Rashtrasant Tukadoji Maharaj Nagpur University, Maharashtra, Electrical Engineering Semester 4, Signal & Systems Syllabus

SIGNAL AND SYSTEMS
Total Credit- 04
Subject Code:- BEEE401T

UNIT I: Introduction to Signals and Systems (06 Hrs)
Signals and systems as seen in everyday life, and in various branches of engineering and science.
Signal properties: periodicity, absolute integrability, determinism and stochastic character. Some
special signals of importance: the unit step, the unit impulse, the sinusoid, the complex
exponential, some special time-limited signals; continuous and discrete time signals, continuous

and discrete amplitude signals. System properties: linearity: additively and homogeneity, shift-
invariance, causality, stability, realizability. Examples.

UNIT II: Behavior of continuous and discrete-time LTI systems (08 Hrs)
Impulse response and step response, convolution, input-output behavior with a periodic
convergent inputs, cascade interconnections. Characterization of causality and stability of LTI

systems. System representation through differential equations and difference equations. State-
space Representation of systems. State-Space Analysis, Multi-input, multi-output representation.

State Transition Matrix and its Role. Periodic inputs to an LTI system, the notion of a frequency
response and its relation to the impulse response.
UNIT III Convolution (04 Hrs)
Convolution Sum, Convolution Integral and Their Evaluation, Time Domain Representation and
Analysis of LTI Systems Based on Convolution and Differential Equations.

UNIT IV Time and Frequency Domain Transformations (17 Hrs)
Fourier series representation of periodic signals, Waveform Symmetries, Calculation of Fourier
Coefficients. Fourier Transform, convolution/multiplication and their effect in the frequency
domain, magnitude and phase response, Fourier domain duality. Review of the Laplace
Transform for continuous time signals and systems, system functions, poles and zeros of system
functions and signals, Laplace domain analysis, solution to differential equations and study of
system behavior, The Discrete-Time Fourier Transform (DTFT) and the Discrete Fourier
Transform (DFT). Parseval's Theorem. The z-Transform for discrete time signals and systems,
system functions, poles and zeros of systems and sequences, z-domain analysis.

UNIT V: Sampling and Reconstruction (07 Hrs)
The Sampling Theorem and its implications. Spectra of sampled signals. Reconstruction, ideal
interpolator, zero-order hold, first-order hold. Aliasing and its effects. Relation between
continuous and discrete time systems. Introduction to the applications of signal and system
theory, filtering, feedback control systems.

Text Books:
1. Oppenheim A.V., Willsky A.S. and Young I.T., “Signals and Systems”, Second Edition,
1997, Prentice Hall.
2. Simon Haykin and Barry Van Veen, “Signals and Systems”, Second Edition, Wiley
International.
Reference Books:
1. R.F. Ziemer, W.H Tranter and J.D.R.Fannin, “Signals and Systems - Continuous and
Discrete”, Forth Edition Prentice Hall.
2. M. J. Roberts, “Signals and Systems”, 2003, Tata McGraw-Hill