Showing papers on "Fourier transform published in 1988"

Iterative Fourier-transform algorithm applied to computer holography

Abstract: In the generation of computer-generated holograms the phase is in many applications a free parameter that can be manipulated to achieve a high diffraction efficiency, a small space–bandwidth product, and a speckle-free reconstruction. An iterative algorithm to determine such phase distributions is described. Experimental verifications are given.

Deep Level Transient Fourier Spectroscopy (DLTFS)—A technique for the analysis of deep level properties

Abstract: The advantages of a DLTS method—the DLTFS method—are presented. In this technique the capacitance-time transients are digitalized, and the discrete Fourier coefficients are formed via numerical Fourier transformation. These coefficients can be used to calculate amplitude and time constant of the transients for discrete trap levels in various ways, thus giving control of the results. This permits automatic control of measuring parameters (e.g. choice of period width and temperature values), automatic evaluation during measurement (e.g. impurity concentration, activation energy and capture cross section), and high measuring accuracy. In contrast to the usual DLTS technique a temperature dependence of the amplitude, leading to errors especially in CC-DLTS and current-DLTS measurements, does not present a source of error. The good noise suppression is a further advantage of the DLTFS method.

Algebras of distributions suitable for phase-space quantum mechanics. I

Abstract: The twisted product of functions on R2N is extended to a *‐algebra of tempered distributions that contains the rapidly decreasing smooth functions, the distributions of compact support, and all polynomials, and moreover is invariant under the Fourier transformation The regularity properties of the twisted product are investigated A matrix presentation of the twisted product is given, with respect to an appropriate orthonormal basis, which is used to construct a family of Banach algebras under this product

Wavelet transform of multifractals.

Abstract: We present the wavelet transform as a mathematical microscope which is well suited for studying the local scaling properties of fractal objects. We apply this technique to probability measures on self-similar Cantor sets and to the golden-mean trajectories on two-tori at the onset of chaos.

Comparison Among Several Numerical Integration Methods for Kramers-Kronig Transformation

Abstract: Several numerical integration methods are compared in order to search out the most effective method for the Kramers-Kronig transformation, using the analytical formula of the Kramers-Kronig transformation of a Lorentzian function as a reference. The methods to be compared involve the use of (1) Maclaurin's formula, (2) trapezium formula, (3) Simpson's formula, and (4) successive double Fourier transform methods. It is found that Maclaurin's formula, in which no special approximation is necessary for the pole part of the integration, gives the most accurate results, and also that its computation time is short. Successive Fourier transform is less accurate than the other methods, but it takes the least time when used without zero-filling. These results have important relevance for programs used to obtain optical constant spectra and to analyze spectral data.

Three-dimensional shape analysis using moments and Fourier descriptors

Abstract: A procedure for using moment-based feature vectors to identify a three-dimensional object from a two-dimensional image recorded at an arbitrary viewing angle and range is presented. A moment form called standard moments, rather than the usual moment invariants, is considered. A standard six-airplane experiment was used to compare different techniques. Fourier descriptors and moment invariants were both compared to the present scheme for normalized moments. Various experiments were conducted using mixtures of silhouette and boundary moments and different normalization techniques. Standard moments gave slightly better results than Fourier descriptors for this experiment; both of these techniques were much better than moment invariants. >

Calculations of the dispersive characteristics of microstrips by the time-domain finite difference method

Abstract: A direct time-domain finite-difference method is used to recharacterize the microstrip. Maxwell's equations are discretized both in time and space and a Gaussian pulse is used to excite the microstrip. The frequency-domain data are obtained from the Fourier transform of the calculated time-domain field values. Since this method is completely independent of all the above-mentioned investigations, the results can be considered as an impartial verification of the published results. The comparison of the time-domain results and those from the frequency-domain methods has shown the integrity of the time-domain computations. This method is very general and can be applied to model many other microwave components. >

Fourier Techniques in X-Ray Timing

Abstract: Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum and the signal variance, including corrections for binning and dead time. The statistical properties of a noise power spectrum are discussed and related to the problems of detection (and setting upper limits) of broad and narrow features in the power spectrum. A “dependent triar” method is discussed to search power spectra consistently for many different types of signal simultaneously. Methods are compared to detect a sinusoidal signal, a case that is relevant in the context of X-ray pulsars.

