scispace - formally typeset
Search or ask a question

Showing papers on "Fourier transform published in 1975"


Journal ArticleDOI
TL;DR: In this article, a detailed description of the analysis of EXAFS data is presented including details of the Fourier transform of the data and the extraction of structural and other physical parameters from these transforms.
Abstract: Fourier transforms of extended x-ray-absorption fine structure (EXAFS) give structural information in the vicinity of each kind of atom, separately, in a wide variety of gaseous, liquid, and solid systems. A detailed description of the analysis of EXAFS data is presented including details of the Fourier transform of the data and the extraction of structural and other physical parameters from these transforms. Included in this description are the measurement of interatomic distances, coordination numbers, disorder effects (thermal and structural), energy-dependent electron scattering amplitudes, inelastic mean free paths, and phase shifts. EXAFS spectra of Ge, Cu, and Ge${\mathrm{O}}_{2}$ are analyzed in detail. Multiple-scattering effects between atoms are generally found to be small. There are no multiple-scattering effects in the first shell of the Fourier transform. The phase shifts introduced by both the absorbing and surrounding atoms empirically appear to be characteristic of the particular atoms and independent of the surroundings for a given class of material. This is of great practical importance because it indicates that EXAFS can be calibrated by measuring known structures and then used to determine unknown ones.

634 citations


Journal ArticleDOI
TL;DR: In this paper, Stein showed that the operator given by convolution with *3$ is bounded from LP to LP for p in the appropriate range for conjugate indices p and p.
Abstract: Jl/(0)ld0 = ƒƒ* f(x)fà(x)dx = fmdè*f(x)dx<\\\\f\\\\p\\\\âd *f\\\\p, for conjugate indices p and p . Thus it suffices to prove that the operator given by convolution with *3$ is bounded from LP to LP for p in the appropriate range. Let K(x) be a radial Schwartz function with K(x) = 1 for \\x\\ < 100, and let Tk(x) = [K(x/2 ) -K(xl2-)] $)(*). It suffices to show there exists e = e(p) > 0 such that \\\\Tk * ƒ \\\\p, < C2~ || ƒ ||p. This follows from interpolating the estimates \\\\Tk * ƒ IL < C2\"~>*/|| f\\\\x and ||rfc *f\\\\2 < 2\\\\f\\\\2. Professor E. M. Stein has extended the range of this result to include p = 2(n + l)/(n + 3). His proof uses complex interpolation of the operators given by convolution with the functions Ba(x) = J0(27t\\x\\)/\\x\\°. Then

482 citations


Journal ArticleDOI
TL;DR: Further calculations of the three-dimensional mode patterns and power outputs from a highpower gas-dynamic laser, including a nonuniform flowing, saturable gain medium plus index inhomogeneities (shocks) inside the laser are presented.
Abstract: We present further calculations of the three-dimensional mode patterns and power outputs from a high-power gas-dynamic laser, including a nonuniform flowing, saturable gain medium plus index inhomogeneities (shocks) inside the laser. The calculations are carried out using a plane-wave or k-space expansion together with the fast Fourier transform. A new expanding-beam coordinate transform converts all diverging or converging sections of the resonator mode into equivalent collimated beam sections. The resulting FFT propagation code is significantly faster than earlier propagation codes using other eigenmode expansions.

317 citations


Journal ArticleDOI
TL;DR: In this paper, an analysis of the factors that influence the performance of a Fourier transform n.m.r. spectrometer including field homogeneity, probe design, transient circuit behaviour, Johnson noise, non linear analysis, phase sensitive detection in quadrature, and signal processing is given.
Abstract: An analysis is given of the factors which influence the performance of a Fourier transform n.m.r. spectrometer including field homogeneity, probe design, transient circuit behaviour, Johnson noise, non linear analysis, phase sensitive detection in quadrature, and signal processing. The building of a spectrometer based upon the analysis of these factors is described, as is the use of a cyclically ordered phase sequence (CYCLOPS) which renders the use of quadrature Fourier transformation easy. Theoretical deductions are experimentally verified, and the performance of the instrument is demonstrated with spectra obtained from caesium and phosphorus resonances.

