*Norma van Surdam Graham*

- Published in print:
- 1989
- Published Online:
- January 2008
- ISBN:
- 9780195051544
- eISBN:
- 9780199872183
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195051544.003.0002
- Subject:
- Psychology, Cognitive Neuroscience

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 ...
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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.Less

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.

*Stephen Handel*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195169645
- eISBN:
- 9780199786732
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195169645.003.0003
- Subject:
- Psychology, Cognitive Psychology

If the goal of sensory systems is to maximize information transmission, there should be a match between the functioning of the sensory systems and the statistical properties of the objects in the ...
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If the goal of sensory systems is to maximize information transmission, there should be a match between the functioning of the sensory systems and the statistical properties of the objects in the environment. Analyses of the distribution of acoustical and visual energies indicate that they follow a power law, 1/f, so that there is a constant relationship between frequency and amplitude, namely equal power in all octave regions. To encode this distribution, the auditory and visual systems use cells that resemble Gabor functions that decorrelate local sensory energy to detect the redundancies such as continuous boundaries that signify objects. There is sparse coding so that only a small number of cells fire for any input and those cells minimize the uncertainty problem by trading frequency resolution with orientation or time resolution. The perceptual outcomes are combined with Bayesian prior probabilities to identify the most likely object.Less

If the goal of sensory systems is to maximize information transmission, there should be a match between the functioning of the sensory systems and the statistical properties of the objects in the environment. Analyses of the distribution of acoustical and visual energies indicate that they follow a power law, 1/f, so that there is a constant relationship between frequency and amplitude, namely equal power in all octave regions. To encode this distribution, the auditory and visual systems use cells that resemble Gabor functions that decorrelate local sensory energy to detect the redundancies such as continuous boundaries that signify objects. There is sparse coding so that only a small number of cells fire for any input and those cells minimize the uncertainty problem by trading frequency resolution with orientation or time resolution. The perceptual outcomes are combined with Bayesian prior probabilities to identify the most likely object.