SIGNALS AND SYSTEMS
UNIT I
SIGNAL ANALYSIS : Analogy between vectors and signals, Orthogonal
signal space, Signal approximation using orthogonal functions, Mean
square error, Closed or complete set of orthogonal functions, Orthogonality
in complex functions, Exponential and sinusoidal signals, Concepts
of Impulse function, Unit step function, Signum function.
UNIT II
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
UNIT III
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, Fourier transforms involving impulse function and Signum
function. Introduction to Hilbert Transform.
UNIT IV
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, Causality and Poly-Wiener
criterion for physical realization, relationship between bandwidth
and rise time.
UNIT V
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 VI
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 VII
LAPLACE TRANSFORMS :Review of Laplace transforms, 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's, Relation between L.T's, and F.T.
of a signal. Laplace transform of certain signals using waveform synthesis.
UNIT VIII
Z"�TRANSFORMS : Fundamental difference between continuous and discrete
time signals, discrete time signal representation using complex exponential
and sinusoidal components, Periodicity of discrete time using complex
exponential signal, Concept of Z- Transform of a discrete sequence.
Distinction between Laplace, Fourier and Z transforms. Region of convergence
in Z-Transform, constraints on ROC for various classes of signals,
Inverse Z-transform, properties of Z-transforms. |
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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 "� Narayan Iyer and K Satya Prasad , Cenage
Pub.
REFERENCES :
1. Signals & Systems - Simon Haykin and Van Veen,Wiley, 2nd Edition.
2. Signals & Systems- K R Rajeswari and B V Rao , PHI
3. Fundamentals of Signals and Systems Michel J. Robert, MGH International
Edition, 2008.
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