289 citations




Journal ArticleDOI
TL;DR: In this paper, a variational trial function for the magnitude of the normalized order parameter of the form f = ϱ/R is assumed, where ϱ is the radial coordinate, R = (p 2 + ξv 2)1/2, and ξ isEnabled v� is a variual core radius parameter.
Abstract: In order to model the core of an isolated vortex in a type II superconductor, a variational trial function for the magnitude of the normalized order parameter of the form f = ϱ/R is assumed, where ϱ is the radial coordinate, R = (p 2 + ξv 2)1/2, and ξ v is a variational core radius parameter. Remarkably simple analytic expressions for the magnetic flux density and supercurrent density that solve Ampere's law and the second Ginzburg-Landau equation are obtained. An analytic result for the free energy of the isolated vortex is then derived by integrating the Ginzburg-Landau free energy functional. The value of ξ v that minimizes the free energy is calculated as a function of the Ginzburg-Landau parameter κ = λ/ξ and is found to range from ξ v = 0.935ξ for κ = 0.707 to ξ v ≈ 1.414ξ for κ > 1. A simple expression for the form factor or the Fourier transform of the flux density is obtained, which may be useful in the analysis of neutron diffraction experiments.

187 citations



Journal ArticleDOI
TL;DR: The theoretical analysis shows that theabsolute value of the ensemble average of the Fourier transform of the simulated EMG approaches the absolute value ofThe Fourier Transform of the motor unit potential.
Abstract: The electromyogram of a single motor unit is studied by considering it as a time function defined by a convolution integral where a point process input passes through a filter whose impulse response is the shape of a single motor unit action potential. The interspike intervals are assumed to be normally distributed, independent random variables. Simulation is performed on a digital computer. The theoretical analysis shows that the absolute value of the ensemble average of the Fourier transform of the simulated EMG approaches the absolute value of the Fourier transform of the motor unit potential. This has been confirmed by simulation except at the very low end of the spectrum. These results are compared with the Fourier transforms of the recorded surface EMG data from human muscles.

107 citations


Journal ArticleDOI
TL;DR: In this article, a new digital Fourier ellipsometer is described which employs a rotating compensator and a fixed analyzer to measure the polarization of light reflected from the sample.

106 citations


Journal ArticleDOI
TL;DR: In this article, a new spectral estimate, called the maximum entropy method, was described, which maximizes the information of a signal under the constraint that the estimated autocorrelation function of the signal is the Fourier transform of the spectral power density.
Abstract: A new spectral estimate, called the maximum entropy method, is described. This estimate was originated by John Parker Burg for use in seismic wave analysis. In the maximum entropy method the entropy, or information, of a signal is maximized under the constraint that the estimated autocorrelation function of the signal is the Fourier transform of the spectral power density. The spectral estimates are calculated in two ways: (1) by minimization of the error power to obtain the coefficients of the prediction error filter, as suggested by Burg, and (2) by a direct solution of the matrix equation using an algorithm due to Norman Levinson. For comparison a Blackman-Tukey technique, calculated with a Hamming window, is used also. We illustrate these three methods by applying them to a composite signal consisting of four sinusoids of unit amplitude: one each at high and low frequencies and two at moderate frequencies with respect to the Nyquist frequency, to which is added white noise of 0.5 amplitude. Results are shown to indicate that the best correspondence with the input spectrum is provided by the Burg technique. Applications of the maximum entropy method to geomagnetic micropulsations reveal complex multiplet structure in the Pc 4, 5 range. Such structure, not previously resolved by conventional techniques, has been predicted by a recent theory of magnetospheric resonances. In a period range 7 orders of magnitude longer than micropulsation periods, analysis of annual sunspot means shows that the 11-yr band is composed of at least three distinct lines. With each of these lines is associated a harmonic sequence. Long periods of the order of 100 yr also are revealed.

Journal ArticleDOI
TL;DR: In this paper, a sharp Hausdorff-Young inequality for the Fourier transform on Lp(Rn) was obtained for the convolution of functions on Rn.
Abstract: This note describes two results: (i) a sharp Hausdorff-Young inequality for the Fourier transform on Lp(Rn) which extends an earlier result of Babenko; and (ii) a sharp form of Young's inequality for the convolution of functions on Rn. That is, best possible constants are obtained for the following Lp(Rn) inequalities: [Formula: see text]



Journal ArticleDOI
TL;DR: This behavior is predicted by a model in which the threshold is governed, not by local contrast or any other feature in the stimulus domain, but rather by the component of maximum magnitude in the two-dimensional Fourier transforms of these stimulus patterns.

