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.
