Fourier Type Research Articles

The Serial Commutator FFT

This brief presents a new type of fast Fourier transform (FFT) hardware architectures called serial commutator (SC) FFT. The SC FFT is characterized by the use of circuits for bit-dimension permutation of serial data. The proposed architectures are based on the observation that, in the radix-2 FFT algorithm, only half of the samples at each stage must be rotated. This fact, together with a proper data management, makes it possible to allocate rotations only every other clock cycle. This allows for simplifying the rotator, halving the complexity with respect to conventional serial FFT architectures. Likewise, the proposed approach halves the number of adders in the butterflies with respect to previous architectures. As a result, the proposed architectures use the minimum number of adders, rotators, and memory that are necessary for a pipelined FFT of serial data, with 100% utilization ratio.

An investigation of the local distortions and the EPR parameters for Cu2+ in 40MgO–(10−x)PbF2–50SiO2–xCuO glasses

The local distortions and electron paramagnetic resonance (EPR) parameters for Cu2+ in 40MgO–(10−x)PbF2–50SiO2–xCuO (MPSC) glasses are theoretically studied at various impurity CuO concentrations x (= 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0 mol %) in a consistent way. Due to the Jahn-Teller effect, the [CuO6]10− clusters are found to experience the moderate tetragonal elongation distortions (characterized by the moderate relative tetragonal elongation ratios ρ ≈ 3%) along C4 axis. With only five adjusted coefficients a1, a2, b1, b2 and ω, the relevant model parameters (Dq, k, ρ, κ and H) are described by the Fourier type functions, which suitably reproduce the corresponding overall varying tendencies and fluctuations of the measured d–d transition bands and EPR parameters with x. The microscopic mechanisms of the varying rules of the relevant quantities with x are discussed in view of the whole decreasing ability of Si4+ to accept electrons and the reverse tendencies due to partial Cu2+ reduced to Cu+ at x ≥ 0.7 mol %. The monotonically increasing tendency of the calculated optical basicity reveals decreasing covalency of the whole glass systems with x.

Spectral collocation solutions to systems of boundary layer type

Three spectral collocation methods, namely Laguerre collocation (LC), Laguerre Gauss Radau collocation (LGRC) and mapped Chebyshev collocation (ChC) are used in order to solve some challenging systems of boundary layer problems of third and second orders. The last two methods enable a Fourier type analysis, mainly (fast) polynomial transformations, which can be used in order to improve the process of optimization of the scaling parameters. Generally, the second method mentioned above produces the best results. Unfortunately they remain sub geometric with respect to the accuracy. However, all methods avoid domain truncation and rather arbitrary shooting techniques. Some challenging problems from fluid mechanics, including non-newtonian fluids are accurately solved.

High-quality three-dimensional reconstruction and noise reduction of multifocal images from oversized samples

Three-dimensional (3-D) reconstruction is an indispensable tool in areas such as biology, chemistry, medicine, material sciences, etc. The sample can be reconstructed using confocal or nonconfocal mode of a microscope. The limitation of the confocal approach is the sample size. Currently used devices work mostly with sample surface area up to 1 cm2. We suggest a three-step method that creates 3-D reconstruction from multifocal images in nonconfocal mode that is qualitatively comparable to the confocal results. Our method, thus, takes advantage of both microscope modes—high-quality results without sample size limitation. The preprocessing step eliminates the additive noise with Linderberg-Levi theorem. The main focus criterion is based on adjusted Fourier transform. In the final step, we eliminate the defective clusters using the adaptive pixel neighborhood algorithm. We proved the effectiveness of our noise reduction and 3-D reconstruction method by the statistical comparisons; the correlation coefficients average 0.987 for all types of Fourier transforms.

Fourier type transforms on Lie symmetry groups

In this paper, we construct operators on a Lie symmetry group which may be regarded as Fourier transforms. Essentially, we integrate solutions generated by Lie symmetries against suitable test functions. We show that this idea leads to a powerful method for solving Cauchy problems for parabolic and hyperbolic equations in two and higher dimensions. We also discuss applications to the elliptic case.

Optical chirp z-transform processor with a simplified architecture.

Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.

