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Gas turbines play a vital role in gas transportation and power generation, but they are prone to instability phenomena that can lead to vibrations, shorten equipment lifespan, and result in catastrophic failures. To tackle these challenges, a paper introduces an integrated approach that leverages advanced techniques like Fourier transform, Neuro-Fuzzy systems, and wavelet analysis for continuous monitoring of the MS5002C turbine's condition. The proposed method begins by collecting operational data and utilizing the Fourier transform to measure vibratory quantities, accurately representing their evolution through spectral data obtained from the analyzed signals. Adaptive inference-based algorithms of neuro-fuzzy systems are then employed to generate turbine failure indicators. This approach enables the development of a model-based fault detection method that compares the actual turbine operation with the estimated operation derived from a pre-established model, enabling the classification of detected faults. To enhance decision-making quality, evaluation, and validation of the diagnostic strategy's performance, a multi-resolution analysis based on the wavelet transform is applied. The presented results from various implementation and validation tests demonstrate the effectiveness of this intelligent diagnostic approach in detecting and analyzing gas turbine vibrations. The paper exhibits promising outcomes in real-time monitoring, ensuring the operational safety of the turbine. [ABSTRACT FROM AUTHOR]

Tight wavelet frames are different from the orthonormal wavelets because of redundancy. By sacrificing orthonormality and allowing redundancy, the tight wavelet frames become much easier to construct than the orthonormal wavelets. Guo, Labate, Lim, Weiss, and Wilson [Electron. Res. Announc. Am. Math. Soc. 10 (2004), 78-87] introduced the theory of wavelets with composite dilations in order to provide a framework for the construction of waveforms defined not only at various scales and locations but also at various orientations. In this paper, we provide the characterization of composite wavelet system to be tight frame for L²(Rn). [ABSTRACT FROM AUTHOR]

Most time series from real-world processes are stained with noise. Therefore, much attention should be paid to data noise removal techniques. In this study, we use the family of biorthogonal wavelet, high-pass, and low-pass filters, to investigate the power of the wavelet method in removing noise from time series data. Using the wavelet discrete transformation, the variability of precipitation and sea surface temperature is analyzed for a southern region of the Caspian Sea. At each stage of decomposition, the previous wave is decomposed into two waves. In this research, the SST and precipitation data are decomposed into several levels based on discrete wavelet transformation. In each level of decomposition, the previous wave is decomposed into two waves. This can be done many times and at each stage, reducing the amount of data. This method is reversible, and the original wave can be reconstructed using the decomposed values. In the study of discrete wavelet transforms, it was observed that the analysis based on wavelets leads to more accurate results. The reconstruction error in the proposed method is shown to be very small. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of the dynamic goniometer, the influence of its bearing unit on the measurement error has been studied. The spectral characteristics of the random error of two dynamic goniometers with similar optical angle sensors and different bearings (air and angular contact ball bearings) have been studied. It is shown that the use of a ball bearing in the goniometer leads to nonstationarity of the random error of angular measurements. Using wavelet analysis and the Allan variation, the random error of the dynamic goniometer has been analyzed, the sources of nonstationarity have been identified, and its potential accuracy has been determined. It has been established that the use of an air bearing allows increasing the accuracy of a dynamic goniometer and bringing its value closer to the accuracy of a static goniometer, in which the influence of the bearing unit is minimized. The results obtained are of interest to users and developers of dynamic goniometers. [ABSTRACT FROM AUTHOR]

