Showing papers on "Harmonic wavelet transform published in 2018"
TL;DR: The classification performance improved after replacing wavelet entropy (THE AUTHORS), wavelet energy (WN), and discrete wavelet transform (DWT) with the proposed SWE, which is superior to THEY, WN, and DWT.
Abstract: Labeling brain images as healthy or pathological cases is an important procedure for medical diagnosis. Therefore, we proposed a novel image feature, stationary wavelet entropy (SWE), to extract brain image features. Meanwhile, we replaced the feature extraction procedure in state-of-the-art approaches with the proposed SWE. We found the classification performance improved after replacing wavelet entropy (WE), wavelet energy (WN), and discrete wavelet transform (DWT) with the proposed SWE. This proposed SWE is superior to WE, WN, and DWT.
81 citations
01 Jun 2018
TL;DR: This paper proposes a method to obtain approximate graph Fourier transforms that can be applied rapidly and stored efficiently, carried out using a modified version of the famous Jacobi eigenvalues algorithm.
Abstract: The fast Fourier transform is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in $\mathcal {O}(n \log n)$ instead of $\mathcal {O}(n^2)$ arithmetic operations. Graph signal processing is a recent research domain that generalizes classical signal processing tools, such as the Fourier transform, to situations where the signal domain is given by any arbitrary graph instead of a regular grid. Today, there is no method to rapidly apply graph Fourier transforms. In this paper, we propose a method to obtain approximate graph Fourier transforms that can be applied rapidly and stored efficiently. It is based on a greedy approximate diagonalization of the graph Laplacian matrix, carried out using a modified version of the famous Jacobi eigenvalues algorithm. The method is described and analyzed in detail, and then applied to both synthetic and real graphs, showing its potential.
65 citations
TL;DR: The authors propose a method for signal feature extraction based on empirical wavelet transform (EWT) and multiscale entropy and the MSEs of components being highly correlated with the original signals are calculated to construct the eigenvectors of transformer vibration signals.
Abstract: To achieve an effective feature extraction for power transformer vibration signals, the authors propose a method for signal feature extraction based on empirical wavelet transform (EWT) and multiscale entropy (MSE). First, transformer vibration signals are decomposed into several empirical wavelet functions (EWFs) with the method of EWT. Then, the frequency characteristics of signals are demonstrated in the time-frequency representation by applying a Hilbert transform to each EWF component. Finally, in order to quantify the extracted features, the MSEs of components being highly correlated with the original signals are calculated to construct the eigenvectors of transformer vibration signals. Several experiments are presented showing the effectiveness of this method compared with the classic empirical mode decomposition method.
51 citations
TL;DR: A fast algorithm based on the undecimated wavelet packet transform (UWPT) to estimate the amplitude of fundamental and harmonic components of stationary as well as a time-varying power signal.
Abstract: Accurate and fast estimation of time-varying harmonics are essential requirements for online monitoring, analysis, and control of electrical power system. This paper presents a fast algorithm based on the undecimated wavelet packet transform (UWPT) to estimate the amplitude of fundamental and harmonic components of stationary as well as a time-varying power signal. The UWPT uses only one cycle of the fundamental frequency for precise measurement of time-varying harmonics while their amplitude has been determined accurately utilizing the time-invariant property of the UWPT. The robustness and accuracy of the proposed technique have been investigated on synthetic as well as experimental test signals using MATLAB tool. Further, the UWPT algorithm has also been implemented on the Xilinx Virtex-6 FPGA ML-605 board, using XSG/ISE design suite 14.2 and its performance, in terms of hardware accuracy, resource utilization as well as timing requirements have been tested using the experimental test signal.
39 citations
TL;DR: A fused load curve clustering algorithm based on wavelet transform (FCCWT) that fuses two groups of clusters with a subalgorithm named cluster fusion to achieve the optimized clusters and outperforms other comparison methods.
Abstract: The electricity load data recorded by smart meters contain plenty of knowledge that contributes to obtaining load patterns and consumer categories. Generally, the daily load curves are clustered first in order to obtain load patterns of each consumer. However, due to the volume and high dimensions of load curves, existing clustering algorithms are not appropriate in this situation. Thus, a fused load curve clustering algorithm based on wavelet transform (FCCWT) is proposed to solve this problem. The algorithm includes two main phases. First, FCCWT applies multilevel discrete wavelet transform (DWT) to convert the daily load curves for dimensionality reduction. Second, it detects clusters at two outputs of the first phase, and then fuses two groups of clusters with a subalgorithm named cluster fusion to achieve the optimized clusters. FCCWT is implemented on datasets of both China and United States. Their clustering performances are evaluated by diverse validity indices comparing with four typical clustering methods. The experimental results show that FCCWT outperforms other comparison methods. Additionally, case analysis of two datasets are also provided to discuss the significance of load patterns.
