## SIGNALS AND SYSTEMS

16EC403

UNIT I
INTRODUCTION TO SIGNALS AND SYSTEMS: Classification of signals – Periodic
and Aperiodic, Energy and Power, Deterministic and Random, Complex exponential and
Sinusoidal signals. Basic Signals, Operations on signals. Systems: Definition and
Classification.
FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS: Representation of
Fourier series, Continuous time periodic signals, properties of Fourier series, Dirichlet‘s
conditions, Trigonometric Fourier series and Exponential Fourier series, Complex Fourier
spectrum. Discrete Time Fourier Series-Properties.

UNIT II
FOURIER TRANSFORMS: Deriving Fourier Transform from Fourier series, Fourier
transform of arbitrary signal, Fourier transform of standard signals, Fourier transform of
periodic signals, properties of Fourier transforms. Discrete Time Fourier TransformProperties.

UNIT III
SIGNAL TRANSMISSION THROUGH LINEAR SYSTEMS: Linear system, impulse
response, Response of a linear system, linear time-invariant (LTI) system, linear time variant
(LTV) system, 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.
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, Introduction to Band Pass sampling.

UNIT IV
CONVOLUTION AND CORRELATION OF SIGNALS: Concept of convolution in time
domain and Frequency domain, Graphical representation of convolution, Convolution
property of Fourier transforms. Cross correlation and auto correlation of functions, properties
of correlation function, Energy density spectrum, Parseval‘s theorem, Power density
spectrum, Relation between auto correlation function and energy/power spectral density
function, Relation between convolution and correlation, Detection of periodic signals in the
presence of noise by correlation, Extraction of signal from noise by filtering.

UNIT V
LAPLACE TRANSFORMS: Review of Laplace transforms (L.T), Partial fraction
expansion, Inverse Laplace transform, Concept of region of convergence (ROC) for Laplace
transforms, Constraints on ROC for various classes of signals, Properties of L.T, relation
between L.T, and F.T. of a signal. Laplace transform of certain signals using waveform
synthesis.
Z–TRANSFORMS: Fundamental difference between continuous and discrete time signals,
discrete time signal representation using complex exponential and sinusoidal components,
Periodicity of discrete time signals, Concept of z-transform of a discrete sequence,
Distinction between Laplace, Fourier and z-transforms, Region of convergence in ztransform,
constraints on ROC for various classes of signals, Inverse z-transform, properties
of z-transforms.

TEXT BOOKS:
1. Signals, Systems & Communications – B.P. Lathi, 2009,BS Publications.
2. Signals and Systems – A.V. Oppenheim, A.S. Willsky and S.H. Nawab, PHI, 2nd Edn.

REFERENCES:
1. Signals and Systems – A. Ramakrishna Rao – 2008, TMH.
2. Linear Systems and Signals – B. P. Lathi, Second Edition, Oxford University press, 2008.
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