Issues are brought to light in the optimization of combustion processes of fuel, depending on the spraying capability of rocket and aircraft engine nozzles. Using the example of the flame of a fuel-injection nozzle, the problem of determining the size of droplets of spray of an optically transparent fluid by the IPI method, based on the analysis of interferometric images of the particles, was studied. A method is proposed for analysis of the IPI image of a drop using a continuous wavelet transform. The spatial distribution of wavelet coefficients was used for the introduction of an integrated measurement, analogous to the spectral density of a signal. The reliability of the estimated sizes of droplets was verified from the results of processing glistening images that are obtained by the direct optical GPT method on focused images of droplets. The focused images and interferometric images of droplets are taken simultaneously. The sizes of droplets obtained by the IPI method and processed with the aid of wavelet and Fourier transforms were compared with the data of the GPT method. It was shown that the wavelet transform application substantially reduces the frequency of occurrence of systematic error of the determination of size, which is most characteristic for large droplets. It was established that the false maxima causing systematic error in the Fourier spectrum were caused by the occurrence of distortions on the boundary of the interferometric image of a drop. It was shown that it is possible to remove these distortions from the basic maximum in the neighborhood of the center of a drop by means of wavelet transform. [ABSTRACT FROM AUTHOR]

In real life applications not all signals are obtained by uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool. Gabardo and Nashed, and Gabardo and Yu filled this gap by the concept of nonuniform multiresolution analysis and nonuniform wavelets based on the theory of spectral pairs for which the associated translation set Λ = f0; r=Ng+2 Z is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we introduce a notion of nonuniform periodic wavelet frame on non-Archimedean field. Using the Fourier transform technique and the unitary extension principle, we propose an approach for the construction of nonuniform periodic wavelet frames on non-Archimedean fields. [ABSTRACT FROM AUTHOR]

Data on frequency and time is not simultaneously available in a Fourier transform. Problems with the Fourier transform have led to the emergence of short-window Fourier analysis which itself has several limitations. The main problem with short-time Fourier transform is related to Heisenberg's uncertainty principle. In the wavelet transform, the signal is analyzed on a set of wavelet functions (coherent states). In quantum mechanics, the coherent state is a type of quantum state which has the minimum value of uncertainty. In the present study, the concepts of quantum mechanics such as the uncertainty principle, Dirac's notation and quantum coherent states are used to present a method for obtaining wavelet functions. [ABSTRACT FROM AUTHOR]

In this paper, wavelet analysis of the cavitating flow over a sphere is reported. Unsteady and dynamic behaviors of cavitation were captured using large eddy simulation (LES) turbulence approach and Sauer mass transfer models. Numerical simulation is implemented under the framework of OpenFOAM within the interPhaseChangeFoam solver. The simulation is conducted over a wide range of cavitation numbers. Two more essential variations, pressures and kinetic energies, were considered at specific points in front and behind of the sphere's body for sufficient simulation period. The oscillations global frequency modes and spectral content of the cavity cloud are computed and analyzed using Fourier and continuous wavelet transformations. The computed results show that the flow fluctuations enhance by increasing the cavitation number. The low-frequency fluctuations play a pivotal role in the cavitating flow and possess almost the same magnitude in all investigated cavitation numbers. The frequencies enhance as the simulation time increases in all cases. One of the primary frequencies that happened in all cavitation numbers in the cavity cloud separation is due to a Strouhal number within the range of 0.046 and 0.05. Therefore, this Strouhal number can be used for the purpose of cloud cavitation detection. • LES simulation of cavitating flow around sphere in OpenFOAM. • Providing a thorough understanding of the wavelet analysis around a sphere for the first time. • Reporting the oscillations global frequency modes and spectral content of the sphere cavity cloud. [ABSTRACT FROM AUTHOR]

In the present paper, we discuss about extension of the wavelet transform on distribution space of compact support and develop the Paley–Wiener–Schwartz type theorem for the wavelet transform on the same. Furthermore, Paley–Wiener–Schwartz type theorem for the wavelet transform is also established using the relation between the wavelet transform and double Fourier transform. [ABSTRACT FROM AUTHOR]

The Sobolev space over local fields is defined. A multiresolution analysis for the Sobolev space is developed. Orthonormal wavelets with respect to these space are constructed and an example is also presented. [ABSTRACT FROM AUTHOR]

