JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year SIGNALS AND STOCHASTIC PROCESS Previous Question Paper (September/October - 2023 - R16)
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
Express signum function using unit step functions.
Answer
The signum function, denoted as sgn(t), is defined as 1 for t > 0, -1 for t < 0, and 0 for t = 0. It can be expressed in terms of the unit step function u(t) as:
Alternatively, it can be written as:
Discuss the concept of orthogonality and explain the term complete set of orthogonal functions.
Answer
Two functions f(t) and g(t) are said to be orthogonal over an interval [t1, t2] if the integral of their product over that interval is zero:
This concept is analogous to orthogonal vectors in Euclidean space, where the dot product of two perpendicular vectors is zero. A set of functions {φn(t)} is called an orthogonal set if every pair of distinct functions in the set satisfies this condition.
A set of orthogonal functions is considered a complete set if no other function exists in the same space that is orthogonal to every function in the set, except for the zero function. In such a set, any arbitrary function f(t) within that space can be represented as a unique linear combination (a generalized Fourier series) of the functions in the set, with the error between the function and its approximation approaching zero as the number of terms increases.
Write notes on complex Fourier spectrum.
Answer
Sign in to view the complete answer paper.
Write properties of trigonometric Fourier series.
Answer
Sign in to view the complete answer paper.
Write any two properties of ROC of Laplace transform.
Answer
Sign in to view the complete answer paper.
Distinguish Laplace, Fourier and Z transforms.
Answer
Sign in to view the complete answer paper.
Write the conditions to be satisfied by a random process to be SSS.
Answer
Sign in to view the complete answer paper.
Write short notes on Poisson random process.
Answer
Sign in to view the complete answer paper.
Define the Auto correlation function.
Answer
Sign in to view the complete answer paper.
Write properties of cross power density spectrum.
Answer
Sign in to view the complete answer paper.
Part B
State and prove convolution property of Fourier transforms.
Answer
Sign in to view the complete answer paper.
Derive the relationship between rise time and bandwidth.
Answer
Sign in to view the complete answer paper.
Discuss Paley – Wiener criterion for physical realizability of filter.
Answer
Sign in to view the complete answer paper.
Present the analogy between vectors and signals.
Answer
Sign in to view the complete answer paper.
Obtain the complex exponential Fourier series for the wave form shown below figure 1 and also plot its magnitude spectrum.
Answer
Sign in to view the complete answer paper.
Find the Fourier transform of signum function.
Answer
Sign in to view the complete answer paper.
Compute the Fourier transform of the signal shown below figure 2.
Answer
Sign in to view the complete answer paper.
Discuss the effects of under sampling.
Answer
Sign in to view the complete answer paper.
Find the Laplace transform and ROC of x(t) = cos(2t) u(t-2)
Answer
Sign in to view the complete answer paper.
Explain the constraints on ROC for various classes of signals in Z-transform.
Answer
Sign in to view the complete answer paper.
Find the laplace transform and its ROC.
Answer
Sign in to view the complete answer paper.
Using time shifting property find the Z transform of x[n] = (2/3)n u[n-1].
Answer
Sign in to view the complete answer paper.
Classify random processes and explain.
Answer
Sign in to view the complete answer paper.
Define auto-correlation function of a random process. Write properties of ACF and prove any two of them.
Answer
Sign in to view the complete answer paper.
A random process X(t) = Acos(ωt+θ), where θ is a uniformly distributed random variable in (0, 2π). Check whether it is WSS or not?
Answer
Sign in to view the complete answer paper.
An LTI system with impulse response h(t) has auto-correlation functions of its input and output represented by RYY(τ), RXX(τ) respectively. Prove that RYY(τ) = RXX(τ) * h(-τ) * h(τ).
Answer
Sign in to view the complete answer paper.
Derive the expression for power density spectrum of a random process.
Answer
Sign in to view the complete answer paper.
Derive the relationship between autocorrelation function and power density spectrum of a random process.
Answer
Sign in to view the complete answer paper.