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The spectral boundary element method for solving two‐dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady‐state example of a semi‐infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time‐varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

This paper presents a methodology, based on the fast Fourier transform (FFT), that improves prior established techniques to solve axisymmetric potential problems with non‐axisymmetric boundary conditions using the boundary element method (BEM). The proposed methodology is highly effective, especially in cases where a large number of harmonics is required. Furthermore, it is optimised at several levels, reaching the maximum possible efficiency. Special concern is given on its implementation on quadratic elements that are of current practice. The method is applicable to any type of boundary elements as well as to a wider class of static and dynamic axisymmetric boundary value problems.

This paper aims to present a single-block memory-based FFT processor design with a conflict-free addressing scheme for field-programmable gate arrays FPGAs with dual-port block memories. This study aims for a single-block dual-port memory-based N-point radix-2 FFT design that uses memory locations and spending minimum clock cycle.

A new memory-based Fast Fourier Transform (FFT) design that uses a dual-port memory block is proposed. Dual-port memory allows the design to perform two memory reads and writes in a single clock cycle. This approach achieves low operational clock and smallest memory simultaneously, excluding some small overhead for exceptional address changes. The methodology is to read from while writing to a memory location, eliminating the need for excess memory and additional clock cycles.

With the minimum memory size and the simplest architecture, radix-2 FFT and single-memory block are used. The number of clock pulses spent for all FFT operations does not provide much advantage for low-point FFT operations but is important for high-point FFT operations. With the developed algorithm, N memory is used, and the number of clock pulses spent for all FFT stages is (N/2 +1)log2N for all FFT operations.

This is an original paper, which has simultaneously in whole or in part been submitted anywhere else.

The paper deals with the development of an improved fast Fourier transform (FFT)-based numerical method for computing the effective properties of composite conductors. The convergence of the basic FFT-based methods is recognized to depend drastically on the contrast between the phases. For instance, the primal formulation is not suited for solving the problems with high conductivity whereas the dual formulation is computationally costly for problems with high resistivity. Consequently, it raises the problem of computing the properties of composites containing both highly conductive and resistive inclusions.

In the present work, the authors' propose a new iterative scheme for solving that kind of problems which is formulated in term of the polarization.

The capability and relevance of this iterative scheme is illustrated through numerical implementation in the case of composites containing squared inclusions. It is shown that the rate of convergence is increased and thus, particularly when the case of high contrasts is considered. The predominance of the polarization based iterative scheme (PBIS) over existing ones is also illustrated in the case of a composite containing both highly conductive and highly resistive inclusions.

The method is easy to implement and uses the same ingredients as the basic schemes: the FFT and the exact expression of the Green tensor in the Fourier space. Moreover, its convergence conditions do not depend on the conductivity properties of the constituents, which then constitutes the main difference with other existing iterative schemes. The method can then be applied for computing the effective properties of composites conductors with arbitrary contrasts.

The purpose of this paper is to present a fully automated numerical tool for computing the effective permeability of porous media from digital images which come from the modern imagery technique.

The permeability is obtained by the homogenization process applied to a periodic rigid solid in which the fluid flow is described by the Stokes equations. The unit cell problem is solved by using the Fast Fourier Transform (FFT) algorithm, well adapted for the microstructures defined by voxels.

Various 3-D examples are considered to show the capacity of the method. First, the case of flow through regular arrays of aligned cylinders or spheres are considered as benchmark problems. Next, the method is applied to some more complex and realistic porous solids obtained with assemblies of overlapping spherical pores having identical or different radii, regularly or randomly distributed within the unit cell.

The use of FFT allows the resolution of high-dimension problems and open various possibilities for computing the permeability of porous microstructures coming from X-ray microtomography.

This paper aims to explore a new way to extract the fault feature of a rolling bearing signal on the basis of a combinatorial method.

By combining local mean decomposition (LMD) with Teager energy operator, a new feature-extraction method of a rolling bearing fault signal was proposed, called the LMD–Teager transform method. The principles and steps of method are presented, and the physical meaning of the time–frequency power spectrum and marginal spectrum is discussed. On the basis of comparison with the fast Fourier transform method, a simulated non-stationary signal was processed to verify the effect of the new method. Meanwhile, an analysis was conducted by using the recorded vibration signals which include inner race, out race and bearing ball fault signal.

The results show that the proposed method is more suitable for the non-stationary fault signal because the LMD–Teager transform method breaks through the difficulty of the Fourier transform method that can process only the stationary signal. The new method can extract more useful information and can provide better analysis accuracy and resolution compared with the traditional Fourier method.