The aim of this study is providing a comprehensive background information related to the roots of both Fourier Transform (FT) and Wavelet Transform (WT) along with an experiment related to applications of WT techniques. The paper describes several applications of WT and provides background information on FT. Fourier Transform (FT) is a concept that has a long history yet several issues related to resolution and uncertainty of time-frequency. Even though there are several adapted forms of FT such as Short Time Fourier Transform (STFT), which intend to solve the problems, certain limitations remain. Wavelet Transform (WT) is an alternative transformation technique emerged in order to fully tackle these diverse and complicated issues. In this paper, the background information related to the roots of FT and WT are given. Some of the problems that WT addresses are examined. WT is a tool that has many advantages among them is noise reduction and compression. We reviewed several studies that use the noise reduction capability of WT alone or combined with other signal processing tools. Discrete Wavelet Transform (DWT) based algorithm is also examined as a noise reduction technique and carried out in MATLAB setting. Analysis on a speech signal which contaminated with keyboard sound also a number spelling female voice containing unknown noise are performed. Different types of thresholding and mother wavelets were in consideration and it was revealed that Daubechies family along with the soft thresholding technique suited our application the most. [ABSTRACT FROM AUTHOR]

Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307] have derived an explicit method for constructing tight wavelet frames on local fields using the machinery of unitary extension principle. Continuing our investigation of wavelet frames on local fields, this paper deals with the establishment of complete characterization of functions in Lebesgue spaces Lp(K), 1 < p < ∞, in terms of their wavelet frame coefficients. [ABSTRACT FROM AUTHOR]

We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation.We test our algorithm with different numerical experiments. [ABSTRACT FROM AUTHOR]

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in was considered by Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998) 209-241]. In this setting, the associated translation set is a spectrum which is not necessarily a group nor a uniform discrete set, given where (an integer) and is an odd integer with such that and are relatively prime and is the set of all integers. The objective of this paper is to construct nonuniform wavelet frame on local fields. A necessary condition and four sufficient conditions for nonuniform wavelet frame on local fields are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet systems in L 2 ( K ) which include the corresponding results of wavelet analysis and Gabor theory as the special cases. We shall also provide a sufficient condition of the completeness of wave packet systems on local fields of positive characteristic subject to some mild conditions. The paper concludes with the necessary and sufficient conditions for the wave packet systems to be wave packet Parseval frames for L 2 ( K ) . [ABSTRACT FROM AUTHOR]

The main objective of this paper is to establish a set of sufficient conditions for nonuniform wavelet frames on local fields of positive characteristic. The conditions proposed are stated in terms of the Fourier transforms of the wavelet system's generating functions. [ABSTRACT FROM AUTHOR]

Orthonormal M-band wavelets are constructed from the orthonormal M-band scaling function. In this paper, we consider the converse problem and prove that if the M-band wavelets are orthonormal, then the corresponding M-band scaling function is also orthonormal. [ABSTRACT FROM AUTHOR]

The spectral crosstalk from neighboring peaks introduces phase ripple errors in Depth-Resolved Wavenumber-Scanning Interferometry (DRWSI), due to the sidelope of window functions of Fourier Transform (FT). To address such a problem, an algorithm, Scale-Frequency Transform (SFT), is proposed for data evaluation of DRWSI. The simulations show that the sidelope decreases from −12.2 dB to −25.5 dB after using SFT. The experimental results in four-surface interferometry as well as six-surface interferometry demonstrate that SFT can reduce the phase ripple errors effectively without spoiling the depth resolution of DRWSI. Therefore, SFT minimizes the effect of spectral crosstalk. It is practical to replace FT with SFT in DRWSI. [ABSTRACT FROM AUTHOR]

Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307] have derived an explicit method for constructing tight wavelet frames on local fields using the machinery of unitary extension principle. Continuing our investigation of wavelet frames on local fields, this paper deals with the establishment of complete characterization of functions in Lebesgue spaces Lp(K), 1 < p < ∞, in terms of their wavelet frame coefficients. [ABSTRACT FROM AUTHOR]

