JNTU B.Tech II SIGNALS AND STOCHASTIC PROCESS Previous Question Paper (November/December - 2018 - R16)

Is the system described by the equation y(t) = x(2t) time invariant or not? Why?

Give the relation between bandwidth and Rise time of a signal.

What are the effects of aliasing and how can you minimize the aliasing error?

Distinguish between series and transform in the Fourier Representation of a signal.

Let X(s) = L{x(t)}, determine the initial value, x(0) and the final value x(∞), for the following signal using initial value and final value theorems.

How the stability of a system can be found in Z-Transform and what is the condition for causality in terms of Z-Transform.

Prove that R_xy(τ) = R_yx(-τ).

If the customers arrive at a bank according to a Poisson process with mean rate 2 per minute, find the probability that during a 1-minute interval no customer arrives.

Prove that the power spectral density of a real random process is an even function.

Find the auto correlation function, whose spectral density is:

Prove that the set sin(mω₀t) and sin(nω₀t) are orthogonal for m ≠ n, where m=0,1,2... and n=0,1,2... over (t₀, t₀ + 2π/ω₀).

Explain the concepts of unit step function and Signum function.

Explain causality and physical reliability of a system and explain Paley-wiener criterion.

Consider a stable LTI system characterized by the differential equation: dy(t)/dt + 2y(t) = x(t). Find its impulse response.

Find the Fourier Transform of the signal x(t) = e^(-at) u(t).

Define sampling theorem for time limited signal and find the Nyquist rate for the following signals: i) rect(t/300) ii) 10 cos(300πt).

Derive the expression for trigonometric Fourier series coefficients.

Determine the exponential form of the Fourier series representation of the signal shown in figure 1.

By using the power series expression technique, find the inverse Z-Transform of the following X(z) = z / (z² - 3z + 2), |z| < 1.

Distinguish between the Laplace, Fourier and Z-Transforms.

Find the Laplace Transform of the periodic, rectangular wave shown in figure 2.

Find the Laplace Transform of following functions: i) Exponential function ii) Unit step function.

Explain the characteristics of a first order and strict sense stationary process using relevant expressions.

State and prove the properties of auto correlation of a random process.

Find the mean, variance and Root Mean Square value of the process, whose auto correlation function is R_xx(τ) = 25 + 36 / (6.25 + τ²).

Consider two random processes x(t) = cos(ωt + θ) and y(t) = cos(ωt + φ), where φ = θ - π/2 and θ is uniformly distributed over (0, 2π), verify |R_xy(τ)|² ≤ R_xx(0)R_yy(0).

Derive the relation between input and output power spectral densities of a linear system.

The cross power spectrum of real random process x(t) and y(t) is given by S_xy(ω) = a + ib, if |ω| ≤ 1, 0 elsewhere. Find the cross correlation function.

Consider a random process X(t) = A₀ cos(ω₀t + θ), where A₀ and ω₀ are constants and θ is a uniform random variable in the interval (0, π), find whether X(t) is WSS process.

Show that S_yy(ω) = |H(ω)|² S_xx(ω), where S_xx(ω) and S_yy(ω) are the power spectral density functions of the input and output respectively and H(ω) is the system transfer function.