Two. Mathematical Preliminary

  1. Jaideva C. Goswami and
  2. Andrew K. Chan

Published Online: 24 NOV 2010

DOI: 10.1002/9780470926994.ch2

Fundamentals of Wavelets: Theory, Algorithms, and Applications, Second Edition

Fundamentals of Wavelets: Theory, Algorithms, and Applications, Second Edition

How to Cite

Goswami, J. C. and Chan, A. K. (2011) Mathematical Preliminary, in Fundamentals of Wavelets: Theory, Algorithms, and Applications, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470926994.ch2

Publication History

  1. Published Online: 24 NOV 2010
  2. Published Print: 10 JAN 2011

Book Series:

  1. Wiley Series in Microwave and Optical Engineering

Book Series Editors:

  1. Kai Chang

Series Editor Information

  1. Texas A&M University, USA

ISBN Information

Print ISBN: 9780470484135

Online ISBN: 9780470926994

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Keywords:

  • mathematical preliminary - mathematical notations and tools, and understanding wavelet theory;
  • biorthogonal basis - in a two-dimensional Euclidean space;
  • digital signals, basic notations and operations - for signal processing techniques

Summary

This chapter contains sections titled:

  • Linear Spaces

  • Vectors and Vector Spaces

  • Basis Functions, Orthogonality, and Biorthogonality

  • Local Basis and Riesz Basis

  • Discrete Linear Normed Space

  • Approximation by Orthogonal Projection

  • Matrix Algebra and Linear Transformation

  • Digital Signals

  • Exercises

  • References