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Spatial Spectral Analysis

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Encyclopedia of Computational Neuroscience

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Definition

Spatial spectral methods are extensions of the well-known Fourier transform in time into the spatial domain. Whereas the basis functions for the Fourier transform are sine and cosine or complex exponentials, the bases used in space often reflect a symmetry of the problem. Common basis sets are plane waves (Cartesian space), Bessel functions (circular and cylindrical symmetry), and spherical harmonics (sphere). Moreover, basis vectors can be derived from the dataset under consideration that are optimal with respect to certain criteria like mean squared error.

Detailed Description

Spectral methods are best known from the Fourier transform that decomposes a time series into its frequency components. Spectral methods in space are applied to datasets that are recorded at different locations in space like EEG (electroencephalography is recorded with up to several hundred electrodes attached to different locations on the scalp surface), MEG (magnetoencephalography measures the...

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References

  • Johnson RA, Wichern DW (2007) Applied multivariate statistical analysis, 7th edn. Prentice Hall, Upper Saddle River, NJ

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  • Nunez PL, Srinivasan R (2006) Electric fields of the brain – the neurophysics of EEG, 2nd edn. Oxford University Press, Oxford

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Author information

Authors and Affiliations

  1. Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, USA

    Dr. Armin Fuchs

Authors
  1. Dr. Armin Fuchs
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Correspondence to Armin Fuchs .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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© 2014 Springer Science+Business Media New York

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Fuchs, A. (2014). Spatial Spectral Analysis. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_419-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_419-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

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