35 citations
TL;DR: Extensive MATLAB simulations, laboratory implementation, field data, and EMTP results show that the proposed adaptive method has better static and dynamic performances in comparison to the other approaches.
Abstract: An adaptive wavelet-based method of phasor and frequency estimations and its application for online monitoring, control, and protective equipment are presented in this paper. The method is recursive with a low computational burden, suited for real-time implementations, and does not need any preprocessing stages. It computes the frequency of the analyzing signal accurately during nominal and off-nominal frequency conditions. To reduce computational errors of the phase angle and amplitude estimations that occur during off-nominal frequency conditions, the proposed method adapts itself according to the frequency drift. The proposed recursive adaptive method along with three other approaches based on recursive wavelet transform, discrete Fourier transform (DFT), and recursive DFT is implemented and compared using MATLAB, considering dynamic and static conditions. The methods are also employed for real-time computation of the phasor and frequency of the recorded data of the South West Interconnected System (SWIS) in Western Australia, and their efficiencies are assessed and compared. In addition, a real 33.3 MVA, 132/23.3 kV transformer located in SWIS is modeled in the electromagnetic transients program (EMTP) software, and the recorded signals have been employed for performance evaluation of the above-mentioned methods. The method is also implemented on a computer-based system in the laboratory and its performance is appraised accordingly. Extensive MATLAB simulations, laboratory implementation, field data, and EMTP results show that the proposed adaptive method has better static and dynamic performances in comparison to the other approaches.
25 citations
TL;DR: An ensemble lossless watermarking scheme is proposed by integrating different concepts like redistributed invariant wavelet transform, discrete fractional Fourier transform, singular value decomposition and visual cryptography within the framework of a single algorithm.
Abstract: An ensemble lossless watermarking scheme is proposed in the present study by integrating different concepts like redistributed invariant wavelet transform, discrete fractional Fourier transform, singular value decomposition (SVD) and visual cryptography within the framework of a single algorithm The invariant wavelet transform helps to obtain the transform domain, which is invariant to flipping and rotation of image, this is followed by discrete fractional Fourier transform to obtain the translation invariant domain Finally, embedding positions are selected based on a key and reliable features are extracted by performing SVD on a window centered at these positions Based on these reliable features a binary map is generated through which a master share is created The corresponding ownership share is produced from the master share and the watermark In verification process the same operations of the embedding process are applied to the test image to obtain the master share and the watermark is recovered by stacking it over the ownership share There are two main features of the proposed scheme (1) The quality of the image to be watermarked do not degrade during the process and (2) the extracted watermark can still be identified even from a seriously distorted image These findings are also demonstrated with the help of a comparative study with several related schemes
23 citations
01 Jan 2018
TL;DR: In this chapter, fast algorithms for the computation of the DFT for d-variate nonequispaced data are described, since in a variety of applications the restriction to equispacedData is a serious drawback.
Abstract: In this chapter, we describe fast algorithms for the computation of the DFT for d-variate nonequispaced data, since in a variety of applications the restriction to equispaced data is a serious drawback. These algorithms are called nonequispaced fast Fourier transforms and abbreviated by NFFT.
21 citations
TL;DR: Shapiro's dispersion and Umbrella theorems for the continuous Hankel wavelet transform were proved in this paper, and local uncertainty principles for set of finite measure were extended to the latter transform.
Abstract: Shapiro’s dispersion and Umbrella theorems are proved for the continuous Hankel wavelet transform. As a side results, we extend local uncertainty principles for set of finite measure to the latter transform.
19 citations
TL;DR: A novel statistical model for the wavelet transform of the acceleration response of a structure based on Gaussian process theory with applications to earthquake damage detection and results of the application and implementation methodology are presented.
17 citations
TL;DR: This work studies the features of the gyrator wavelet transform, which can find a role in different applications such as edge enhancement, image encryption, image hiding, and watermarking.
Abstract: The gyrator transform is a linear canonical transform, which generates the rotation of an optical signal in position-spatial frequency planes. Gyrator wavelet transform is a relatively newer optical information processing tool obtained by combining the gyrator transform with the wavelet transform. This combination provides multi-resolution analysis of an image which is twisted in spatial frequency planes. The proposed tool satisfies basic algebraic properties, such as the linearity property and Parseval's theorem. Considering the usefulness of this tool, here a study of features, applications, and implementation of the gyrator wavelet transform is presented. This work studies the features of the gyrator wavelet transform, which can find a role in different applications such as edge enhancement, image encryption, image hiding, and watermarking.
