'orthonormal'에 해당되는 글 1

  1. 2008.11.08 강의노트, 강의정리 - Kreyszig: ODEs: series solutions of ODEs

강의노트, 강의정리 - Kreyszig: ODEs: series solutions of ODEs


Sturm-Liouville problems


orthogonality

  • the most important property of eigenfunction of Sturm-Liouville problems is orthogonality.
  • orthogonal definition

funtions

 defined on some interval
 are called orthogonal on this interval with respect to the weight function
 if for all m and all n different from m,


  • orthogonal function 중 communication theory 분야에서 많이 이용되는 function 에는 sinusoidal function (advanced: exponential family with Euler's theory), sinc function 등이 있다.
  • the Fourier series [각주:1] is a particular type of orthogonal series that is very useful in solving engineering problems, especially commnication problem. the orthogonal functions that are used are either sinusoids or, equivalently, complex exponential functions. mathematicians generally call any orthogonal series a Fourier series. (text: digital and analog communication system, p68)




     * reference: 강의노트, 강의정리: Comm theory and System: intro, basic concepts

  1. orthogonality에 대한 이해를 배경으로 function을 표현 할 수 있는 한가지 방법인 Fourier series을 이해 할 수 있다. [본문으로]