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Description

Signals and systems as seen in everyday life, and in various branches of

engineering and science, energy and power signals, continuous and

discrete time signals, continuous and discrete amplitude signals, system

properties: linearity, additivity and homogeneity, shift-invariance,

causality, stability, realizability.

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II Linear shift-invariant (LSI) systems, impulse response and step response,

convolution, input-output behaviour with aperiodic convergent inputs,

characterization of causality and stability of linear shift invariant systems,

system representation through differential equations and difference

equations, Periodic and semi-periodic inputs to an LSI system, the notion

of a frequency response and its relation to the impulse response

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III Fourier series representation, Fourier transform, convolution/multiplication

and their effect in the frequency domain, magnitude and phase response,

Fourier domain duality , Discrete-Time Fourier Transform (DTFT) and the

Discrete Fourier transform (DFT), Parseval's Theorem, the idea of signal

space and orthogonal bases, the Laplace transform, notion of Eigen

functions of LSI systems, a basis of Eigen functions, region of

convergence, poles and zeros of system, Laplace domain analysis, solution

to differential equations and system behaviour.

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IV The z-Transform for discrete time signals and systems-Eigen functions,

region of convergence, z-domain analysis.

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V The sampling theorem and its implications- spectra of sampled signals,

reconstruction: ideal interpolator, zero-order hold, first-order hold, and so

on, aliasing and its effects, relation between continuous and discrete time

systems.