## Fouriers Lawseriesanalysis

The French mathematician Jean Baptiste Joseph Fourier (1768-1830) formulated the mathematically demonstrable generalization (Fourier's law) that any complex periodic pattern (such as sound waves) may be described as a particular sum of a number of "sine waves" (i.e., a wave form characterized by regular oscillations with a set period and amplitude such that the displacement amplitude at each point is proportional to the sine of the phase angle of the displacement; a "pure tone" is propagated as a sine wave). The sine waves so used are called a Fourier series, and the description itself is called a Fourier analysis. Thus, a Fourier analysis is a mathematical procedure whereby any intensity pattern may be broken down into a number of sine-wave components, and such an analysis may be applied to visual stimulation as well as to auditory phenomena. That is, any visual stimulus can be broken down into sine waves with different spatial frequencies, amplitudes, contrasts, and phases. Fourier's theorem is a mathematical proof that any periodic function can be decomposed by Fourier analysis into a Fourier series that is a sum of sine and cosine terms with suitable constants. The notion behind Fourier analyses in vision is that the visual system carries out an analysis by breaking a scene down into a number of sine-wave components. This information is contained in the firing of spatial frequency detectors (neurons that fire best to specific frequencies). The visual system then uses the information from these neurons to carry out the reverse process, called Fourier synthesis, in which the information is combined to create the visual scene. See also AUDITION/HEAR-ING, THEORIES OF; OHM'S ACOUSTIC/ AUDITORY LAW; SET THEORY; VISION/ SIGHT, THEORIES OF. REFERENCES

Fourier, J. B. J. (1822/1955). Theorie analytique de la chaleur. New York: Dover.

Herivel, J. (1975). Joseph Fourier: The man and the physicist. Oxford, UK: Oxford University Press. Kaufman, L. (1979). Perception: The world transformed. New York: Oxford University Press. Bloomfield, P. (2000). Fourier analysis of time series. New York: Wiley.

FOURIER'S THEOREM. See FOURIER'S LAW/SERIES/ANALYSIS.

FOVEAL CONE HYPOTHESIS. Many theories concerning the mechanisms of color vision have been proposed over several decades. D. B. Judd provides a summary table of a few of the better-known visual theories, including the following information: theorists' names, the anatomical location, fundamental colors, and chief limitations of the theories. Regarding retinal cone function and color response, there are two major contending hypotheses of the functioning of foveal cones: the single-receptor theory - states that all receptors are able to respond to all parts of the color spectrum; and the triple-receptor theory - states that the receptors belong to one of three groups, those that are sensitive either to red, or green, or blue. Additionally, two other color vision hypotheses have been proposed:

R. Granit and H. Hartridge's polychromatic hypothesis, and H. Hartridge's cluster hypothesis. See also COLOR VISION, THEORIES/LAWS OF; GRANIT'S COLOR VISION THEORY; HARTRIDGE'S POLYCHROMATIC VISION THEORY; VISION/ SIGHT, THEORIES OF. REFERENCE

Judd, D. B. (1951). Basic correlates of the visual stimulus. In S. S. Stevens (Ed.), Handbook of experimental psychology. New York: Wiley.

## Conquering Fear In The 21th Century

The Ultimate Guide To Overcoming Fear And Getting Breakthroughs. Fear is without doubt among the strongest and most influential emotional responses we have, and it may act as both a protective and destructive force depending upon the situation.

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