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.