Basis Functions in the Analysis of Evoked Potentials

  • Donald C. Martin
  • David Borg-Breen
  • Veronica Buffington
Part of the The Downstate Series of Research in Psychiatry and Psychology book series (DSRPP, volume 2)


ER data may be reduced to a more compact form by approximating the original responses by a linear combination of functions. Two main classes of approximating functions are discussed. The first of these are fixed basis functions. These are functions that do not depend upon the data. These are sine-cosine (Fourier), Walsh-Hadamard (square waves), Haar functions (square wave impulse func tions) , and polynomials. The other functions are random in that they depend upon the data. These arise from various multivariate statistical procedures. The procedures discussed are principal components, factor analysis, union-intersection tests, and canonical correlation.

Some of the relative advantages of each of the methods are discussed. The fixed basis function methods are relatively fast and simple to compute. The multivariate methods are difficult to compute but tend to be better approximations because they depend upon the sample to select the functions. The multivariate test statistics based upon the union-intersection principle may be interesting because, in some cases, they both generate test statistics and characteristic waveforms. Most of these methods have not been used enough to offer any concrete recommendations.

Fourier, polynomial, Walsh-Hadamard, Haar, principal compon ents and factor analysis are compared in a least squares sense for goodness of fit for average evoked responses for 43 subjects. The principal components procedure will always result in a best fit. Factor analysis was the next best approximation with Fourier approximation next best and sometimes better. The Walsh-Hadamard and Haar were not as good but might well be satisfactory for some types of analysis, especially in view of their computational efficiency. Polynomial approximations are poor for low degree polynomials but improve more rapidly than the Walsh-Hadamard and the Haar approximations. Polynomial approximations are not as good as Fourier for these data and they are slower to compute.

The direct use of multivariate methods may be impractical due to the large matrices involved. However, hybrid methods that use Fourier, Walsh-Hadamard or Haar functions to reduce the dimensions and then use principal components or union-intersection tests may prove useful.


Canonical Correlation Analysis Multivariate Method Evoke Potential Walsh Function Haar Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • Donald C. Martin
    • 1
  • David Borg-Breen
    • 1
  • Veronica Buffington
    • 1
  1. 1.Departments of Biostatistics and PsychiatryUniversity of WashingtonSeattleUSA

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