SLIM: Spectral localization by imaging

Abstract: Nonspectroscopic magnetic resonance (MR) imaging often shows that a slice is composed of several compartments, each of which can be assumed to have a spatially homogeneous magnetic resonance spectrum, e.g., a limb composed of fat, muscle, bone marrow, and tumor. We show how to use structural information from such a nonspectroscopic image in order to increase the efficiency of subsequent localized spectroscopic measurements. Specifically, knowledge of the boundaries of N compartments makes it possible to reconstruct compartmental spectra from spectroscopic signals from an entire cross section with N or more different degrees of phase encoding. Experimental studies of a two-compartment phantom show that this method (SLIM) can be used to derive regional hydrogen spectra of a single slice from signals with as few as 2 phase-encoding steps, although Fourier transform chemical-shift imaging requires 64 steps to achieve a result of comparable accuracy. SLIM required only 16 phase-encoding steps to obtain accurate regional single slice spectra in a human limb with three compartments. Spectra of similar quality, obtained by Fourier transform chemical-shift imaging, required 256 to 1024 steps.

Peak factor minimization using a time-frequency domain swapping algorithm

Abstract: An algorithm is presented to minimize the peaks in the time domain of bandlimited Fourier signals. This method has the ability to compress signals effectively without disturbing their spectral magnitudes. A computationally efficient algorithm is presented that leads to strongly compressed signals (crestfactors of 1.41 compared to 1.67). The method is applicable not only to flat spectrum magnitudes but to any frequency domain energetic distribution. >

Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure

Abstract: A new technique is presented to measure the frequency dependent complex modulus simultaneously at several frequencies instead of consecutively as in a frequency sweep. For this purpose, the strain in a dynamical mechanical experiment is prescribed as a superposition of several different modes (three in our case). The resulting stress is decomposed into sinusoidal components, each of them characterized by their frequency, amplitude, and phase shift with respect to the corresponding strain component. Phase shift and amplitude are expressible in a frequency dependent complex modulus. A single experiment gives, therefore, values for the complex modulus at a set of prescribed frequencies. The method was demonstrated on three stable viscoelastic fluids and was applied to determine the instant of sol-gel transition (gel point) of a crosslinking polymer.

Gravity inversion of an interface above which the density contrast varies exponentially with depth

Abstract: Mapping of an interface above which the density contrast varies exponentially with depth, as is common at the basement surface of sedimentary basins, is efficiently achieved by a theoretically precise gravity method which can be applied to either profile data or twodimensional data. The contrast in mass above the interface is modeled by an array of vertical rectangular prisms with density contrasts varying exponentially with depth. Gravity anomalies due to the prisms are calculated in the wavenumber domain and then converted to the space domain. The precision of the inverse numerical Fourier transform in this procedure is significantly increased by a shift‐sampling technique based on the discrete Fourier deviation equation. Depth to the interface is determined by iterative adjustment of the vertical extent of the prisms in accordance with observed gravity anomaly data. The basement surface of the Los Angeles basin, California, calculated by this method, closely duplicates the published configuration based...

Profile analysis for microcrystalline properties by the Fourier and other methods

Abstract: In the 1960s the Fourier and variance methods superseded the use of the FWHM and integral breadth in detailed studies of microcrystalline properties. Provided that due allowance is made in the analysis for systematic errors, particularly the effects of truncation of diffraction line profiles at a finite range, these remain the best methods for characterising crystallite size and shape, microstrains and other imperfections in cases where accuracy is important. However, the application of the Fourier, variance and related methods in general requires that the diffraction lines are well resolved and it is thus restricted to materials with high symmetry or which exhibit a high degree of preferred orientation. Most materials, on the other hand, including many of technological importance, have complex patterns with severe overlapping of peaks. The introduction of pattern-decomposition methods, whereby a suitable model is fitted to the total diffraction pattern to give profile parameters for individual lines, means that microcrystalline properties can now be studied for any crystalline material or mixture of substances. The use of the FWHM and integral breadth has been given a new lease of life; though the information is less detailed than is given by the Fourier and variance methods and systematic errors are in general greater, self-consistent estimates of crystallite size and microstrains are obtained.

A phased translation function

Abstract: A phased translation function, which takes advantage of prior phase information to determine the position of an oriented molecular replacement model, is examined. The function is the coefficient of correlation between the electron density computed with the prior phases and the electron density of the translated model, evaluated in reciprocal space as a Fourier transform. The correlation coefficient used in this work is closely related to an overlap function devised by Colman, Fehlhammer & Bartels [in Crystallographic Computing Techniques (1976), edited by F. R. Ahmed, K. Huml & B. Sedlacek, pp. 248–258. Copenhagen: Munksgaard]. Tests with two protein structures, one of which was solved with the help of the phased translation function, show that little phase information is required to resolve the translation problem, and that the function is relatively insensitive to misorientation of the model.

