JNTU
JNTU B.Tech II SIGNALS AND STOCHASTIC PROCESS Previous Question Paper (April/May - 2018 - R16)
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. Each question carries 10 marks.
PART - A
What is meant by Total response?
Answer
The total response of a linear system is the sum of the zero-input response (the output due only to initial conditions) and the zero-state response (the output due only to the input signal).
Define Unit step function and Signum function.
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, -1 for t < 0, and 0 at t = 0.
State “time shift” property of Fourier transform.
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Define aliasing effect? How can you overcome?
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What is the time shifting property of Z transform?
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Define inverse Laplace transform. State the linearity property for Laplace transforms.
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Give an example of evolutionary random process.
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List the properties of Cross correlation function.
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Define wiener khinchine relations.
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State any two properties of cross-power density spectrum.
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PART - B
Define the error function while approximating signals and hence derive the expression for condition for orthogonality between two waveforms f1(t) and f2(t).
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Obtain the impulse response of an LTI system defined by dy(t)/dt + 2y(t) = x(t). Also obtain the response of this system when excited by e-2t u(t).
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State and prove sampling theorem for band limited signals.
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State and prove Differentiation and integration properties of Fourier Transform.
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Obtain the expressions to represent trigonometric Fourier coefficients in terms of exponential Fourier coefficients.
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Determine the inverse Laplace of the following functions.
1 / (s(s+1)(s+3))
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(3s2+8s+6) / ((s+8)(s2+6s+1))
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Find the Inverse Z transform of X(z) = (z+2)/(z2-4z+3) ; |z| < 3/4
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Find the Z transform of x[n] = an+1 u[n+1].
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X(t) is a random process with mean=3 and Autocorrelation function Rxx(τ) = 10[exp(-0.3|τ|)+2]. Find the second central Moment of the random variable Y=X(3)-X(5).
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X(t)=2ACos(Wct+2θ) is a random Process, where ‘θ’ is a uniform random variable, over (0,2π). Check the process for mean ergodicity.
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A random process is defined as X(t) = A Cos(ωot +Θ), where Θ is a uniformly distributed random variable in the interval (0,π/2). Check for its wide sense stationarity? A and ωo are constants.
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Given the auto correlation function for a stationary ergodic process with no periodic components is RXX(τ) = 25+4/(1+6τ2). Find mean and variance of process X(t).
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Compare and contrast Auto and cross correlations.
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If Y(t) = A Cos(w0t+θ)+N(t), where ‘θ’ is a uniform random variable over (-π,π), and N(t) is a band limited Gaussian white noise process with PSD=K/2. If ‘θ’ and N(t) are independent, find the PSD of Y(t).
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Given RXX(τ) = Ae-α|τ| and h(t) = e-βt u(t). Find the spectral density of the output Y(t).
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