From a very modest presentation as an introductory composition of wavelets by Chui in 1992 to a very specialist and advanced monographs by Meyer in 1990, and by Daubechies in 1992, one will certainly experience the beauty of this subject, which in the recent time has attracted both the pure and applied mathematicians. Wavelet transform, more correctly called the integral wavelet transform, is one of the two entities of the wavelet analysis. Possibly the window Fourier trans- form, also called the Gabor transform (first introduced by Gabor in 1946), is the initiation for wavelet transform. In this brief note we attempt to discuss some of its aspects. [ABSTRACT FROM AUTHOR]

We construct several families of tight wavelet frames in L 2 ( R 2 ) associated to the quincunx matrix. A couple of those families has five generators. Moreover, we construct a family of tight wavelet frames with three generators. Finally, we show families with only two generators. The generators have compact support, any given degree of regularity, and any fixed number of vanishing moments. Our construction is made in Fourier space and involves some refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. In addition, we will use well known results on construction of tight wavelet frames with two generators on R with the dyadic dilation. The refinable functions we use are constructed from the Daubechies low pass filters and are compactly supported. The main difference between these families is that while the refinable functions associated to the five generators have many symmetries, the refinable functions used in the construction of the others families are merely even. [ABSTRACT FROM AUTHOR]

Periodic wavelet frames have gained considerable popularity in recent years, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. In this article, we introduce the concept of periodic wavelet frame on local fields of positive characteristic and show that under weaker conditions the periodization of any wavelet frame constructed by the unitary extension principle with dilation factor 𝔭−1is a periodic wavelet frame on local fields. Moreover, based on the mixed extension principle and Fourier-based techniques of the wavelet frames, we present an explicit method for a pair of dual periodic wavelet frames on local fields of positive characteristic. [ABSTRACT FROM PUBLISHER]

Orthogonal wavelet packets lack symmetry, which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of Fourier transforms. We also show how to obtain several new Riesz bases of the space L2(K) by constructing a series of subspaces of these wavelet packets. Finally, we provide algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets. [ABSTRACT FROM AUTHOR]

We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual. [ABSTRACT FROM AUTHOR]

A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 풵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 풵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups. [ABSTRACT FROM AUTHOR]

The comparative ability of the Fourier transform (FFT) and discrete wavelet transform (DWT) algorithms in assessing muscle fatigue during sub-maximal repetitive dynamic exertion was investigated in this study. Surface electromyography data recorded from the upper trapezius muscle during forty minutes of repetitive upper extremity exertion performed by 10 male participants were used in the analysis. Multi-model regression analysis was performed to study the trend in the power values of the different frequency bands estimated using the FFT and DWT algorithms. Less variability and higher statistical significance was observed for the power value trend computed using the DWT algorithm compared to the FFT algorithm. The regression models provided a better fit for the power values estimated under more fatigued condition compared to the less fatigued condition. The lower frequency bands of 23–46 Hz and 46–93 Hz exhibited the expected and consistent power trend independent of the algorithm (DWT or FFT) used. For the exertions tested in this study, a cubic or curvilinear model explained the fatigue development process with a higher precision than the linear models. [ABSTRACT FROM AUTHOR]

We present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that the risk measures can be efficiently calculated in terms of accuracy and CPU time. Besides, we provide a theoretical result about the shape of the resulting probability density. This a priori knowledge, allows us to enhance the efficiency and effectiveness of the proposed methods. Finally, we assess the accuracy of the approach in the presence of convexity or concavity properties of the financial portfolios. [ABSTRACT FROM AUTHOR]

The projection method is a simple way of constructing functions and filters by integrating multidimensional functions and filters along parallel superplanes in the space domain. Equivalently expressed in the frequency domain, the projection method constructs a new function by simply taking a cross-section of the Fourier transform of a multidimensional function. The projection method is linked to several areas such as box splines in approximation theory and the projection-slice theorem in image processing. In this paper, we shall systematically study and discuss the projection method in the area of multidimensional framelet and wavelet analysis. We shall see that the projection method not only provides a painless way for constructing new wavelets and framelets but also is a useful analysis tool for studying various optimal properties of multidimensional refinable functions and filters. Using the projection method, we shall explicitly and easily construct a tight framelet filter bank from every box spline filter having at least order one sum rule. As we shall see in this paper, the projection method is particularly suitable to be applied to frequency-based nonhomogeneous framelets and wavelets in any dimensions, and the periodization technique is a special case of the projection method for obtaining periodic wavelets and framelets from wavelets and framelets on Euclidean spaces. [ABSTRACT FROM AUTHOR]

