Signals Processing I

Unit 1

Introduction: Integrated approach for continuous, discrete-time cases.

Signals: Classification of signals, continuous – discrete time; even / odd signals, periodic / nonperiodic 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 systems. LTI system response of LTI system - convolution, properties (continuous / discrete) - LTI systems – differential / difference equation representation.

Unit 2

Fourier Series: Fourier series - Half range Expansions - Parseval’s Identity - Transform integrals¬ - Fourier Integrals - Fourier integral theorem. Sine and Cosine Integrals. Fourier analysis of continuous time signals and systems: Fourier series for periodic signals - Sine and Cosine Transforms - Fourier transform – properties of continuous time FT - Sampling: Sampling theorem - reconstruction of signal – aliasing.

Unit 3

Laplace Transform analysis of systems: Laplace Transforms, Inverse Transforms, Linearity, Shifting, Transforms of Derivatives and Integrals – ROC - inverse LT - unilateral LT - Frequency response of continuous time LTI systems, response of electronic circuits with initial conditions using Lapalce transforms. Z-Transform: Definition – ROC - inverse z-transform – properties - transform analysis of LTI Systems - Frequency response of discrete time LTI systems. Inter relationship between different representations and transforms.