Journal ArticleDOI
TL;DR: In this paper, the Kramers-Kronig integrals are derived without recourse to complex analysis (except in evaluating the Fourier transform of sgn (t)) from the time domain result, a Fourier series method for numerical evaluation of causality relations is derived.
Abstract: Using a time domain method the Kramers-Kronig integrals are derived without recourse to complex analysis (except in evaluating the Fourier transform of sgn (t)). From the time domain result, a Fourier series method for numerical evaluation of causality relations is derived. This method eliminates the need to use numerical integration, the use of logarithms in evaluating the function and the consideration of Cauchy principal parts. Through the use of the fast Fourier transform algorithm the calculation can be vary rapid. The accuracy of the technique is considered.

Journal ArticleDOI
TL;DR: In this paper, a finite Fourier transform of the observed limb darkening function was used to achieve reduced sensitivity to atmospheric and instrumental effects and heightened sensitivity to the shape of the intrinsic limb lightening function.
Abstract: A new technique for locating the edge of the Sun is proposed. The technique uses a finite Fourier transform of the observed limb darkening function to achieve reduced sensitivity to atmospheric and instrumental effects and heightened sensitivity to the shape of the intrinsic limb darkening function. A theory is developed that predicts these sensitivities. In order to facilitate wider application, general relations are calculated. A testing program which complements the theory is also reported. The location of the edge is shown to be influenced only by solar phenomena down to the milli-arcsecond range. (AIP)


Journal ArticleDOI
TL;DR: In this paper, the use and importance of dynamic stiffness influence coefficients in flexural forced vibrations of structures composed of beams are described and the dynamic forces can be either harmonic or general transient forces.

Journal ArticleDOI
TL;DR: The construction and the performance of a double-beam Michelson-type Fourier spectrometer are described and the pure rotational spectra of H(2)O and CO have been recorded.
Abstract: The construction and the performance of a double-beam Michelson-type Fourier spectrometer are described. The instrument covers a wavenumber range from 10 cm−1 to 450 cm−1 with a maximum resolution of 0.025 cm−1 and an accuracy of frequency within ±0.001 cm−1. The optical path difference is measured by means of an He–Ne gas laser. To illustrate the general performance of the instrument, the pure rotational spectra of H2O and CO have been recorded.

Journal ArticleDOI
TL;DR: In this paper, the authors derived an explicit expression for the amplitude with which each acoustic mode is generated by the Fourier transform of the solution, which amounts to solving the equation for a source distribution of fixed frequency and wavenumber.

ReportDOI
01 Jan 1975
TL;DR: In this paper, the authors describe a filter design and test results for a subprogram with a source list of subprograms and a test set of sub-programs.-~-------;----------------------------------------------... Acknowledgment
Abstract: -~-------;----------------------------------------------... Acknowledgment---------------------------------------------------Introduction--------------------------------------~--------------Filter design----------------------------------------------------Algorithms-------------------------------------------------------Filter tests-----------------------------------------------------Discussion-------------------------------------------------------References---------------------------~---------------------------Appendix 1.----Source listing of subprograms---------------------2.----Test results---------------------------------------

Book
10 Mar 1975
TL;DR: The Fourier transform and the nilmanifold have been studied in the literature as mentioned in this paper, as well as elementary transformation theory, and theta functions and distinguished subspaces.
Abstract: The fourier transform and the nilmanifold ?\N.- Functions on ?\N and theta functions.- Elementary transformation theory.- Cohomology and theta functions.- Theta functions and distinguished subspaces.

Patent
Kato Makoto1
31 Jul 1975
TL;DR: In this paper, a phase mask comprised of a rectangular array of phase shifting areas arranged in a pseudo-random pattern is illuminated with a beam of electromagnetic radiation, and the array of pseudorandomly phase shifted beams is focused on a Fourier transform plane on which the power spectrum of the beams distributes in two orthogonal directions from its center maxima.
Abstract: A phase mask comprised of a rectangular array of phase shifting areas arranged in a pseudo-random pattern is illuminated with a beam of electromagnetic radiation. The array of pseudo-randomly phase shifted beams is focused on a Fourier transform plane on which the power spectrum of the beams distributes in two orthogonal directions from its center maxima. The phase shifting areas are arranged in such a manner that there is an approximately equal number of phase shifts for each of the different phase shifting areas with a constant phase relation between orthogonally adjacent phase shifting areas. The center maxima of the spectrum is confined to a rectangular-shaped area and uniformly distributed by suitably selecting the number of different phase shifts. Coherent noise on the reconstructed image is effectively eliminated.

