Introduction: Basic signals in continuous
and discrete time domain. Classification of signals: periodic / aperiodic,
even/odd, deterministic/stochastic, energy/power
Singular functions: ramp, step &
impulse, Representing a system as a mapping of I/O signals
Representing a system in terms of differential and
difference equation respectively.
Classification of systems: causal/non
causal, time varying/time invariant, stable/unstable invertible / non invertible
& lumped & distributed parameters.
Fourier analysis of continuous time signals : Orthogonal
functions, Fourier series representation in terms of sine , cosine, exponential.
Complex Fourier series, Properties of Fourier series Convergence of Fourier
series Gibbs phenomenon, Fourier transform & its properties. Fourier
transform of singular functions
Energy density spectrum
Continuous time systems: Linear
differential equations, Representation by impulses, systems impulse response
& convolution integral. Evaluation & Interpretation of Convolution
integral. System stability in time and frequency domain. Transient & steady
state response of linear systems. Frequency response of linear system.
Response of systems to causal periodic inputs.
Laplace Transform: Convergence, properties
of Laplace transform, double sided transform, application of Laplace transform
to solutions of differential equations, relationship between Fourier &
Z-transform : Definition, convergence,
properties & inversion of Z-properties, single & double sided transform.
Analysis of discrete time systems using Z-transform Relationship between Laplace
Random signals: Introduction, discrete time random process. Random variables, Stochastic process, first ,second order statistics, moment, correlation and co-variance stationary process, ergodicity.
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