TL;DR: A novel method for parameter estimation of Newton’s rings is proposed based on concise fractional Fourier transform (CFRFT) and evaporation rate based water cycle algorithm (ER-WCA), and a pretreatment technology is further proposed to solve uneven illumination of actual Newton's rings.
TL;DR: In this paper, the adaptive harmonic wavelet transform (AHWT) is used for feature extraction in the time-frequency domain, which can identify the critical features in Lamb wave signals to realize effective and robust decision making in structural damage detection.
TL;DR: A theory for generalized shift-invariant and sampling spaces associated with the fractional Fourier transform is developed and the numerical results validate the theoretical derivations.
TL;DR: The results of experiments show that the proposed fast algorithm and the proposed transform can significantly accelerate the full-search-equivalent pattern matching process and outperform state-of-the-art methods.
Abstract: Pattern matching is widely used in signal processing, computer vision, and image and video processing. One efficient approach is to perform pattern matching in a transform domain that has good energy packing ability and so allows early rejection of most mismatched candidates. Calculating the transforms of pixels in sliding windows requires much computation, and so fast algorithms are employed. Existing methods require $O(u)$ additions per pixel for projecting input pixels onto $u~2\text{D}$ basis vectors. In this paper, we propose a new 2D transform, called asymmetric 2D Haar transform, and extend it to wavelet packets that contain exponentially large number of bases. A basis selection algorithm is then proposed to search for the optimal basis in the wavelet packets. A fast algorithm is also developed, which can compute $u$ projection coefficients with only $O(\log u)$ additions per pixel. The results of experiments show that the proposed fast algorithm and the proposed transform can significantly accelerate the full-search-equivalent pattern matching process and outperform state-of-the-art methods.
TL;DR: The proposed adaptive harmonic window function is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise, and the satisfactory results show that the adaptive harmonicwindow function can be successfully applied to the actual engineering signal processing.
Abstract: The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise. The relationship between windowing transform and filtering is analyzed first in the paper. The advantage of adjustable time-frequency window of wavelet transform is introduced. Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed. The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed, and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded. Thirdly, by extending the harmonic wavelet transform, the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper. Then comparing with the Hanning window, the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown, and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented. Finally, the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise, and the satisfactory results are achieved. The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.
TL;DR: A nonsubsampled compactly supported shearlet transform (NSCSST) is introduced, which possesses multi-scale, multi-direction, translation invariance and spatial localization characteristics that are very important for image fusion in transform domain.
Abstract: Multi-focus image fusion, which aims to combine multi-focus images of a scene to construct an all-in-focus image, has become a major topic in image processing. Different methods have been proposed in spatial or transform domain. But many methods usually suffer from fusion quality degradations, such as contrast reduction, artificial edges, and discontinuous phenomena at boundaries of focused regions, which may cause issues when going for further processing. In order to overcome these problems, we introduce a nonsubsampled compactly supported shearlet transform (NSCSST), which possesses multi-scale, multi-direction, translation invariance and spatial localization characteristics that are very important for image fusion in transform domain. The transform can be implemented sequentially by the shear transform and the separable anisotropic nonsubsampled wavelet transform (SANSWT). Furthermore, we propose a new image fusion method based on NSCSST. It consists of two aspects: multi-direction fusion and transform domain fusion, which respectively correspond to the shear transform and the SANSWT of NSCSST. For each sheared image pair, the SANSWT coefficients are firstly fused by the transform domain fusion rules. And then, the final fused image is obtained by the multi-direction fusion rules, ranging from the simple averaging method to the proposed complex genetic algorithm based method. Experimental results show that our method outperforms some other methods, such as the method based on bilateral gradient, the method based on nonsubsampled contourlet transform, the method based on simultaneous empirical wavelet transform, and the method based on guided filtering.
TL;DR: The algorithm of SFT (sparse Fourier transform) is firstly used for monochromatic light spectrum reconstruction and two methods of the modern spectrum estimation, AR (Auto-Regressive) model and MUSIC (Multiple Signal Classification) are considered as high resolution spectrum estimation algorithms.
TL;DR: In this article, Dhaouadi et al. defined and studied the q-wavelet and the continuous qwavelet transform associated with this harmonic analysis and established some results (Plancherel's formula, inversion formula, etc.).
Abstract: In this paper, we present some new elements of harmonic analysis related to the q-Bessel Fourier transform introduced earlier in Dhaouadi (Bull Math Anal Appl 5(2):42–60, 2013), Dhaouadi et al. (J Inequal Pure Appl Math 7(5):171, 2006), we define and study the q-wavelet and the continuous q-wavelet transform associated with this harmonic analysis. Thus, some results (Plancherel’s formula, inversion formula, etc.) are established. Next, we prove a Calderon’s formula and an analogue of Heisenberg’s inequality for the continuous q-wavelet transform.
