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Walsh Spectra


Date: 03/07/2002 at 10:12:27
From: E Laurie
Subject: Power spectra

What are Walsh Spectra? I'm starting from scratch here.


Date: 03/07/2002 at 11:26:52
From: Doctor Douglas
Subject: Re: Power spectra

Hi, Ewan.

Thanks for submitting your question to the Math Forum.

You may be familiar with Fourier spectra, which specify the amplitude 
(and phase) of various sinusoidal functions in a given input.

Walsh spectra are similar, except that instead of sinusoidal 
functions, Walsh functions are used. These are piecewise constant 
(equal to +1 or -1) and relatively simple to describe. Like sinusoidal 
functions, they form a complete and orthogonal set, which makes them 
useful for function decomposition. For more information on Walsh 
functions, take a look at:

  Mathworld - Eric Weisstein's World of Mathematics
  http://mathworld.wolfram.com/WalshFunction.html   

  Carlos A. Cunha Filho - Model decomposition with Walsh functions in
    nonlinear traveltime inversion
  http://sepwww.stanford.edu/public/docs/sep70/carlos1/paper_html/node5.html   

I hope this helps you get started.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Functions

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