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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 & Laplace transform.

Z-transform : Definition, convergence, properties & inversion of Z-properties, single & double sided transform. Analysis of discrete time systems using Z-transform Relationship between Laplace & Z-transform.

Random signals: Introduction, discrete time random process. Random variables, Stochastic process, first ,second order statistics, moment, correlation and co-variance stationary process, ergodicity.

<<2002 Samsoft Technologies>>

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