Structured random measurements in signal processing

AbstractCompressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A synthesis of correlations on quantification of free convective heat transfer in inclined air-filled hemispherical enclosures

Recent works have examined the thermal and dynamical aspects of natural convection occurring in tilted hemispherical cavities whose disk constitutes the hot active wall. The influence of some important aspects on the natural flows have been considered such as the Rayleigh Number, the disk inclination angle with respect to the horizontal plane and the thermal boundary condition on the disk (Dirichlet, Neumann). Combinations of these parameters have been treated in steady state as well as is transient regime. Correlations of Nusselt–Rayleigh type (steady state) and Nusselt–Rayleigh–Fourier type (transient regime) that allow quantifying the heat transfer are proposed in these surveys. The objective of this paper is to synthesize and summarize these works in order to facilitate their implementation in engineering applications.

Fourier–type tests involving martingale difference processes

ABSTRACTWe develop testing procedures which detect if the observed time series is a martingale difference sequence. Furthermore, tests are developed that detect change–points in the conditional expectation of the series given its past. The test statistics are formulated following the approach of Fourier–type conditional expectations first proposed by Bierens (1982) and have the advantage of computational simplicity. The limit behavior of the test statistics is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test. The performance of the bootstrap version of the test is compared in finite samples with other methods for the same problem. A real–data application is also included.

Similarity problems in noncommutative polydomains

In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results such as Rota's model theorem for operators with spectral radius less than one, Sz.-Nagy characterization of operators similar to isometries (or unitary operators), and the refinement obtained by Foiaş and by de Branges and Rovnyak for strongly stable contractions. We also provide analogues of these results in the context of joint similarity of commuting tuples of positive linear maps on the algebra of bounded linear operators on a separable Hilbert space. An important role in this paper is played by a class of noncommutative cones associated with positive linear maps, the Fourier type representation of their elements, and the constrained noncommutative Berezin transforms associated with these elements. It is shown that there is an intimate relation between the similarity problems and the existence of positive invertible elements in these noncommutative cones and the corresponding Berezin kernels.

Diagnosis of Agricultural Crops Using Light(<Feature>Control and Diagnosis by Light in Plant Production)

Measurement using light, for example, spectroscopy, is rapid, low cost and easy for maintenance of the instrument, and used for diagnosis of agricultural crops. Visible-near infrared method has been used non-destructively measuring color of leaf and near infrared method measuring fruit quality for practical use, respectively. On the other hand, infrared spectrophotometers have also evolved fourier transformation type. Therefore, ultraviolet, visible, near-infrared and infrared spectroscopy method is mainly described. Moreover, nitrate ions determination using light was also focused for mainly vegetables.

Recent Advances on Rotational Spectroscopy and Microwave Spectroscopic Techniques

Rotational spectroscopy is a branch of fundamental science to study the rotational spectra of molecules, free radicals and ions based on the quantum mechanics. It has great applications on many fields such as radio astronomy and atmospheric remote sensing. In this paper we reviewed the basic theory of rotational spectroscopy, two different types of Fourier transform microwave spectrometers, spectroscopic analysis of certain typical cases, and future prospect of the microwave spectroscopic techniques as well.

Empirical Nu–Ra–Fo relationships for natural convection in air-filled hemispherical enclosures. Isothermal and inclined disk with dome oriented downwards

Correlations of Nusselt–Rayleigh–Fourier type proposed in this work allow quantifying of the transient convective heat transfer occurring in air-filled hemispherical cavities. The disk, initially at ambient temperature, is suddenly heated and kept isothermal. Throughout the heating process, the dome is maintained at ambient temperature. The radius of the cavity, associated with the temperature difference imposed between the disk and the dome, involves a large Rayleigh number range, varying between 104 and 5×108. The disk can be inclined with respect to the horizontal plane at an angle varying between 90° (vertical disk) and 180° (horizontal disk with dome downwards) by steps of 10°. The numerical approach is based on the finite volume method. The proposed empirical relationships in transient regime are linked to the steady state Nusselt–Rayleigh ones. They are obtained via the analysis of results corresponding to many combinations of the Rayleigh number and the disk inclination angle. The relationships are new since the considered geometry associated with the inclinations of the isothermal disk has not been treated previously. They constitute an important tool for the thermal design of engineering systems involved as they allow determining the convective heat transfer during the transient regime. They can be applied in several fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics.

