JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II SIGNALS AND SYSTEMS Previous Question Paper (March - 2022 - R13)
Answer any five questions
All questions carry equal marks
Main
Derive the relation between unit step function and signum function along with their appropriate definitions.
Answer
The unit step function u(t) is defined as 1 for t > 0 and 0 for t < 0. The signum function sgn(t) is defined as 1 for t > 0 and -1 for t < 0. To relate them, observe that u(t) transitions from 0 to 1 at t=0, while sgn(t) transitions from -1 to 1. We can express the signum function as a combination of unit steps: sgn(t) = u(t) - u(-t). Conversely, since u(t) + u(-t) = 1, we can substitute u(-t) = 1 - u(t) into the signum expression to get sgn(t) = u(t) - (1 - u(t)), which simplifies to the relation
Determine the complex Fourier series expansion of a triangular signal with period T=4 and fundamental frequency of
Answer
For a triangular wave x(t) with period T=4, let the signal be defined as x(t) = 1 - |t| for -2 < t < 2. The fundamental frequency is ω₀ = 2π/T = π/2. Since the signal is even, the sine terms in the Fourier series vanish (bₙ = 0). The DC component a₀ is the average value, which is 0.5. The coefficients aₙ are calculated using the integral
Determine the inverse Fourier Transform of the spectrum shown in Figure 1.
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State and prove the following property of Fourier Transform: Multiplication in time domain.
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Discuss sampling of continuous time signals.
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Find the Nyquist rate and the Nyquist interval for the signal
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Explain how a function can be represented by a closed or a complete set of mutually orthogonal functions.
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Check whether the following systems are linear time invariant systems or not:
i)
ii)
iii)
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Clearly discuss the filter characteristics of linear systems and mention conditions for distortionless transmission of a signal through the system.
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Find the impulse response of the system shown in Figure 2. Find the transfer function. What would be its frequency response? Sketch the response.
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Derive an expression that relates Energy Spectral Density and Autocorrelation function.
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State and prove convolution property of Fourier transforms.
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Find the Power, rms value and sketch the PSD for the following signal:
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Find the initial and final values of signal x(t) whose Laplace transform is
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Find inverse of the following Laplace transform
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Explain the concept of Z-transform of a discrete time sequence.
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Find the transform X(z) and sketch the pole-zero with the ROC for each of the following sequences:
i)
ii)
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