The evolution of the wave function in a curve crossing problem computed by a fast Fourier transform method

Abstract: We develop a unitary fast Fourier transform method for solving time dependent curve crossing problems. The procedure is described in detail and is illustrated by calculations for a two curve, one‐dimensional example. The time evolution of the wave function and mean nuclear positions and energies for each curve are shown and discussed.

Abel inversion using fast Fourier transforms.

Abstract: A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given.

Tauberian theorems for generalized functions

Abstract: Notation and Definitions.- 1: Some Facts on the Theory of Distributions.- 1. Distributions and their properties.- 1. Spaces of test functions.- 2. The space of distributions D?(O).- 3. The space of distributions S?(F).- 4. Linear operations on distributions.- 5. Change of variables.- 6. L -invariant distributions.- 7. Direct product of distributions.- 8. Convolution of distributions.- 9. Convolution algebras of distributions.- 2. Integral transformations of distributions.- 1. The Fourier transform of tempered distributions.- 2. Fourier series of periodic distributions.- 3. The B -transform of distributions.- 4. Fractional derivatives (primitives).- 5. The Laplace transform of tempered distributions.- 6. The Cauchy kernel of the tube domain TC.- 7. Regular cones.- 8. Fractional derivatives (primitives) with respect to a cone.- 9. The Radon transform of distributions with compact support in an odd-dimensional space.- 3. Quasi-asymptotics of distributions.- 1. General definitions and basic properties.- 2. Automodel (regularly varying) functions.- 3. Quasi-asymptotics over one-parameter groups of transformations.- 4. The one-dimensional case. Quasi-asymptotics at infinity and at zero.- 5. The one-dimensional case. Asymptotics by translations.- 6. Quasi-asymptotics by selected variable.- 2: Many-Dimensional Tauberian Theorems.- 4. The General Tauberian theorem and its consequences.- 1. The Tauberian theorem for a family of linear transformations.- 2. The general Tauberian theorem for the dilatation group.- 3. Tauberian theorems for nonnegative measures.- 4. Tauberian theorems for holomorphic functions of bounded argument.- 5. Admissible and strictly admissible functions.- 1. Families of linear transformations under which a cone is invariant.- 2. Strictly admissible functions for a family of linear transformations.- 3. Admissible functions of a cone.- 4. Some examples of admissible functions of a cone.- 6. Comparison Tauberian theorems.- 1. Preliminary theorems.- 2. The comparison Tauberian theorems for measures and for holomorphic functions with nonnegative imaginary part.- Comments on Chapter 2.- 3: One-Dimensional Tauberian Theorems.- 7. The general Tauberian theorem and its consequences.- 1. The general Tauberian theorem and its particular cases.- 2. Quasi-asymptotics of a distribution f from S+? and a function arg f?.- 3. Tauberian theorem for distributions from the class .- 4. The decomposition theorem.- 8. Quasi-asymptotic properties of distributions at the origin.- 1. The general case.- 2. Quasi-asymptotics of distributions from H and asymptotic properties of the reproducting functions of measures.- 9. Asymptotic properties of the Fourier transform of distributions from M+.- 1. Asymptotic properties of the Fourier transform of finite measures.- 2. Asymptotic properties of the Fourier transform of distributions from M+.- 3. The Abel and Cezaro series summation with respect to an automodel weight.- 10. Quasi-asymptotic expansions.- 1. Open and closed quasi-asymptotic expansions.- 2. Quasi-asymptotic expansions and convolutions.- 4: Asymptotic Properties of Solutions of Convolutions Equations.- 11. Quasi-asymptotics of the fundamental solutions of convolution equations.- 1. Quasi-asymptotics and convolution.- 2. Quasi-asymptotics of the fundamental solutions of hyperbolic operators with constant coefficients.- 3. Quasi-asymptotics of the solutions of the Cauchy problem for the heat equation.- 12. Quasi-asymptotics of passive operators.- 1. The translationally-invariant passive operators.- 2. The fundamental solution and the Cauchy problem.- 3. Quasi-asymptotics of passive operators and their fundamental solutions.- 4. Differential operators of the passive type.- 5. Examples.- Comments on Chapter 4.- 5: Tauberian Theorems for Causal Functions.- 13. The Jost-Lehmann-Dyson representation.- 1. The Jost-Lehmann-Dyson representation in the symmetric case.- 2. Inversion of the Jost-Lehmann-Dyson representation in the symmetric case.- 3. The Jost-Lehmann-Dyson representation in the general case.- 14. Automodel asymptotics for the causal functions and singularities of their Fourier transforms on the light cone.- 1. Some preliminary results and definitions.- 2. The main theorems.- 3. On forbidden asymptotics in the Bjorken domain.- 4. Asymptotic properties of the two-point Wightman function.- Comments on Chapter 5.