Corrigendum to “A Fourier type transform on translation invariant valuations on convex sets”

Corrigendum to “A Fourier type transform on translation invariant valuations on convex sets”

On thermal control of devices contained in inclined hemispherical cavities with dome oriented downwards and subjected to transient natural convection

In this study, relationships of Nusselt–Rayleigh–Fourier type are proposed for the case of air-filled hemispherical cavity whose dome is oriented downwards and maintained isothermal. Its disk is subjected to a constant heat flux and inclined at an angle varying between 90° (vertical position) and 180° (disk horizontal with dome oriented downwards). The numerical approach is performed in transient regime by means of the finite volume method for Rayleigh numbers in the range of 104−5×108. These results are confirmed at steady state by measurements done for some configurations in a previous study for the same Rayleigh and inclination ranges. Otherwise, they complete other surveys considering inclination angles varying between 0° (horizontal cavity with dome oriented upwards) and 90° (vertical cavity) for a wider range of Rayleigh numbers. The correlations allow thermal control of devices submitted to natural convection in hemispherical cavities during the time preceding the steady state after their switch on.

Design and experimental research on a visible-near infrared spatial modulating Fourier transform spectrometer based on micro multi-step mirrors

A type of spatial modulating micro Fourier transform spectrometer (FTS) based on micro multi-step mirrors (MMSMs) is designed and manufactured in this paper. The interference system is based on Michelson interferometer, using two MMSMs instead of plane mirrors in two arms. The recovered spectrum is simulated with different distances between MMSMs and the detector, and the influence of diffraction on the recovered spectrum is analyzed. The edge-enlarging method for the MMSMs is proposed to eliminate edge noise, and the influence of surface roughness of MMSMs on the recovered spectrum is also analyzed. Moreover, the way of manufacturing the MMSMs is investigated. 2014 Tianjin University of Technology and Springer-Verlag Berlin Heidelberg.

Fourier type potential energy function for conformational change of selected organic functional groups

The energy changes associated with internal rotation of a functional group in a molecule depend on the topology of the chemical environment. Energies obtained from electron structure and force-field calculations have been analyzed by Fourier expansions. The findings show that rotation around bonds connecting atoms without lone pairs can be described with a one term Fourier-series. In contrast, two or three terms are needed if the connected atoms have lone pairs. The analysis inspires adoption of a simplified Fourier expansion that reproduces the data well, suggesting that Fourier-type-series with few terms are useful in describing any internal rotation analytically.

DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH FOURIER'S TYPE HEAT CONDUCTION

We study the Timoshenko system with Fourier's type heat conduction in the one-dimensional (whole) space. We observe that the dissipative structure of the system is of the regularity-loss type, which is somewhat different from that of the dissipative Timoshenko system studied earlier by Ide–Haramoto–Kawashima. Moreover, we establish optimal L2decay estimates for general solutions. The proof is based on detailed pointwise estimates of solutions in the Fourier space. Also, we introuce here a refinement of the energy method employed by Ide–Haramoto–Kawashima for the dissipative Timoshenko system, which leads us to an improvement on their energy method.

Matrix Fourier Transforms and Application

In this work, we introduce in an explicit form a special types of matrix Fourier transforms on real axis and real semi- axis: matrix cos- transforms, matrix sin- transforms and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for solving analytically the problems of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of vector heat conduction equation,vector wave equation and vector Poisson equation is obtained.

Influence of annealing on the structure of silica glass

Two types of high-purity synthetic silica glasses were annealed with different processes in precision annealing furnace. The thermal stress and structure of samples were analyzed by two types of stress instruments and Fourier transform infrared spectrometer. After being annealed at 1 070 °C for 6 days and then cooled slowly, optical path difference (OPD) caused by stress in the center and edge of Type III silica glass with a diameter of 150 mm and thickness of 50 mm decreased from 6 to 2 nm/cm. Meanwhile, with the same annealing process, fictive temperature of small-size Type III glass decreased to 939 °C, and structural stability of silica glass was improved. In addition, after being annealed at 1 100 °C for 5 hours and then cooled slowly, internal stress in Type IV silica glass with a thickness of 1 mm was basically eliminated, and its fictive temperature decreased from 1 421 to 966 °C.