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Article
Publication date: 1 June 2004

Martin Zwick

Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type…

Abstract

Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also readily implemented. Fourier methods may thus enhance the power of RA for data analysis and data mining.

Details

Kybernetes, vol. 33 no. 5/6
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 August 2004

C.Y. Xiong, J. Zhang, M. Li, J. Fang and S. Yi

In this paper, two transform methods, the Fourier transform (FT) and the wavelet transform (WT) methods, are utilized to process moiré fringes for the strain analysis of…

Abstract

In this paper, two transform methods, the Fourier transform (FT) and the wavelet transform (WT) methods, are utilized to process moiré fringes for the strain analysis of electronic packaging. With the introduction of fringe carriers, those transform techniques need only one fringe pattern for each deformation state. The strain modulation to the carrier frequency can be subtracted by filtering as the pattern is transformed into spectrum domain by the fast‐FT processing, and the deformation field can thus be restored by the inverse FT transform after spectral shifting. The WT method expands the pattern information involved in the fringe carrier in both spatial domain and spectral domain to analyze the deformation distribution in this combined space. By changing the transform scales in the processing, the wavelet transform offers multi‐resolution analysis for the deformation field with high gradients.

Details

Microelectronics International, vol. 21 no. 2
Type: Research Article
ISSN: 1356-5362

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Article
Publication date: 1 February 1973

K.G. BEAUCHAMP

An introduction is given to the generation and use of new transform techniques which have important applications in binary control and processing methods. A comparison is…

Abstract

An introduction is given to the generation and use of new transform techniques which have important applications in binary control and processing methods. A comparison is made between the fast Fourier transform and the equivalent fast Walsh transform together with the steps required to produce a transform algorithm and computer program. Some applications of the transform are then discussed and which include spectral analysis, filtering, non‐linear control and communications uses. 18 references to current work in these applications areas are included.

Details

Kybernetes, vol. 2 no. 2
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 13 November 2017

Jianhua Cai

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.

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

Industrial Lubrication and Tribology, vol. 69 no. 6
Type: Research Article
ISSN: 0036-8792

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Article
Publication date: 24 November 2020

Qi Xiao, Rui Wang, Hongyu Sun and Limin Wang

The paper aims to build a new objective evaluation method of fabric pilling by combining an integrated image analysis technology with a deep learning algorithm.

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Abstract

Purpose

The paper aims to build a new objective evaluation method of fabric pilling by combining an integrated image analysis technology with a deep learning algorithm.

Design/methodology/approach

Series of image analysis techniques were adopted. First, a Fourier transform transformed images into the frequency domain. The optimal resolution matrix of an exponential high-pass filter was determined by combining the energy algorithm. Second, the multidimensional discrete wavelet transform determined the optimal division level. Third, the iterative threshold method was used to enhance images to obtain a complete and clear pilling ball images. Finally, the deep learning algorithm was adopted to train data from pilling ball images, and the pilling levels were classified according to the learning features.

Findings

The paper provides a new insight about how to objectively evaluate fabric pilling grades. Results of the experiment indicate that the proposed objective evaluation method can obtain clear and complete pilling information and the classification accuracy rate of the deep learning algorithm is 94.2%, whose structures are rectified linear unit (ReLU) activation function, four hidden layers, cross-entropy learning rules and the regularization method.

Research limitations/implications

Because the methodology of the paper is based on woven fabric, the research study’s results may lack generalizability. Therefore, researchers are encouraged to test other kinds of fabric further, such as knitted and unwoven fabrics.

Originality/value

Combined with a series of image analysis technology, the integrated method can effectively extract clear and complete pilling information from pilled fabrics. Pilling grades can be classified by the deep learning algorithm with learning pilling information.

Details

International Journal of Clothing Science and Technology, vol. 33 no. 4
Type: Research Article
ISSN: 0955-6222

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Article
Publication date: 16 September 2013

Vincent Monchiet and Guy Bonnet

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 8 August 2016

Vladimir Kobelev

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite…

Abstract

Purpose

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.

Design/methodology/approach

The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.

Findings

The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.

Research limitations/implications

Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.

Practical implications

The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.

Originality/value

The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 19 June 2017

Bo Sun, Yadan Zeng, Houde Dai, Junhao Xiao and Jianwei Zhang

This paper aims to present the spherical entropy image (SEI), a novel global descriptor for the scan registration of three-dimensional (3D) point clouds. This paper also…

Abstract

Purpose

This paper aims to present the spherical entropy image (SEI), a novel global descriptor for the scan registration of three-dimensional (3D) point clouds. This paper also introduces a global feature-less scan registration strategy based on SEI. It is advantageous for 3D data processing in the scenarios such as mobile robotics and reverse engineering.

Design/methodology/approach

The descriptor works through representing the scan by a spherical function named SEI, whose properties allow to decompose the six-dimensional transformation into 3D rotation and 3D translation. The 3D rotation is estimated by the generalized convolution theorem based on the spherical Fourier transform of SEI. Then, the translation recovery is determined by phase only matched filtering.