Background Numerous signal processing techniques have been proposed for automated spindle detection on EEG recordings with varying degrees of success. While the latest techniques usually introduce computational complexity and/or vagueness, the conventional techniques attempted in literature have led to poor results. This study presents a spindle detection approach which relies on intuitive pre-processing of the EEG prior to spindle detection, thus resulting in higher accuracy even with standard techniques. New method The pre-processing techniques proposed include applying the derivative operator on the EEG, suppressing the background activity using Empirical Mode Decomposition and shortlisting candidate EEG segments based on eye-movements on the EOG. Results/comparison Results show that standard signal processing tools such as wavelets and Fourier transforms perform much better when coupled with apt pre-processing techniques. The developed algorithm also relies on data-driven thresholds ensuring its adaptability to inter-subject and inter-scorer variability. When tested on sample EEG segments scored by multiple experts, the algorithm identified spindles with average sensitivities of 96.14 and 92.85% and specificities of 87.59 and 84.85% for Fourier transform and wavelets respectively. These results are found to be on par with results obtained by other recent studies in this area. [ABSTRACT FROM AUTHOR]

Abstract: Epilepsy is one of the most common neurological disorders with 0.8% of the world population. The epilepsy is unpredictable and recurrent, so it is very difficult to treat. In this paper, we propose a new Electroencephalography (EEG) seizure detection method by using the dual-tree complex wavelet (DTCWT) – Fourier features. These features achieve perfect classification rates (100%) for the EEG database from the University of Bonn. These classification rates outperform a number of existing EEG seizure detection methods published in the literature. However, it should be mentioned that several recent works also achieved this perfect classification rate (100%). Our proposed method should be as good as these works since our method only performs the DTCWT transform for up to 5 scales and our method only conducts the FFT to the 4th and 5th scales of the DTCWT decomposition. In addition, we could replace the conventional FFT in our method by sparse FFT so that our method could be even faster. [Copyright &y& Elsevier]

We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L²(Rd), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dimensions. Both the refinable functions and the wavelets can be made as smooth as desired. Estimates for the supports of these scaling functions and wavelets, are given. [ABSTRACT FROM AUTHOR]

We establish the Heisenberg-Pauli-Weyl uncertainty inequalities for Fourier transform and the continuous wavelet transform on the Heisenberg group. [ABSTRACT FROM AUTHOR]

Quaternion-valued functions have been used as a model for colour images and have recently been studied using various Fourier-type transforms. We develop some fundamental wavelet theory for quaternionic signals using the Fourier kernel introduced by Brackx, De Schepper, and Sommen in [1]. We present several analogs to classical wavelet theory, such as the quadrature mirror filter condition. We also include necessary design conditions for a wavelet basis to have desired regularity and sufficient design conditions which will guarantee compact support. Due to the difficulty in constructing orthogonal wavelet bases, we present some theory for biorthogonal wavelet bases and construct a few examples. [ABSTRACT FROM AUTHOR]

Abstract: Phase demodulation techniques from one fringe pattern have been widely studied because it can measure dynamic objects by capturing single image. These techniques mainly include Fourier transform (FT), windowed Fourier transform (WFT), and wavelet transform (WT). FT has been widely used to demodulate phase information from single deformed fringe pattern on smooth objects. However, for objects having discontinuities and/or large slopes, FT cannot obtain correct phase at the edges because of its global processing. WFT and WT have been applied to nonstationary fringe pattern analysis. Since local fringe information used to extract phase information, WFT and WT are better than FT for phase calculation at discontinuities and/or slopes. In this paper, we discuss the pro and con of the three methods on phase calculation at discontinuities and/or slopes. Simulated and experimental data are tested at edges in order to confirm which method is appropriate to measure objects having discontinuities by using one-frame fringe pattern acquisition method. [Copyright &y& Elsevier]