Calculation of an OMIT map

Abstract: A space-group-general computer program to compute an OMIT map using fast Fourier transforms is presented. In this procedure an asymmetric unit of the unit cell is divided into several boxes. For each box a set of phases is calculated by the inverse Fourier transforms of the existing electron density distribution which has been modified so that the electron density values in and around that box is a constant. An OMIT map is then calculated for each box by the Fourier transforms of the observed amplitudes with these phases. The computer program may be used to reduce bias in electron density maps during model building and refinement of macromolecules. The procedure was used to detect error in the atomic model of a derivative of ribonuclease (personal communication by J. Nachman, National Cancer Institute, Frederick, Maryland, USA).

Applying harmonic balance to almost-periodic circuits

Abstract: A new Fourier transform algorithm for almost-periodic functions (the APFT) is developed. It is both efficient and accurate. Unlike previous attempts to solve this problem, the new algorithm does not constrain the input frequencies and uses the theoretical minimum number of time points. Also presented is a particularly simple derivation of harmonic Newton (the algorithm that results when Newton's method is applied to solve the harmonic balance equations) using the APFT; this derivation uses the same matrix representation used in the derivation of the APFT. Since the APFT includes the DFT (discrete Fourier transform) as a special case, all results are applicable to both the periodic and almost-periodic forms of harmonic Newton. >

Resonance frequency of a rectangular microstrip patch

Abstract: The microstrip-patch resonant frequency problem is formulated in terms of an integral equation using vector Fourier transforms. Using Galerkins's method in solving the integral equation, the resonant frequency of the microstrip patch is studied with both Chebyshev polynomials and sinusoidal functions as basis functions. In the case of the Chebyshev polynomials, the edge singularity is included, but it is not important for convergence. Furthermore, the resonant frequency of the microstrip patch is ascertained with a perturbation calculation. The results for Galerkin's method and experiments are in good agreement. The perturbation calculation agrees asymptotically with Galerkin's method. With the aim of developing a computer-aided design formula, the solutions obtained by Galerkin's method are interpolated with a three-variable polynomial. >

Fourier acceleration of iterative processes in disordered systems

Abstract: Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.

A novel principle for optimization of the instantaneous Fourier plane coverage of correction arrays

Abstract: A novel principle for the design of correlation arrays is introduced, based upon the maximization of the distance between samples. Simulated annealing is applied to the problem of finding solutions for moderate numbers of elements (up to 12). The resulting arrays have symmetric crystalline structures. >

A study of the structure of human complement component factor H by Fourier transform infrared spectroscopy and secondary structure averaging methods.

Abstract: Fourier transform infrared spectroscopy was used to investigate the secondary structure of human complement component factor H in H2O and 2H2O buffers. The spectra show a broad amide I band which after second-derivative calculations is shown to be composed of three components at 1645, 1663, and 1685 cm-1 in H2O and at 1638, 1661, and 1680 cm-1 in 2H2O. The frequencies of these components are consistent with the existence of an extensive antiparallel beta-strand secondary structure. The exchange properties of the amide protons of factor H as measured in 2H2O buffers are rapid and lead to an estimate of NH proton nonexchange that is comparable with those for small globular proteins. Human factor H is constructed from a linear sequence of 20 short consensus repeats with a mean of 61 residues in each one. To investigate the secondary structure further, secondary structure predictions were carried out on the basis of an alignment scheme for 101 sequences for these repeats as found in human factor H and 12 other proteins. These predictions were averaged in order to improve the reliability of the calculations. Both the Robson and the Chou-Fasman methods indicate significant beta-structural contents. Residues 21-51 in the 61-residue repeat show a clear prediction of four strands of beta-structure and four beta-turns. A structural model based on antiparallel beta-strands in the secondary structure is proposed and discussed.(ABSTRACT TRUNCATED AT 250 WORDS)

Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments

Abstract: Experimental demonstrations of deterministic phase retrieval based on the Teague-Streibl irradiance transport equation are presented. A new technique is proposed, in which the transport equation is solved by the Fourier transform method for a periodic boundary condition with high spatial carrier frequency, which is created by making a light beam with unknown phase distribution pass through a grating. Quantitative phase measurements were performed by experiments without recourse to interferometry, and the results were found to be in good agreement with theory.