|13040306||SIGNAL AND SYSTEM ANALYSIS||L||T||P||C|
|Version1.1||Date of Approval:||3||0||0||3|
The students will learn and understand
- Types of signals and their characteristics.
- Representation of discrete and continuous signals.
- Determination of system response for a signal.
- Fourier and Z transform techniques as tool for signal analysis.
On completion of this course, the students will be able to
- Demonstrate an understanding of the relation among the transfer function, convolution, and the impulse response, by explaining the relationship, and using the relationship to solve forced response problems.
- Demonstrate an understanding of the relationship between the stability and causality of systems and the region of convergence of their Laplace transforms, by correctly explaining the relationship, and using the relationship to determine the stability and causality of systems.
- Explain the role of convolution in the analysis of linear time invariant systems, and use convolution to determine the response of linear systems to arbitrary inputs.
More seriously, signals are functions of time (continuous-time signals) or sequences in time
(discrete-time signals) that presumably represent quantities of interest. Systems are operators thataccept a given signal (the input signal) and produce a new signal (the output signal). Of course,this is an abstraction of the processing of a signal.
From a more general viewpoint, systems are simply functions that have domain and range that aresets of functions of time (or sequences in time). It is traditional to use a fancier term such asoperator or mapping in place of function, to describe such a situation. However we will not be soformal with our viewpoints or terminologies. Simply remember that signals are abstractions oftime-varying quantities of interest, and systems are abstractions of processes that modify thesequantities to produce new time-varying quantities of interest.
This subject are about the mathematical representation of signals and systems. The mostimportant representations we introduce involve the frequency domain – a different way of lookingat signals and systems, and a complement to the time-domain viewpoint. Indeed engineers andscientists often think of signals in terms of frequency content, and systems in terms of their effecton the frequency content of the input signal. Some of the associated mathematical concepts andmanipulations involved are challenging, but the mathematics leads to a new way of looking at theworld.
- P. Ramakrishna Rao, `Signal and Systems’ 2008 Ed., Tata McGraw Hill, New Delhi, ISBN 1259083349, 9781259083341
- CChi-Tsong Chen, `Signals and Systems’, 3rd Edition, OxfordUniversity Press, 2004, ISBN 0195156617, 9780195156614
Unit I: Introduction to Signals
6 lecture hours
Definition, types of signals and their representations: continuous-time/discrete-time, periodic/non-periodic, even/odd, energy/power, deterministic/ random, one dimensional/ multidimensional; commonly used signals (in continuous-time as well as in discrete-time): unit impulse, unit step, unit ramp (and their inter-relationships),exponential, rectangular pulse, sinusoidal; operations on continuous-time and discrete-time signals (including transformations of independent variables)
Unit II: Laplace-Transform (LT) and Z-transform (ZT)
6 lecture hours
One-sided LT of some common signals, important theorems and properties of LT, inverse LT, solutions of differential equations using LT, Bilateral LT, Regions of convergence (ROC), One sided and Bilateral Z-transforms, ZT of some common signals, ROC, Properties and theorems, solution of difference equations using one-sided ZT, s- to z-plane mapping
Unit III: Fourier Transforms (FT):
9 lecture hours
Definition, conditions of existence of FT, properties, magnitude and phase spectra, Some important FT theorems, Parseval’s theorem, Inverse FT, relation between LT and FT, Discrete time Fourier transform (DTFT), inverse DTFT, convergence, properties and theorems, Comparison between continuous time FT and DTFT.
Unit IV :Introduction to Systems
9 lecture hours
Classification, linearity, time-invariance and causality, impulse response, characterization of linear time-invariant (LTI) systems, unit sample response, convolution summation, step response of discrete time systems, stability, convolution integral, co-relations, signal energy and energy spectral density, signal power and power spectral density, properties of power spectral density.
Unit V: Time and frequency domain analysis of systems
9 lecture hours
Analysis of first order and second order systems, continuous-time (CT) system analysis using LT, system functions of CT systems, poles and zeros, block diagram representations; discrete-time system functions, block diagram representation, illustration of the concepts of system bandwidth and rise time through the analysis of a first order CT low pass filter.
Mode of Evaluation: The theory performance of students are evaluated.
Relationship between the Course Outcomes (COs) and Program Outcomes (POs)
|Mapping between Cos and POs|
|Sl. No.||Course Outcomes (COs)||Mapped Programme Outcomes|
|1||Demonstrate an understanding of the relation among the transfer function, convolution, and the impulse response, by explaining the relationship, and using the relationship to solve forced response problems.||1|
|2||Demonstrate an understanding of the relationship between the stability and causality of systems and the region of convergence of their Laplace transforms, by correctly explaining the relationship, and using the relationship to determine the stability and causality of systems.||2|
|3||Explain the role of convolution in the analysis of linear time invariant systems, and use convolution to determine the response of linear systems to arbitrary inputs.