**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.