Combining the advantage of the local mean decomposition and the Teager energy operator, the LMD–Teager method suits the nature of the fault signal. A marginal spectrum obtained from the LMD–Teager method minimizes the estimation bias brought about by the non-stationarity of the fault signal. So, the LMD–Teager transform has better analysis accuracy and resolution than the traditional Fourier method, which provides a good alternative for fault diagnosis of the rolling bearing.

The detection of H₂ concentrations in concentrations undetectable by the conventional detection method of surface acoustic wave (SAW) sensors based on frequency shift, by correlating analyte presence with Fourier spectra components.

Fast Fourier Transform (FFT) and autocorrelation analysis of phase noise in a SnO2-coated SAW sensor was performed. Fourier spectra were obtained by FFT from the SAW sensor resonance frequency instability, in the absence of analyte, and for H₂ concentrations between 0.08 and 0.4 per cent.

All analyte concentrations are below the sensor limit of detection, which is 0.8 per cent for H₂. Although these analyte concentrations caused no significant change in the resonance frequency of the SAW resonator, the FFT spectra presented several modifications, namely, the appearance of a new peak and the decrease of randomness. The authors consider that the effect is because of the chaotic behavior of the temporal dependence of the SAW resonance frequency. This explanation is substantiated by the decrease observed in the SAW oscillator autocorrelation function, which is an indication for a chaotic behavior.

As chaotic systems are extremely sensitive to perturbation, measurement methods based on chaos diagnosis could potentially greatly improve the SAW detection.

Fourier spectra components were correlated with analyte presence in concentrations undetectable by the conventional SAW detection method based on frequency shift.

The purpose of this paper is to research an auto generation method of developing FFT image and image pattern for textile based on FFT theory.

In the research, a program was developed to generate FFT images using the FFT algorithm. The process of auto generation FFT image can be divided into the following steps: initializing the size of image, painting source image, giving the color pattern, transforming FFT image by FFT, designing mask template, and image pattern combining by point diagram. These image patterns can be used to apply on the textile.

The results showed that the FFT images can be used for textile designer directly. The FFT images can also be used as elements for textile image design such as clothing. The auto generation FFT images by FFT reflect different modern sense of beauty from traditional geometric images.

There are many parameters that affect the art effect of FFT image generating by FFT algorithm. However, there is no discussion about the relationship between the parameters and art effect. Three dimension effects are not obvious in the simulation results by virtual clothing software.

The paper presents a fundamental understanding of the property of the FFT image generating by FFT algorithm and application method of the image pattern in clothing.

The authors proposed a new method of fast time delay measurement for integrated pulsar pulse profiles in X-ray pulsar-based navigation (XNAV). As a basic observation of exact orientation in XNAV, time of arrival (TOA) can be obtained by time delay measurement of integrated pulsar pulse profiles. Therefore, the main purpose of the paper is to establish a method with fast time delay measurement on the condition of limited spacecraft’s computing resources.

Given that the third-order cumulants can suppress the Gaussian noise and reduce calculation to achieve precise and fast positioning in XNAV, the proposed method sets the third-order auto-cumulants of standard pulse profile, the third-order cross-cumulants of the standard and the observed pulse profile as basic variables and uses the cross-correlation function of these two variables to estimate the time delay of integrated pulsar pulse profiles.

The proposed method is simple, fast and has high accuracy in time delay measurement for integrated pulsar pulse profiles. The result shows that compared to the bispectrum algorithm, the method improves the precision of the time delay measurement and reduced the computation time significantly as well.

To improve the performance of time delay estimation in XNAV systems, the authors proposed a novel method for XNAV to achieve precise and fast positioning.

Compared to the bispectrum algorithm, the proposed method can improve the speed and precision of the TOA’s calculation effectively by using the cross-correlation function of integrated pulsar pulse profile’s third-order cumulants instead of Fourier transform in bispectrum algorithm.

The purpose of this paper is to propose an identification method of acquiring aircraft mode characteristics based on fast Fourier transform and half-power bandwidth method, aiming at the common oscillation met in flight test.

The feasibility of this method is demonstrated through derivation; the robustness analysis is conducted through three examples, and finally the method was applied on a set of sideslip angle record from flight test.

The derivation and numerical analysis both show that the presented method can have high accuracy and good robustness under coupled mode and noise condition.

The method proposed is of robustness, and it is concise and easy to apply on flight data record.

This paper demonstrates the feasibility of half power bandwidth to be applied on oscillation mode characteristics identification from flight data record, which is different from other method applied.