Appendix b: hilbert spaces overview

OpenStax

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Fields and complex numbers

2 The complex field

4 Euler's formula

5 Calculating with complex numbers

2 Vector spaces

Cauchy-schwarz inequality

2 The cauchy-schwarz inequality

3 Statement of the cauchy-schwarz inequality

4 Proof of the cauchy-schwarz inequality

5 Additional mathematical implications

6 Matched filter detector

7 Background concepts

8 Signal comparison

9 Pattern detection

10 Cauchy-schwarz inequality video lecture

11 Cauchy-schwarz inequality summary

Common hilbert spaces

Orthonormal basis expansions

Haar wavelet basis

Orthonormal bases in real and complex spaces

Plancharel and parseval's theorems

1 Parseval's theorem

2 Prove: plancherel theorem

3 Periodic signals power

4 Plancharel theorem

5 Plancharel theorem

6 Plancharels theorem demonstration

7 Parseval's theorem: a different approach

8 Parseval's theorem

Approximation and projections in hilbert space

Source: OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15

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