Lectures related to Signals & Systems II: Difference Equations and Operators

Partial Fraction Expansion

Introduces Partial Fraction Expansion as a valuable tool for analyzing stable LTI systems.

Signals & Systems II: Roots, Equations, and Impulse Responses

Explores roots verification, stability, reproduction modeling, Z transform, and LTI systems realization.

Signals & Systems II: Difference Equations and Inverse Operators

Explores difference equations, impulse response, BIBO stability, and inverse operators in signal processing.

Difference Equations

Covers the concept of difference equations and properties of causal vs. stable systems.

Frequency Response of LTI Systems

Explores LTI systems, impulse response, convolution, system properties, and frequency response, including low-pass and band-pass filters.

LTI Systems Properties

Covers the properties of Linear Time-Invariant (LTI) systems and their implications.

Z-Transforms: Poles and Zeros

Explores Z-Transforms, Poles, Zeros, and their applications in discrete-time systems and Linear Time-Invariant systems.

Signals & Systems II: Vector Analogy and Discrete Signals

Explores the link between DTFT, Z-transforms, and Fourier transforms, vector analogy, and discrete signals.

Difference Equations: Roots and Solutions

Explores characteristic polynomials, stability conditions, homogeneous solutions, and transfer functions in difference equations.

Fourier and Laplace Transforms: Concepts and Applications

Provides an overview of Fourier and Laplace transforms, their properties, and applications in signal analysis.

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Fourier Transform: Derivatives and Formulas

Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Fourier Transform and Differential Equations

Discusses the Fourier transform and its application to solving differential equations, focusing on the wave equation and its transformations.

Fourier Transform: Derivatives and Laplace Transform

Explores the Fourier transform properties with derivatives and introduces the Laplace transform for signal transformation and solving differential equations.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Discrete Systems: Relations, Linear Dynamics, and Operators

Covers discrete systems, linear dynamics, causality, impulse response, convolution, and operators' effects.

Laplace Transform: Solving Differential Equations

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.

Discrete Systems Theory

Covers difference equations, dynamic systems, linearity, and impulse response in discrete systems.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.