Abstract: In recent years more and more long-term broadband data sets are collected in geosciences. Therefore there is an urgent need of algorithms which semi-automatically analyze and decompose these data into components which are associated with different processes. In the past, the standard tools for decomposing data sets were based on either the Fourier or the Wavelet Transform. In this paper we investigate the novel approaches Empirical Mode Decomposition and Sparse Decomposition as well as the Harmonic and Wavelet Decomposition for long-term sea floor pressure data analysis. In a comparative investigation conducted with these tools were applied to real and synthetic sea floor pressure data sets. Our results indicate that none of the methods is entirely suited for this objective, but Sparse Decomposition performs best except for computing efficiency. [Copyright &y& Elsevier]

Abstract: As rock bolts have become one of the main support systems in tunnels and underground structures, the integrity of the rock bolts affects the safety of these types of structures. The purpose of this study is the evaluation of rock bolt integrity using Fourier and wavelet transforms of guided ultrasonic waves. Rock bolt specimens with various defect ratios are embedded into a large scale concrete block in the laboratory and in the rock mass in the field. Guided waves are then generated by a piezo disk element and measured by an acoustic emission sensor. The captured signals are analyzed in the frequency domain using the Fourier transform, and in the time–frequency domain using the wavelet transform based on a Gabor wavelet. The magnitude spectrum obtained from the Fourier transform shows that a portion of high frequency content increases with an increase in the defect ratio. The peak values in the time–frequency domain represent the interval of travel time of each echo. The energy and phase velocities of the guided waves increase with the defect ratio. This study shows that the magnitude spectrum ratio and the energy and phase velocities may be indicators for the evaluation of rock bolt integrity. [Copyright &y& Elsevier]

We investigate two commonly used methods of obtaining the solution of the one-dimensional Hubard model, in the regime of infinite intrasite Coulomb repulsion U, that is the nested Bethe ansatz and the Gutzwiller projection operator approach. These two formalisms give rise to different kinds of the wavefunctions, received via the additional operator and as a general feature, in Gutzwiller and Bethe methods, respectively. We consider the finite system consisting of three particles on a four site closed chain. We investigate the consequences of the dissimilarities in the translational symmetry of the representations of the Hamiltonian for these two approaches. We look for the proof of the decoupling of the spin and charge degrees of freedom, known in context of high-temperature superconductors, in this case. [ABSTRACT FROM AUTHOR]

Abstract: Hyperspectral imagers are built line-by-line similar to images acquired by pushbroom sensors. They can experience striping artifacts due to variations in detector response to incident imagery. In this research, a method for hyperspectral image de-striping based on wavelet analysis and adaptive Fourier zero-frequency amplitude normalization has been developed. The algorithm was tested against three other de-striping algorithms. Hyperspectral image bands of different scenes with significant striping and random noise, as well as an image with simulated noise, were used in the testing. The results were assessed visually and quantitatively using frequency domain Signal-to-Noise Ratio (SNR), Root Mean Square Error (RMSE) and/or Peak Signal-to-Ratio (PSNR). The results demonstrated the superiority of our proposed algorithm in de-striping hyperspectral images without introducing unwanted artifacts, yet preserving image details. In the noise-induced image results, the proposed method reduced RMSE error and improved PSNR by 3.5dB which is better than other tested methods. A Combined method, integrating the proposed algorithm with a generic wavelet-based de-noising algorithm, showed significant random noise suppression in addition to stripe reduction with a PSNR value of 4.3dB. These findings make the algorithm a candidate for practical implementation on remote sensing images including high resolution hyperspectral images contaminated with stripe and random noise. [Copyright &y& Elsevier]