Journal ArticleDOI
TL;DR: In this paper, a hybrid-mode solution for the characteristic impedance of microstrip on Iossless dielectric substrate is obtained by applying the method of moments in the Fourier transform domain.
Abstract: This paper presents a hybrid-mode solution for the characteristic impedance of microstrip on Iossless dielectric substrate. A solution to the hybrid-mode equations is obtained by applying the method of moments in the Fourier transform domain. Numerical results are presented showing the frequency dependence of both wavelength and characteristic impedance for single and coupled strips. These results are compared with those of other investigators in the low-frequency range.

Journal ArticleDOI
TL;DR: In this article, the spin-lattice relaxation time (T1) of both ring and methyl deuterons have been measured in toluene d8 by the Fourier transform inversion recovery method.
Abstract: The spin–lattice relaxation time (T1) of both ring and methyl deuterons have been measured in toluene‐d8 by the Fourier transform inversion recovery method. Measurements were made over the temperature range −35 to 200 °C, and over the pressure range 1 bar to 4 kbar. Viscosities and densities were also measured over most of this range. The T1 data are analyzed in terms of correlation times for isotropic overall molecular reorientation and internal rotation of the methyl group. Using pressure as a variable enables us to separate effects of density and temperature on overall and internal motion of the toluene molecule. Activation energies and activation volumes are reported. The experimental data are interpreted in terms of various theoretical models for the motional dynamics. The rotational diffusion model and the Enskog theory are used to discuss overall motions. For the case of internal motion of the methyl groups, the Langevin model is also considered. Large angle reorientation appears to be important in...

Journal ArticleDOI
TL;DR: In this paper, a series of LnNi(CO)o-n derivatives (n = 0-3) were obtained f0r.13C N M R spectra and analyzed in terms of the electron donor-acceptor abilities of the ligands.
Abstract: 13C N M R spectra have been obtained f0r.a series of LnNi(CO)o-n derivatives (n = 0-3) where L = PR3, PPhzY, PPhY2, P(OR')3, and Pc13 (R = Me, Et, Bu, Ph; R' = Me, Et, l-Pr, Ph; Y = C1, Me, OMe, OPh). The effect upon the carbonyl chemical shift of the replacement of X by Y substituents in X3-nYnPNi(C0)3 derivatives appears to be additive, as is the effect of the sequential replacement of carbonyl by phosphorus ligands. An excellent correlation is observed between the carbonyl chemical shifts and either the infrared stretching force constants or Kabachnik's a parameters. These data are analyzed in terms of the electron donor-acceptor abilities of the ligands.

Journal ArticleDOI
TL;DR: In this article, the combination of double irradiation and a simple two-pulse spin echo sequence is used for detecting homonuclear decoupling in a complex spectrum, which is a powerful and sensitive method.
Abstract: It is shown that the combination of double irradiation and a simple two-pulse spin echo sequence is a powerful and sensitive method for detecting homonuclear decoupling in a complex spectrum.

Journal ArticleDOI
TL;DR: In this paper, the Fourier transform of the field to be interpreted and the field generated by an equivalent surface is used to estimate the average depth of the sources and a distribution function for the depths and then a complete and very economical algorithm for the calculation of the corresponding equivalent surface.
Abstract: Transformation of gravity or magnetic anomaly maps into isodepth maps of a surface separating two homogeneous media may be accomplished by (1) systematically estimating an average depth and density or magnetization contrast for the surface and (2) using an iterative method to adjust local depths compared to the average depth of the surface. Average depth, density or magnetization contrast, and iterative adjustment of local depths are determined using the Fourier transform of the field to be interpreted and that of the field generated by an equivalent surface. This leads us to propose a method of estimating the average depth of the sources and a distribution function for the depths and then a complete and very economical algorithm for the calculation of the corresponding equivalent surface.