SIGNAL AND SYSTEMS
BEG333EC
Year: III
Semester: I
Teaching Schedule
Hours/Week
Theory
Tutorial
Practical
3
2
3/2
Examination Scheme
Internal Assessment
Theory
Practical
20
25
Theory
80
Final
Practical
-
Total
125
Course Objective/s:
1. To study the basics of signals, their types and properties.
2. To study the basics of systems and their behavior
3. To understand the Fourier Series and fourier transform representation of signals
1. Signals and Systems:
(10 hrs)
1.1. Definition of continuous and discrete time signals
1.2. Classification and properties of Signals, Periodic and Aperiodic, even and odd, energy
and power signals, Deterministic and random signals, exponential and sinusoidal signals,
rectangular pulses, step function, signum functions, sinc functions, delta functions.
1.3. Transformation in independent variable of signals: time scaling, time shifting, frequency
shifting, amplitude scaling, level shifting, time reversal.
1.4. Representation of continuous time signals by its sample - Sampling theorem, Reconstruction
of a Signal from its samples, aliasing
1.5. Systems: Continuous time and Discrete time, interconnection of system, basic
properties- Linearity, Causality, time invariance, stability, memory, invertibility system
2. Linear Time Invariant Systems
(8 hrs)
2.1 Continuous Time LTI systems: The convolution Integral- Representation of CT signal in
terms of Impulses and Unit Impulse Response.
2.2 Introduction to Discrete time LTI system: convolution Sum- Representation of DT signal
in terms of Impulses and Unit Impulse Response. Graphical representation of convolution
2.3 Properties of LTI systems – Commutative, Distributive, Associative, Memory,
Invertability, Causality, Stability, unit step response of LTI systems
2.4 Causal LTI systems Described by Differential and difference equations
2.5 Block Diagram representation of LTI systems, RC filtering of rectangular pulse
3 Fourier series representation
(10 hrs)
3.1 Introduction to Fourier Series, Definition of periodic continuous time and discrete time
signals: period, fundamental and harmonics
3.2 Fourier Series Representation of Continuous-time and Discrete-time periodic signals Harmonically related complex exponential, trigonometric, polar representation, Analysis
and synthesis of periodic signals, Convergence of Fourier Series, Gibbs Phenomenon,
Spectral representation of periodic signals using line spectrum for magnitude and phase
spectrum
3.3 Properties of continuous time and Discrete time Fourier series: linearity, time and
frequency shifting, time scaling, differentiation, convolution, multiplication, Symmetry
relationships, even and odd functions, Parseval’s Relations.
3.4 Examples of continuous time filters described by differential equation – RC low pass and
RC high pass filter
3.5 Examples of continuous time filters described by differential equation – Recursive and
Non-recursive
4 Fourier Transform analysis
(8 hrs)
4.1 Definition of the forward and reverse Fourier transforms
4.1 Representation of Aperiodic continuous time and discrete time Fourier Transform,
Magnitude, phase, and energy density spectrum, Fourier Transform for periodic signal.
4.2 Fourier transform of the Dirac delta function, the signum function , the step function, the
periodic function, and the constant
4.3 Properties of Fourier Transform: Linearity, Periodicity, Duality, Time shifting and scaling
property, Convolution property, Modulation property; Parseval’s relations.
5
Energy and Power
(6 hrs)
5.1 Cross correlation and auto correlation of functions, properties of correlation function
5.2 Energy density function, Power density function, Parseval’s theorem for periodic signals
and finite energy signals, Relation between auto correlation function and energy/power
spectral density function.
5.3 Relation between convolution and correlation, Detection of periodic signals in the
presence of noise by correlation, Extraction of signal from noise by filtering.
6 Transmission of Signals :
(3 hrs)
6.1 Input-Output relationships in the frequency domain, Transfer Function
6.2 Distortionless transmission, ideal low pass filter and impulse response, Step response of
ideal low pass filter
Laboratory:
1. Plotting of signal and its transformations using MATLAB
2. Convolution, Fourier Series and Fourier Transform simulation in MATLAB.
3. Analysis of signals in Spectrum Analyzer
4. Observation of rectangular pulse through transmission cable
References:
1. A. V. Oppenheim and A. S. Willsky, "Signals and Systems", Second Edition, PHI
publication
2. A. D. Poularikas and S. Seely, “Signals and Systems”, 2nd Edition, PWS-Kent
publishers, 1991.
3. S. Haykin and B.V. Veen, “Signals and Systems”, John Wiley and Sons, Inc.
Marking Schemes
S. No.
Chapter
Hours
Marks*
1
Signals and Systems
10
18
2
Linear Time Invariant Systems
8
14
3
Fourier series representation
10
18
4
Fourier transform analysis
8
14
5
Energy and Power
6
10
6
Transmission of signals
3
6
* Marks are allocated according to the hours but can be little variation depending on the pattern of the
question.