(SEM III) THEORY EXAMINATION 2017-18 SIGNAL AND SYSTEM

This document contains the complete B.Tech (Semester III) Theory Examination 2017–18 question paper for the subject Signal and System (REC-303). The paper consists of two printed pages, carries 70 marks, and evaluates a student's understanding of continuous-time and discrete-time signals, system properties, Fourier analysis, Laplace transform, Z-transform, autocorrelation, convolution, sampling, and LTI system behavior.
 

Section A – Short Conceptual Questions (14 Marks)

Section A includes seven brief questions (2 marks each) designed to test fundamental concepts of signal representation, system classification, and transform properties. The topics include:

Checking periodicity and fundamental time period of a given signal expression

DTFT of causal exponential sequences

Determining whether a system is time variant and causal

Stating the convolution property for continuous and discrete signals

Finding Laplace transform and Region of Convergence (ROC) for exponential signals

Sketching unit step-based signals

Using the Final Value Theorem to find the final value of a signal

These questions test a student's basic analytical skills in representing and transforming signals.
 

Section B – Analytical & Problem-Solving Questions (21 Marks)

Students must attempt any three out of five questions. These are detailed problems involving calculation, sketching, and transform analysis:

Sketching autocorrelation function for x(t)=e−atu(t)x(t) = e^{-at}u(t)x(t)=e−atu(t)

Performing convolution of given discrete-time sequences

Fourier transform of rectangular and exponential signals, including magnitude and phase spectrum

Finding inverse Laplace transform from a rational function with given ROC

Stating and proving the Sampling Theorem and explaining under-sampling effects

This section tests understanding of mathematical tools used in signal processing.
 

Section C – Long Descriptive Questions (35 Marks)

Q3 – Signal Properties & Even-Odd Decomposition

Classification of signals

Proving power of energy signal = 0 over infinite time

Plotting a complex signal using step and ramp functions and extracting its even and odd parts

Q4 – System Properties & Signal Energy

Determining if a continuous-time system is static/dynamic, linear/nonlinear, shift variant/invariant, causal, and stable

Finding energy and power of periodic and decaying exponential signals

Q5 – LTI System Analysis

Finding impulse response of the second system h2(n)h_2(n)h2​(n) using parallel LTI system properties and given frequency response

Fourier transform of x(t)=e−atu(t)x(t) = e^{-at}u(t)x(t)=e−atu(t) and sketching magnitude & phase spectrum

Q6 – Laplace Transform Properties & Z-Transform

Proving linearity of Laplace transform

Transform of a time-scaled and shifted function

Obtaining system function H(z)H(z)H(z) from a difference equation, plotting poles & zeros, and specifying ROC

Q7 – Sampling & Filter Characteristics

Determining discrete-time signals obtained after sampling two sinusoids at 40 Hz

Explaining bandwidth and rise time of a low-pass filter and proving the relation

• tr=0.35Bt_r = \frac{0.35}{B}tr​=B0.35​

These problems test critical thinking in system behavior, transform properties, LTI analysis, and frequency-domain interpretation.
 

Summary

The Signal and System (REC-303) exam paper comprehensively evaluates student skills in:

Continuous & discrete signal representation

System classification & LTI properties

Convolution, autocorrelation & signal energy

Fourier, Laplace & Z-transform analysis

Sampling and aliasing

Frequency response of LTI systems

It is a valuable academic resource for engineering students studying communication systems, control systems, and digital signal processing.