Signals and Systems
Signals and Systems
Signals and Systems
II ECE I SEM
CONTENTS
SYLLABUS
UNIT I: INTRODUCTION TO SIGNALS AND SIGNAL ANALYSIS AND FOURIER
SERIES
UNIT II: FOURIER TRANSFORMS AND SAMPLING
UNIT III: SIGNAL TRANSMISSION THROUGH LINEAR SYSTEMS
UNIT IV: CONVOLUTION AND CORRELATION OF SIGNALS
UNITV:LAPLACETR AND FORMS AND Z–TRANSFORMS
UNITWISE IMPORTANT QUESTIONS
MODEL PAPAERS
JNTU PREVIOUS QUESTION PAPERS
SIGNALS AND SYSTEMS
OBJECTIVES:
Knowledge of basic elementary signals and its representation and analysis concepts
Knowledge of frequency-domain representation and analysis concepts using Fourier analysis
tools, Z-transform.
Concepts of the sampling process.
Mathematical and computational skills needed to understand the principal of LTI Systems.
Mathematical and computational skills needed to understand the principal of convolution &
correlation.
UNIT I:
INTRODUCTION TO SIGNALS: Elementary Signals- Continuous Time (CT) signals, Discrete Time (DT)
signals, Classification of Signals, Basic Operations on signals.
FOURIER SERIES: Representation of Fourier series, Continuous time periodic signals, Dirichlet’s
conditions, Trigonometric Fourier Series, Exponential Fourier Series, Properties of Fourier series,
Complex Fourier spectrum.
UNIT II:
FOURIER TRANSFORMS: Deriving Fourier transform from Fourier series, Fourier transform of arbitrary
signal, Fourier transform of standard signals, Properties of Fourier transforms.
SAMPLING: Sampling theorem – Graphical and analytical proof for Band Limited Signals, impulse
sampling, Natural and Flat top Sampling, Reconstruction of signal from its samples, effect of under
sampling – Aliasing.
UNIT III:
SIGNAL TRANSMISSION THROUGH LINEAR SYSTEMS: Introduction to Systems, Classification of
Systems, Linear Time Invariant (LTI) systems, system, impulse response, Transfer function of a LTI
system. Filter characteristics of linear systems. Distortion less transmission through a system, Signal
bandwidth, System bandwidth, Ideal LPF, HPF and BPF characteristics.
UNIT IV:
CONVOLUTION AND CORRELATION OF SIGNALS: Concept of convolution in time domain, Cross
correlation and auto correlation of functions, properties of correlation function, Energy density
spectrum, Parseval’s theorem, Power density spectrum, Relation between convolution and correlation.
UNIT V:
LAPLACE TRANSFORMS: Review of Laplace transforms, Inverse Laplace transform, Concept of region of
convergence (ROC) for Laplace transforms, Properties of L.T’s relation between L.T’s, and F.T. of a signal.
Z–TRANSFORMS: Concept of Z- Transform of a discrete sequence. Distinction between Laplace, Fourier
and Z transforms, Region of convergence in Z-Transform, Inverse Z- Transform, Properties of Z-
transforms.
TEXT BOOKS:
1. Signals, Systems & Communications - B.P. Lathi, BS Publications, 2003.
2. Signals and Systems - A.V. Oppenheim, A.S. Willsky and S.H. Nawab, PHI, 2nd Edn.
3. Signals and Systems – A. Anand Kumar, PHI Publications, 3rd edition.
REFERENCE BOOKS:
1. Signals & Systems - Simon Haykin and Van Veen,Wiley, 2nd Edition.
2. Network Analysis - M.E. Van Valkenburg, PHI Publications, 3rd Edn., 2000.
3. Fundamentals of Signals and Systems Michel J. Robert, MGH International Edition, 2008.
4. Signals, Systems and Transforms - C. L. Philips, J. M. Parr and Eve A. Riskin, Pearson
education.3rd Edition, 2004.
OUTCOMES:
Upon completing this course the student will be able to:
Understand the basic elementary signals & determine the Fourier series for Continuous Time
Signals.
Analyze the signals using FT, LT, ZT.
Concepts of the sampling process.
Mathematical and computational skills needed to understand the principal of LTI Systems.
Understand the principal of convolution & correlation.
UNIT I
1.1 INTRODUCTION
Anything that carries information can be called a signal. Signals constitute an important part of
our daily life. A Signal is defined as a single- valued function of one or more independent
variables which contain some information. A signal may also be defined as any physical quantity
that varies with time, space or any other independent variable. A signal may be represented in
time domain or frequency domain. Human speech is a familiar example of a signal. Electric
current and voltage are also examples of signals. A signal can be a function of one or more
independent variables. A signal can be a function of time, temperature, position, pressure,
distance etc. If a signal depends on only one independent variable, it is called a one-dimensional
signal, and if a signal depends on two independent variable, it is called a two-dimensional signal.
Discrete-time signals are signals which are defined only at discrete instants of time. For those
signals, the amplitude between the two time instants is just not defined. For discrete time signal
the independent variable is time n, and it is represented by x(n).
There are following four ways of representing discrete-time signals:
1. Graphical representation
2. Functional representation
3. Tabular representation
4. Sequence representation
FOURIER SERIES:
UNIT II
FOURIER TRANSFORMS:
SAMPLING:
UNIT III
1 INTRODUCTION
Convolution is a mathematical way of combining two signals to form a third signal. Convolution
is important because it relates the input signal and impulse response of the system to the output
of the system. Correlation is again a mathematical operation that is similar to convolution.
Correlation also uses two signals to form a third signal. It is very widely used in practice,
particularly in communication engineering. Basically, it compares two signals in order to
determine the degree of similarity between them. Radar, Sonar and digital communications uses
correlation of signals very extensively. Correlation may be cross correlation or auto correlation.
When one signal is correlated with itself to form another signal, it is called auto correlation.
2. CONCEPT OF CONVOLUTION
An arbitrary driving function x(t) can be expressed as a continuous sum of impulse functions.
The response y(t) is then given by the continuous sum of responses to various impulse
components. In fact , the convolution integral precisely expresses the response as a continuous
sum of responses to individual impulse components.
UNIT V