Chapter

Some Mathematics

Norma van Surdam Graham

in Visual Pattern Analyzers

Published in print December 1989 | ISBN: 9780195051544
Published online January 2008 | e-ISBN: 9780199872183 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195051544.003.0002

Series: Oxford Psychology Series

 Some Mathematics

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This chapter provides the mathematical background for using Fourier Analysis (Linear Systems Analysis) to study visual pattern analyzers. It introduces sinusoidal, Gabor, and delta functions as applied to descriptions of neurons' receptive fields and visual stimuli. It describes how a linear system's responses to simple stimuli can predict the system's responses more generally. Bandwidth is the range of values along a dimension to which a system can respond and is represented in the system's Fourier Transform. The chapter provides insight into how bandwidth depends on the particular properties of a system's weighting function (receptive field) and presents a table of the relationships. Because different investigators have described bandwidth using different measures, a table of conversions among the bandwidth measures is provided. An appendix at the end of the chapter presents the material more formally.

Keywords: Fourier; linear systems; sinusoids; receptive field; Gabor functions; delta functions; selectivity of analyzers; bandwidth

Chapter.  22045 words.  Illustrated.

Subjects: Neuropsychology

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