Findings

No explicit features and planar segments should be contained in the input data of the method. The experimental results illustrate the parameter independence, high reliability and efficiency of the novel algorithm in registration of feature-less scans.

Originality/value

A novel global descriptor (SEI) for the scan registration of 3D point clouds is presented. It inherits both descriptive power of signature-based methods and robustness of histogram-based methods. A high reliability and efficiency registration method of scans based on SEI is also demonstrated.

Details

Industrial Robot: An International Journal, vol. 44 no. 4
Type: Research Article
ISSN: 0143-991X

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Article
Publication date: 2 October 2017

S. Saha Ray

The purpose of this paper is to consider the time-splitting Fourier spectral (TSFS) method to solve the fractional coupled Klein–Gordon–Schrödinger (K-G-S) equations. A…

Abstract

Purpose

The purpose of this paper is to consider the time-splitting Fourier spectral (TSFS) method to solve the fractional coupled Klein–Gordon–Schrödinger (K-G-S) equations. A time-splitting spectral approach is applied for discretizing the Schrödinger-like equation and along with that, a pseudospectral discretization has been accurately utilized for the temporal derivatives in the Klein–Gordon-like equation. Furthermore, the time-splitting scheme is proved to be unconditionally stable. Numerical experiments guarantee high accuracy of the TSFS scheme for the K-G-S equations. Here, the derivative of fractional order is taken in the Riesz sense.

Design/methodology/approach

The focus of this paper is to study the Riesz fractional coupled K-G-S equations using the TSFS method. This method is dependent on evaluating the solution to the given problem in small steps, and treating the nonlinear and linear steps separately. The nonlinear step is made in the time domain, while the linear step is made in the frequency domain, which necessitates the use of Fourier transform back and forth. It is a very effective, powerful and efficient method to solve the nonlinear differential equations, as in previous works (Bao et al., 2002; Bao and Yang, 2007; Muslu and Erbay, 2003; Borluk et al., 2007), the initial and boundary-value problem is decomposed into linear and nonlinear subproblems. Summarizing the technique of the TSFS method, it can be stated that first the Schrödinger-like equation is solved in two splitting steps. Then, the Klein–Gordon-like equation is solved by discretizing the spatial derivatives by means of the pseudospectral method.

Findings

The utilized method is found to be very efficient and accurate. Moreover, the time-splitting spectral scheme is found to be unconditionally stable. By means of thorough study, it is found that the spectral method is time-reversible, is gauge-invariant and also conserves the total charge. Moreover, the results have been graphically presented to exhibit the accuracy of the proposed methods. Apart from that, the numerical solutions have been also compared with the exact solutions. Numerical experiments establish that the proposed technique manifests high accuracy and efficiency.

Originality/value

To the authors’ best knowledge, the Riesz fractional coupled K-G-S equations have been for the first time solved by using the TSFS method.

Details

Engineering Computations, vol. 34 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 16 July 2021

Dure Jabeen, S.M. Ghazanfar Monir, Shaheena Noor, Muhammad Rafiullah and Munsif Ali Jatoi

Watermarking technique is one of the significant methods in which carrier signal hides digital information in the form of watermark to prevent the authenticity of the…

Abstract

Purpose

Watermarking technique is one of the significant methods in which carrier signal hides digital information in the form of watermark to prevent the authenticity of the stakeholders by manipulating different coefficients as watermark in time and frequency domain to sustain trade-off in performance parameters. One challenging component among others is to maintain the robustness, to limit perceptibility with embedding information. Transform domain is more popular to achieve the required results in color image watermarking. Variants of complex Hadamard transform (CHT) have been applied for gray image watermarking, and it has been proved that it has better performance than other orthogonal transforms. This paper is aimed at analyzing the performance of spatio-chromatic complex Hadamard transform (Sp-CHT) that is proposed as an application of color image watermarking in sequency domain (SD).

Design/methodology/approach

In this paper, color image watermarking technique is designed and implemented in SD using spatio-chromatic – conjugate symmetric sequency – ordered CHT. The color of a pixel is represented as complex number a*+jb*, where a* and b* are chromatic components of International Commission on Illumination (CIE) La*b* color space. The embedded watermark is almost transparent to human eye although robust against common signal processing attacks.

Findings

Based on the results, bit error rate (BER) and peak signal to noise ratio are measured and discussed in comparison of CIE La*b* and hue, saturation and value color model with spatio-chromatic discrete Fourier transform (Sp-DFT), and results are also analyzed with other discrete orthogonal transforms. It is observed from BER that Sp-CHT has 8%–12% better performance than Sp-DFT. Structural similarity index has been measured at different watermark strength and it is observed that presented transform performs better than other transforms.

Originality/value

This work presents the details and comparative analysis of two orthogonal transforms as color image watermarking application using MATLAB software. A finding from this study demonstrates that the Complex Hadamard transform is the competent candidate that can be replaced with DFT in many signal processing applications.

Details

World Journal of Engineering, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1708-5284

Keywords

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