This paper presents the analysis, development, and implementation of a wavelet modulation (WM) technique for three-phase voltage-source (VS) six-pulse inverters. The WM technique is based on sampling three continuous-time (CT) sinusoidal reference modulating signals in a nonuniform recurrent manner using three sets of scale-based linearly combined wavelet basis functions. These CT signals are recovered from their samples by a three-phase VS six-pulse inverter, which is activated by three sets of synthesis scale-based linearly combined wavelet basis functions. Each set of synthesis basis functions is generated for activating one leg of the three-phase inverter in order to recover one CT reference modulating signal. The WM technique is implemented for both simulation and experimental performance testing. The performances of the WM technique are compared with those obtained using the space vector modulation, random pulsewidth modulation, and hysteresis band current control techniques under the same loading conditions. Simulation and experimental test results show that the proposed WM technique is able to switch a three-phase VS six-pulse inverter to produce outputs with significantly improved fundamental components and low harmonic contents. [ABSTRACT FROM PUBLISHER]

Abstract: Fringe pattern analysis in coded structured light constitutes an active field of research. Techniques based on first projecting a sinusoidal pattern and then recovering the phase deviation permit the computation of the phase map and its corresponding depth map, leading to a dense acquisition of the measuring object. Among these techniques, the ones based on time-frequency analysis permit to extract the depth map from a single image, thus having potential applications measuring moving objects. The main techniques are Fourier Transform (FT), Windowed Fourier Transform (WFT) and Wavelet Transform (WT). This paper first analyzes the pros and cons of these three techniques, then a new algorithm for the automatic selection of the window size in WFT is proposed. This algorithm is compared to the traditional WT using adapted mother wavelet signals both with simulated and real objects, showing the performance results for quantitative and qualitative evaluations of the new method. [Copyright &y& Elsevier]

Abstract: Sequency-ordered complex Hadamard transform (SCHT) is a novel discrete orthogonal transform and has been applied to spectrum analysis and image watermarking. In this paper, a novel SCHT based shape descriptors, termed SCHDs, is proposed and applied to image retrieval. SCHDs first expresses the shape boundary as a 1-D complex signal, and SCHT is then applied to it. The resulting transform coefficients are used to characterize the shapes. This description scheme is applied to shape based image retrieval, and the experimental results show that the proposed SCHDs outperforms Fourier descriptors (FDs) and wavelet transform combined with Fourier transform based method (WFDs). [Copyright &y& Elsevier]

Abstract: A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a method of estimation of frequency groups with 200Hz bandwidth in the frequency range from the 50th harmonic up to 9kHz. The method consists of the application of a fast Fourier transform (FFT) for wavelet coefficients after input signal decomposition and partial synthesis for chosen frequency bands. It enables the computational complexity of the algorithm to be reduced and also attenuates influence of the fundamental component and low-frequency harmonics, as required by IEC Standard 61000-4-7. The particulars of this method are shown and analysis for a chosen wavelet family is provided. Further, the algorithm and its implementation in real device for power quality monitoring is presented. Finally, the results of measurements of two testing signals are shown. The required attenuation of fundamental component and required accuracy was obtained. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new approach for the detection and classification of single and combined power quality (PQ) disturbances is proposed using fuzzy logic and a particle swarm optimization (PSO) algorithm. In the proposed method, suitable features of the waveform of the PQ disturbance are first extracted. These features are extracted from parameters derived from the Fourier and wavelet transforms of the signal. Then, the proposed fuzzy system classifies the type of PQ disturbances based on these features. The PSO algorithm is used to accurately determine the membership function parameters for the fuzzy systems. To test the proposed approach, the waveforms of the PQ disturbances were assumed to be in the sampled form. The impulse, interruption, swell, sag, notch, transient, harmonic, and flicker are considered as single disturbances for the voltage signal. In addition, eight possible combinations of single disturbances are considered as the PQ combined types. The capability of the proposed approach to identify these PQ disturbances is also investigated, when white Gaussian noise, with various signal to noise ratio (SNR) values, is added to the waveforms. The simulation results show that the average rate of correct identification is about 96% for different single and combined PQ disturbances under noisy conditions. [ABSTRACT FROM AUTHOR]

