Some Background

  • Jacob BenestyEmail author
  • Jingdong Chen
  • Chao Pan
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


In this chapter, we present in a very concise way some fundamental aspects of linear spaces, orthogonal functions, and orthogonal polynomials. Three family of orthogonal polynomials (Legendre, Chebyshev, and Jacobi), of great importance to us, are discussed. Most of the presented results are taken from [1, 2, 3]; so all the stated theorems are given without proofs. The interested reader who wants to go deeper into these topics is invited to check the mentioned references and the very rich literature on this subject. The results presented here serve as a preparation for differential beamforming in forthcoming chapters.


  1. 1.
    Davis HF (1989) Fourier series and orthogonal functions. Dover, New YorkGoogle Scholar
  2. 2.
    Chihara TS (2011) An introduction to orthogonal polynomials. Dover, New YorkGoogle Scholar
  3. 3.
    Shen J, Tan T, Wang L-L (2011) Spectral methods-algorithms, analysis and applications. Springer, BerlinGoogle Scholar
  4. 4.
    Abramowitz M, Stegun IA (eds) (1970) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover, New YorkGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.INRS-EMT, University of QuebecMontrealCanada
  2. 2.Northwestern Polytechnical UniversityXi’anChina

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