204191: Signals & Systems

Credit 03 + 01 = 04

Unit I Introduction to Signals & Systems

Signals: Introduction, Graphical, Functional, Tabular and Sequence representation of Continuous and
Discrete time signals. Basics of Elementary signals: Unit step, Unit ramp, Unit parabolic, Impulse,
Sinusoidal, Real exponential, Complex exponential, Rectangular pulse, Triangular, Signum, Sinc and
Gaussian function.
Operations on signals: time shifting, time reversal, time scaling, amplitude scaling, signal addition,
subtraction, signal multiplication. Communication, control system and Signal processing examples.

Classification of signals: Deterministic, Random, periodic , Non periodic, Energy , Power, Causal , Non-
Causal, Even and odd signal.

Systems: Introduction, Classification of Systems: Lumped Parameter and Distributed Parameter System,
static and dynamic systems, causal and non-causal systems, Linear and Non- linear systems, time variant
and time invariant systems, stable and unstable systems, invertible and non- invertible systems.

Unit II Time domain representation of LTI System

Input-output relation, definition of impulse response, convolution sum, convolution integral, computation
of convolution integral using graphical method for unit step to unit step, unit step to exponential,
exponential to exponential, unit step to rectangular and rectangular to rectangular only. Computation of
convolution sum. Properties of convolution. System interconnection, system properties in terms of impulse
response, step response in terms of impulse response.

Unit III Fourier Series

Fourier series (FS) representation of periodic Continuous Time (CT) signals, Dirichlet condition for
existence of Fourier series, orthogonality, basis functions, Amplitude and phase response, FS representation of CT signals using trigonometric and exponential Fourier series. Applications of Fourier series, properties of Fourier series and their physical significance, Gibbs phenomenon.

Unit IV Fourier Transform

Fourier Transform (FT) representation of aperiodic CT signals, Dirichlet condition for existence of Fourier
transform, evaluation of magnitude and phase response, FT of standard CT signals, Properties and their
significance, Interplay between time and frequency domain using sinc and rectangular signals, Fourier
Transform for periodic signals.

Unit V Laplace Transform

Definition of Laplace Transform (LT), Limitations of Fourier transform and need of Laplace transform,
ROC, Properties of ROC, Laplace transform of standard periodic and aperiodic functions, properties of
Laplace transform and their significance, Laplace transform evaluation using properties, Inverse Laplace
transform based on partial fraction expansion, stability considerations in S domain, Application of Laplace
transforms to the LTI system analysis.

Unit VI Probability and Random Variables

Probability: Experiment, sample space, event, probability, conditional probability and statistical
independence, Bayes theorem, Uniform and Gaussian probability models.
Random variables: Continuous and Discrete random variables, cumulative distributive function,
Probability density function, properties of CDF and PDF. Statistical averages, mean, moments and
expectations, standard deviation and variance.

Text Books:
1. Simon Haykins and Barry Van Veen, “Signals and Systems”, Wiley India, 2nd Edition.

2. M.J. Roberts “Signal and Systems”, Tata McGraw Hill 2007.
Reference Books:
1. Charles Phillips, “Signals, Systems and Transforms”, Pearson Education, 3 rd Edition.

2. Peyton Peebles, “Probability, Random Variable, Random Processes”, Tata Mc Graw Hill, 4
th Edition.
3. A. Nagoor Kanni “Signals and Systems”, Mc Graw Hill, 2nd Edition.