Syllabus - Signals and Systems (EI302)

CLASSIFICATION OF SIGNALS & SYSTEMS

Continuous-Time and Discrete-Time Signals- Unit Impulse, Unit Step, Ramp, Exponential & Sinusoidal Signals. Periodic & aperiodic signals, Deterministic and random signals, Energy and Power signals. Continuous-Time and Discrete-Time Systems. Classification, Static & dynamic, Linear and non-linear, Causal and non-caausal, Time variant and invariant, Continuous-Time LTI Systems: The Convolution Integral. Discrete-Time LTI Systems: The Convolution Sum.

ANALYSIS OF CONTINUOUS & DISCRETE TIME SIGNALS

Fourier series Representation of Continuous-Time Periodic Signals, Properties, Continuous-Time Fourier Transform (CTFT), The Fourier Transform for Periodic Signals, Properties of the CTFT, Duality, Sinc and signum function, Sampling Theorem, Aliasing, Discrete Time Fourier series Properties, Discrete-Time Fourier Transform (DTFT). Properties of the DTFT. Parseval's Theorem, Central ordinate theorem.

LAPLACE TRANSFORM

Definition, Region of Convergence, Inverse Laplace Transform, Properties, Analysis and Characterization of LTI Systems Using the Laplace Transform, The Unilateral Laplace Transform, Casualty and stability in continuous time LTI system, System realization through Block-diagram representation and system interconnection, State variable analysis, State space Models, Solution of State equation, The state-transition matrix, Concept of Controllability and Observability.

Z-TRANSFORM

Definition, Region of Convergence. Inverse z-Transform. Properties, Some Common z-Transform Pairs. Analysis and Characterization of LTI Systems Using z-Transforms. System Function Algebra and Block Diagram Representations. The Unilateral z-Transforms. Casualty and stability in continuous time LTI system, Group delay, Phase delay.

RANDOM VARIABLES & RANDOM PROCESS

Sets and Sample Spaces Random Variables Continuous and Discrete, Cumulative distribution Function (CDF), Probability Density Function (PDF), Expectation and Moments, Types of Random Processes, Ergodicity, Auto-correlation Function (ACF) & Cross correlation Function (CCF), Power Spectral Density, Wiener–Khinchin–Einstein theorem, Central limit theorem, Transmission of a random process through a Linear Filter. Central Limit Theorem, Mixing of a Random process with sinusoidal process.