourier transform.
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List the properties of Auto correlation.
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Determine the Laplace transform for x(t) = e-atu(t), a > 0.
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Write down the relationship between Fourier Transform and Laplace Transform.
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Unit I
Obtain the orthogonality component of complex signal and Correlation coefficients.
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State the Energy of the sum of Orthogonal signals.
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Find the trigonometric Fourier Series for the exponential x(t) = e-t/2 over the interval 0 ≤ t ≤ π.
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Unit II
Find the fourier transform of: i) x(t) = u(t) ii) x(t) = eatu(-t), a > 0.
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State the following Fourier transform properties: i) convolution ii) time shifting.
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How to reconstruct a signal from its samples using interpolation. Explain.
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What are the effect of under sampling? And discuss different types of samplings.
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Unit III
Determine the Unit impulse response h(t) for a system specified by the equation (D2 + 3D + 2)x(t) = Df(t).
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What are the specific criteria for designing an analog filter?
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What are the necessary conditions for distortion less Transmission? Derive them.
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Find the loop current y(t) of the RLC circuit for the input, when all initial conditions are zero.
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Unit IV
Convolute x(t) = e-tu(t) and h(t) = u(t - 3) using graphical representation.
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State and prove convolution property of Fourier Transform.
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State and derive Convolution theorem.
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Find the energy of signal f(t) = e-atu(t). Determine the Frequency W(rad/s) so that the energy contributed by the spectral components below W is 95% of Signal Energy.
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Unit V
Consider an LTI system with system function H(s) = 1/((s+1)(s-2)), obtain the system response and ROC in S-Plane.
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Find the Laplace transform of x(t) = t.e-atu(t).
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Consider the given signal x[n] = bn, b > 0. Obtain the z-transform along with ROC.
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Consider a system with system function H(z) = 1/(1 - 0.5z-1), |z| > 0.5, obtain h(n).
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