Introduction: Integrated approach for continuous and discrete - time cases.
Signals: Classification of signals, Continuous - Discrete time, Even / Odd signals, Periodic/ Non-periodic signals, Deterministic / Random signals, Energy / Power signals, Basic operations on signals, Basic (Continuous / Discrete) signals - unit step, unit impulse, sinusoidal and complex exponential signals etc.
Systems (Continuous / Discrete): Representation, Classification – Linear / Nonlinear, Causal / Noncausal, Time invariant / Time variant, with / without memory, BIBO stability, Feedback system, LTI system – Response of LTI system, Convolution, Properties (Continuous / Discrete), LTI systems – Differential / Difference equation representation and solution, MATLAB exercises for generation of signals.
Fourier analysis of continuous time signals and systems: Fourier series for periodic signals, Fourier transform - Properties of continuous time FT, Frequency response of continuous time LTI systems, MATLAB exercises for Fourier Series and Fourier Transforms.
Fourier analysis of discrete time signals and systems: Discrete time Fourier series, Discrete Time Fourier transform - Properties of DTFT, Frequency response of discrete time LTI systems, Laplace Transform analysis of systems: ROC, Inverse LT, Unilateral LT, Solving differential equation with initial conditions.
Sampling: Sampling theorem, Reconstruction of signal, Aliasing, Sampling of discrete time signals, Sampling of real time signals from PT, Reconstruction and Analysis of such signals, MATLAB exercises for generation of signals.
z-Transform: Definition, ROC, Inverse z-Transform, Properties, Transform analysis of LTI Systems.
Interrelationship amongst different representation and Transforms.