Signals & Systems (SS)
EC-402-
Unit 1Introduction of Signals and Systems
Definition of signal · Classification of signals and representation (continuous‑time, discrete‑time, even/odd, periodic/aperiodic, random/deterministic, energy/power, one/multidimensional, standard signals) · Basic operations on signals for continuous‑time / discrete‑time · Transformation of independent and dependent variables · Definition of system and its classification (CT/DT, linear/non‑linear, time‑variant/time‑invariant, causal/non‑causal, state/dynamic system) · Interconnection of systems · System properties: linearity (additivity, homogeneity), shift‑invariance, causality, stability, realizability
-
Unit 2Linear Time‑Invariant Systems
Introduction to LTI systems · Impulse response representation for LTI systems · Convolution · Properties of the impulse‑response representation for LTI systems · Difference equation for LTI systems · Block diagram representations (direct form‑I, direct form‑II, transpose, cascade, parallel) · Impulse response of DT‑LTI system and its properties
-
Unit 3z‑Transform
Introduction to the z‑transform · Region of convergence (ROC) of finite‑duration sequences · ROC of infinite‑duration sequences · Relation between discrete‑time Fourier transform and z‑transform · Properties of the ROC · Properties of the z‑transform · Inverse z‑transform · Analysis of discrete‑time LTI systems using the z‑transform · Unilateral z‑transform
-
Unit 4Fourier Analysis of Discrete‑Time Signals
Introduction to Fourier analysis of discrete‑time signals · Properties and applications of discrete‑time Fourier series · Representation of aperiodic signals · Fourier transform and its properties · Convergence of the discrete‑time Fourier transform · Fourier transform for periodic signals · Applications of the DTFT
-
Unit 5State‑Space Analysis and Multi‑Input Multi‑Output Representation
State‑space analysis and multi‑input, multi‑output representation · State‑transition matrix and its role · The sampling theorem and its implications · Spectra of sampled signals · Signal reconstruction