Signal theory

OpenStax

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Introduction and motivation

0.1 Introduction and motivation

0.2 Course overview

0.3 Signal theory

0.4 Operator theory

0.5 Optimization theory

1 Mathematical review

1 Convergent sequences, cauchy sequences, and complete spaces

1.1 Convergence

1.2 Cauchy sequences

1.3 Complete metric spaces

2 Continuity and convergence of functions

3 Vector spaces

4 Normed spaces

5 Topological concepts

6 Inner product spaces and hilbert spaces

7 The ell_2 space

8 Orthogonality

9 Gram-schmidt process

10 Projection theorem

11 Least squares estimation in hilbert spaces

12 The hilbert space of random variables

12.1 Random variable spaces

12.2 Probability – notation primer

12.3 A hilbert space of random variables

12.4 A hilbert space of random vectors

12.5 Minimum mean square error estimation

13 Infinite-dimensional hilbert spaces

Functionals and operators

Linear functionals

2 Linear operators

3 Properties of linear operators

4 Fundamental subspaces of an operator

5 Adjoint operators

6 Matrix representations of linear operators

7 Eigendecomposition of linear operators

8 The karhuenen-loeve transform

9 Singular value decomposition

Optimization in hilbert spaces

1 Local optimization

2 Calculus of variations

3 Constrained optimization

4 Second order conditions

5 Constrained optimization with inequality constraints

6 Fenchel duality

Source: OpenStax, Signal theory. OpenStax CNX. Oct 18, 2013 Download for free at http://legacy.cnx.org/content/col11542/1.3

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