L103 Convolution operation of signals| Properties of Convolution

Опубликовано: 23 Февраль 2023
на канале: Techzion

501

Module I: Classification of Signals and Systems: Representation of signals, Basic Operation on Signals, Elementary Signals, representation of signals using elementary signals, Classification of Signals: Deterministic and random, periodic and non-periodic, Energy and power, causal and non-causal, even and odd signals, Classification of Systems: lumped and distributed parameters, static and dynamic, causal and non-causal, linear and non-linear, time variant and time invariant, stable and unstable, invertible and non-invertible

Module II: Fourier Representation of Signals: Representation of Continuous Time Fourier Series (CTFS), the existence of the Fourier series, the trigonometric form of a Fourier series, cosine representation, wave symmetry, exponential Fourier series, Fourier spectrum, power representation using Fourier series, Gibbs phenomenon, and properties of CTFS
Fourier Transform: Fourier transform of non-periodic functions, Magnitude and phase representations of the Fourier transform, existence of the Fourier transform, the Fourier transform of standard signals, properties of continuous time Fourier transform, Fourier transform of periodic signals, introduction to the Hilbert transform
Module III: Z Transform: Introduction, some common sequences Z transforms, finite duration sequences, and Z transforms and convergence regions Properties of the region of convergence, Properties of the Z transform, Inverse Z transform, LTI system transform analysis Stability and causality, difference equation solution using the Z transform
Module IV: Linear Time Invariant Systems: Response of a Continuous Time LTI System and Convolution Integral Using a Graphical Method, Properties of continuous time LTI systems, Eigenfunctions of continuous time LTI systems, Systems described by Differential Equations, Response of a discrete time LTI system, Convolution Sum, Properties of a discrete time LTI system, Eigenfunctions of Discrete Time LTI Systems, Systems described by Difference Equations
Module V: Time and Frequency Characterization of Signals and Systems: The magnitude-phase representation of the Fourier transform, and the magnitude-phase representation of the frequency response of LTI systems: Linear and nonlinear phases, group delay
Text Books:
1. Signals & Systems: Alan Oppenheim & Alan Wilsky, S Nawab, PHI.(Unit-IV) 4.

Reference Books:
1. Simon Haykin, Signals and Systems, 2nd Edition, Wiley India.
2. Signals, Systems and Communications: B.P. Lathi, BS Publications.
Reference Programming Languages:

1. Python : Open source
2. MATLAB