| 释义 |
Fourier|ˈfʊərɪeɪ|
The name of J. B. J. Fourier (1768–1830), French mathematician, used attrib. or in the possessive to designate certain principles enunciated by him and many mathematical expressions and techniques arising out of his work, as Fourier analysis, the analysis of a periodic function into a number of simple harmonic functions or, more generally, into a series of functions from any orthonormal set; Fourier's law, that any non-sinusoidal periodic vibration can be regarded as the sum of a number of sinusoidal vibrations each having a frequency that is an integral multiple of some fundamental frequency; Fourier('s) series, a series of the form ½a0 + (a1 cos x + b1 sin x) + (a2 cos 2x + b2 sin 2x) + {ddd}, where the constants a0, a1, b1, etc. are defined in terms of a function f(x) to which the series may converge; Fourier's theorem, (a) that if a function f(x) satisfies certain conditions within the interval -π {slle} x {slle} π, it can be represented within that interval by a Fourier series; (b) (see quot. 1880); Fourier transform, a function f(x) related to a given function g(t) by the equation (2π)½f(x) = ∫∞-∞ g(t)e{pm}itxdt, used to represent a non-periodic function by a spectrum of sinusoidal functions. Also Fourier coefficient, Fourier expansion, Fourier integral, Fourier transformation, etc.
1834Rep. Brit. Assoc. 1833 343 If the interval of the roots be determined, by the application of Fourier's theorem of the succession of signs of the original function X and its derivatives. 1842A. De Morgan Differential & Integral Calculus xx. 641 In applying Fourier's theorem..to discontinuous functions, we find that at the point where the discontinuity takes place, and a function which generally can have but one value might be expected to have two, it takes neither, and gives only the mean between them. 1877Rayleigh Theory of Sound I. ii. 24 The pre⁓eminent importance of Fourier's series in Acoustics. 1880G. S. Carr Synopsis Pure & Appl. Math. I. i. 134 Fourier's Theorem.—Fourier's functions are..f(x), f′(x), f{pp}(x){ddd}fn(x){ddd}As x increases, Fourier's functions lose one change of sign for each root of the equation f(x) = 0, through which x passes, and r changes of sign for r repeated roots. 1884A. Daniell Text Bk. Princ. Physics v. 127 Longitudinal vibrations of a string or rod..whose ends are held fixed obey the same principles as transverse vibrations. Fourier's law holds good. 1902E. T. Whittaker Course Mod. Anal. vii. 152 The question arises..whether the Fourier expansion is unique. 1911Proc. R. Soc. A. LXXXV. 14 We can also sum the series of the products of the Fourier coefficients of two such functions. 1912Phil. Mag. 6th Ser. XXIV. 866 Fourier's integral. 1923Proc. Cambr. Philos. Soc. XXI. 463 The notion of Fourier transforms arises from Fourier's integral formula,..which gives..reciprocal relations..connecting the two functions f(x) and F(x). 1929V. Bush Operational Circuit Analysis x. 186 Direct operational methods may be regarded as shorthand processes of evaluating and tabulating the results of Fourier analysis. 1936Discovery Apr. 114/2 All sound-waves (except those from a flute, closed organ-pipe, etc.) are composed of many combined vibrations whose composition follows Fourier's law. 1957R. S. Longhurst Geom. & Physical Optics xi. 226 The Fraunhofer pattern is the Fourier transform of the amplitude across the diffracting aperture and vice versa. 1963R. W. Ditchburn Light (ed. 2) iv. 89 The ‘top-hat curve’ shown in fig. 4.6 can be represented by an appropriate Fourier series..for all values of x0 because the curve to be represented is periodic. 1964Oceanogr. & Marine Biol. II. 14 The correlation coefficient fu(τ) is related by a Fourier transformation to the spectrum function Fu(n). 1965Pearson & Maler Introd. Circuit Anal. ix. 439 The Fourier transform..is useful in analyzing pulses from a frequency standpoint. 1967Condon & Odishaw Handbk. Physics (ed. 2) ii. iii. 26/2 The part of F(t) effective in exciting the oscillator is the component in its Fourier integral representation associated with the natural frequency of the oscillator.
Hence vbl. uses, as Fourier-analyse, Fourier-transform vbs.; Fourier-transformed ppl. adj.
1962W. B. Thompson Introd. Plasma Physics vi. 108 To get a numerical value, the curve may be Fourier analysed, and the effect of each harmonic component discovered. 1967Oceanogr. & Marine Biol. V. 24 For several North Sea ports..continuous sea-level records were Fourier-analysed to determine if any non-tidal periods were present. 1968C. G. Kuper Introd. Theory Superconductivity iv. 57 These Fourier-transformed quantities. 1970Nature 5 Sept. 1032/1 The Fourier co⁓efficients..could then be inversely Fourier transformed to reconstruct the specimen in three dimensions. |