Abstract: At present there are many methods that could deal well with frontal view face recognition. However, most of them cannot work well when there is only single example image per person. In order to deal with this problem of single example image per person is stored in the system in the real-world application. In this paper, a comparative study of the AFMT, Fourier-AFMT and Taylor-AFMT are identified for face recognition. And then, we present hybrid Fourier-AFMT framework based face recognition for feature extraction. Firstly, both directionality of edges and intensity facial features are extracted and secondly fuse two kinds of features and classify with correlation coefficient method (CCM). Experiments are implemented on YALE and ORL face databases to demonstrate the efficient of proposed methods. The experimental results show that the average recognition accuracy rates of our proposed fuse multiple feature domains much higher than that of single feature domain. [ABSTRACT FROM AUTHOR]

Abstract: We present a fast algorithm to compute the partial transformation of a function represented in an adaptive pseudo-spectral multi-wavelet representation to a partial Fourier representation. Such fast transformations are useful in many contexts in physics and engineering, where changes of representation from a piece wise polynomial basis to a Fourier basis. The algorithm is demonstrated for a Gaussian in one and in three dimensions. For 2D, we apply this approach to a Gaussian in a periodic domain. The accuracy and the performance of this method is compared with direct summation. [Copyright &y& Elsevier]

To cope with the problem of frequency aliasing in Mallat algorithm, which makes traditional discrete wavelet transform (DWT) inappropriate for feature extraction in some cases, an improved algorithm composed of sub-band reconstruction and Fourier transform is suggested through which the original signal could be split into a series of sub-bands of different frequencies with little distortion both in time and frequency domains. This strategy is developed to extract local features from analytical signals accurately as well as straightforwardly. Some NIR spectra have been selected as examples to demonstrate the availability and application of the proposed method. [ABSTRACT FROM AUTHOR]

An improved method which considers the use of Fourier and wavelet transform based analysis to infer and extract 3D information from an object by fringe projection on it is presented. This method requires a single image which contains a sinusoidal white light fringe pattern projected on it, and this pattern has a known spatial frequency and its information is used to avoid any discontinuities in the fringes with high frequency. Several computer simulations and experiments have been carried out to verify the analysis. The comparison between numerical simulations and experiments has proved the validity of this proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Fracture detection as applied to reservoir characterization is a key step towards modeling of fractured reservoirs. While different methods have been proposed for detection and characterization of fractures and fractured zones, each is associated with certain shortcomings that prevent from their full use in different related engineering application environments. In this paper a new method is proposed for detection of fractured zones and fracture density in which water saturation log data is utilized. For detection of fractures, we have used wavelet transform and properties of wavelets that are highly suitable for detection of changes and local features of data. To choose the optimum mother wavelet, we have used energy matching strategy in which a wavelet with the highest energy match between spectral energy of the signal at the dominant frequency band and the coefficient energy at the same band of wavelet decomposition of the signal is selected. We have used wavelet packet for a more narrow frequency band selection and enhanced results. Decomposing the water saturation data using wavelets showed that the majority of information of the original log is hidden at low frequency bands. As a result, approximated section of wavelet transform of data was used for fracture detection, while shale volume (or gamma ray) log data was used to filter part of the errors in prediction and identification of the uncertain zones. This increased the accuracy of the results by 70%. Finally, a linear relation was derived between energy of approximated section of water saturation log and fracture density, allowing us to estimate the number of fractures in each fractured zone. The method was applied to four wells belonging to one of the Iranian oilfields located in the southwest region of the country and the results are promising. The use of large volume of data and the subsequent analysis increased the generalization ability of the proposed method. [Copyright &y& Elsevier]

Abstract: Fourier transform-based semblance analysis compares two time series on the basis of their phase as a function of frequency. This approach can be extended using wavelets to allow the phase comparison of two datasets to be performed as a function of both time and wavelength. This paper further extends the previous work in two directions; firstly it demonstrates how to display the correlation between multiple (not just two) datasets, and secondly it introduces wavelet-based semblance filtering which allows a pair of datasets to be processed to extract components with any degree of correlation. Matlab source code is available from the IAMG server at www.iamg.org. [Copyright &y& Elsevier]