Concept

Orthogonal functions

Related lectures (15)

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Analysis and Synthesis of Deterministic Signals

Explores the representation of signals as vectors, projection theorem, orthogonal functions, and examples.

Vector Representation of Signals

Explores the vector representation of signals, orthogonal functions, and Fourier series.

Quantum Physics: Orbital Angular Momentum

Delves into orbital angular momentum in quantum physics, emphasizing spherical harmonics' significance and normalization conditions.

Signals & Systems I: Vector Approximation and Signal Comparison

Explores vector approximation, signal detection, correlation, Fourier series, and signal comparison in signals and systems.

LLL Algorithm

Covers the LLL algorithm for lattice reduction and discusses Hermite's constant and Minkowski's theorem.

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Nonlinear Equations: Convergence and Taylor Polynomials

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

Error Analysis for Galerkin Scheme

Covers the error analysis for the Galerkin scheme and the importance of Galerkin orthogonality.

Canonical Correlation Analysis: Exercises Solutions

Presents solutions to exercises on Canonical Correlation Analysis, exploring correlation, Gram matrices, kernel matrices, and vector properties.

Non-parametric Regression: Smoothing Techniques

Explores non-parametric regression techniques, including splines, bias-variance tradeoff, orthogonal functions, wavelets, and modulation estimators.

Discrete Fourier Transform: Lecture 12

Explores the Discrete Fourier Transform, Fast Fourier Transform, orthogonal functions, and trigonometric approximations.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Complex Analysis: Laplace and Fourier Transforms

Discusses complex analysis, focusing on Laplace transforms, Fourier series, and the heat equation's solutions and uniqueness.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.