Signal representation and approximation in vector spaces

OpenStax

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1 Metric spaces

Normed vector spaces

Inner product spaces

Properties of inner products

Complete vector spaces

Hilbert spaces in signal processing

Linear combinations of vectors

Vector subspaces

Signal approximation in a hilbert space

Linear operators

Linear independence

Orthogonal bases

Computing the best approximation

Matrix representation of the approximation problem

Orthobasis expansions

Parseval's and plancherel's theorems

Error of the best approximation in an orthobasis

Approximation in ℓ_p norms

Source: OpenStax, Digital signal processing. OpenStax CNX. Dec 16, 2011 Download for free at http://cnx.org/content/col11172/1.4

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