JNTU
JNTU B.Tech III SIGNALS AND SYSTEMS Previous Question Paper (February - 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
List out the properties of impulse function.
Answer
The unit impulse function, denoted by δ(t), possesses the following key properties:
- Sifting Property: The integral of the product of a function x(t) and a shifted impulse function yields the value of the function at the impulse location: ∫ x(t)δ(t - t₀) dt = x(t₀)
- Sampling Property: Multiplying a function by an impulse function samples the function at the instant the impulse occurs: x(t)δ(t - t₀) = x(t₀)δ(t - t₀)
- Scaling Property: The impulse function satisfies the relation: δ(at) = (1/|a|)δ(t)
- Area Property: The total area under the impulse function is unity: ∫ δ(t) dt = 1
Find the Energy of the signal.
Answer
The energy E of a continuous-time signal x(t) is defined as the integral of the square of its absolute value over all time:
For a discrete-time signal x[n], the energy is defined as the sum of the squares of its absolute values:
To calculate the energy, square the signal amplitude at every point, integrate or sum the resulting values over the entire duration of the signal, and ensure the result is finite for the signal to be classified as an energy signal.
State the Parseval’s Theorem of Fourier Series.
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Find the Fourier Transform of the unit step signal.
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Find the convolution between two impulse functions.
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Define Paley wiener criterion.
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List out the Properties of ROC.
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Find the Z-Transform of the unit step sequence.
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Determine the Energy Spectral density function of a signal.
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Find the Nyquist rate of the signal.
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PART - B
Define signal space. Give an example of a signal space, and define the term ‘Basis set’ for a signal space.
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Find the relationship between unit step signal and signum function.
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If x(t) is defined for -1 to 1, then sketch the transformed signal.
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Determine the fundamental frequency of the signal x(t) = cos(πt/3) + sin(πt/4).
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Find the TFS of a quarter wave odd symmetric periodic signal.
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Consider a rectified sine wave signal x(t) defined by x(t) = sin(πt). Find the complex exponential Fourier series of x(t).
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Find the Fourier Transform of a signal x(t) = e^(-a|t|).
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Find and sketch the Fourier Spectrum of the signal x(t) = 1/t.
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Find and sketch the impulse response of an Ideal LPF.
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Find the necessary and sufficient condition on the impulse response h(t) such that system is BIBO Stable.
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Verify that the impulse response of the LTI system y'(t) + y(t) = x(t) is h(t) = e^(-2t)u(t).
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Is this system i) Memoryless? ii) Causal? iii) Stable? Justify your answer.
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State and prove final value Theorem of Laplace transform.
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The input and output relationship of the continuous time system is y''(t) - y'(t) - 2y(t) = x(t). Determine the step response of the system when the system is causal.
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State and prove Convolution Theorem of Z-transform.
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Find the Z-Transform of the signal x(n) = (1/2)^n u(n) + (1/3)^n u(n).
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State and prove Uniform Sampling Theorem for band limited signals with the necessary mathematical equations. Also sketch the neat graphs (in time domain, frequency domain).
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State and prove the relationship between Auto correlation function and Energy Spectral density function.
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Find the Power spectral density of the signal x(t) = cos(πt/3) + sin(πt/4).
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