TL;DR: In this article, the impulse wavelet transform was applied to composite plate to detect damages and a lifting scheme method was used to optimize the wavelet function with respect to the characteristics of the signal.
Abstract: Damage detection using the wavelet transform was investigated and appropriate approaches to raising the method’s sensitivity level were proposed. In addition, the current study attempted to implement the impulse wavelet design algorithm in order to present appropriate wavelet function with respect to the characteristics of the signal. The initial wavelet function corresponding to the impulse response of composite plate was achieved using impulse wavelet algorithm in time domain. The function was optimized using lifting scheme method. To detect damages, an appropriate signal was selected through applying wavelet transform. To enhance damage identification, first, the edges’ effect of wavelet transform was removed, then a higher accuracy was observed by summing the wavelet coefficients in all scale factors for each mode shape and the wavelet coefficients for all mode shapes. The article also presents a quantitative measure to compare different wavelets.
TL;DR: In this paper, the authors considered the quaternionic unitary representation of a locally compact group and established a continuous wavelet transform by means of a special case of such representations.
Abstract: In this paper we consider the new concept of the quaternionic unitary representation of a locally compact group to the unitary group of a quaternionic Hilbert space, and study its properties. Also, we establish a continuous wavelet transform by means of a special case of such representations to extend the continuous wavelet transform related to semidirect product groups. The results may be useful in development of wavelet theory.
01 Jan 2018
TL;DR: A novel two dimensional (2D) Fast Fourier Transform technique for efficient reconstruction of a 2D image and Radix-\(4^n\) technique used here provides significant savings in memory required in the intermediate stages and considerable improvement in latency.
Abstract: Reconstruction of a signal from its subset is used in various contexts in the field of signal processing. Image reconstruction is one such example which finds widespread application in face recognition, medical imaging, computer vision etc. Image reconstruction is computationally complex, and efficient implementations need to exploit the parallelism inherent in this operation. Discrete Fourier Transform (DFT) is a widely used technique for image reconstruction. Fast Fourier Transform (FFT) algorithms are used to compute DFTs efficiently. In this paper we propose a novel two dimensional (2D) Fast Fourier Transform technique for efficient reconstruction of a 2D image. The algorithm first applies 1D FFT based on radix-\(4^n\) along the rows of the image followed by same FFT operation along columns, to obtain a 2D FFT. Radix-\(4^n\) technique used here provides significant savings in memory required in the intermediate stages and considerable improvement in latency. The proposed FFT algorithm can be easily extended to three dimensional and higher dimensional FFTs. Simulated results for image reconstruction based on this technique are presented in the paper. 64 point FFT based on radix-\(4^3\) has been implemented using 130nm CMOS technology and operates at a maximum clock frequency of 350 MHz.
TL;DR: Medina, Juan Miguel, and Calderon as discussed by the authors have published a paper entitled "Cientificas Cientifica y Tecnicas: A Review of the Nacional Institute of Matematica of Argentina".
Abstract: Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Saavedra 15. Instituto Argentino de Matematica Alberto Calderon; Argentina
01 Jan 2018
TL;DR: A new watermarking technique is composed of the finite ridgelet transform, discrete wavelet transform (DWT), and singular value decomposition (SVD) and the security of the watermark information is provided using the Arnold scrambling technique.
Abstract: In this chapter, existing watermarking techniques for the speech signal and its various features are described. A new watermarking technique is composed of the finite ridgelet transform (FRT), discrete wavelet transform (DWT), and singular value decomposition (SVD). The security of the watermark information is provided using the Arnold scrambling technique. The encrypted watermark information is inserted into hybrid coefficients (singular values of approximation wavelet coefficients of ridgelet coefficients) of the speech signal using an additive watermarking approach. This technique is used for copyright protection of the speech signal over a communication channel.
TL;DR: In this paper, a new family of wavelets derived from the underdamped response of second-order linear-time-invariant (LTI) systems is introduced.
Abstract: In this paper, a new family of wavelets derived from the underdamped response of second-order Linear-Time-Invariant (LTI) systems is introduced. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. We show that it is possible to recover back the original signal once the Second-Order Underdamped LTI (SOULTI) wavelet is applied to decompose the signal. It is found that the SOULTI wavelet transform of a signal satisfies a linear differential equation called the reconstructing differential equation, which is closely related to the differential equation that produces the wavelet. Moreover, a time-frequency resolution is defined based on two different approaches. The new transform has useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signa...
TL;DR: By application of denoising BER, the performance is further improved in shift invariant ADCHWT OFDM compared to its earlier version Discrete Cosine Harmonic Wavelet Transform (DCHWT) and its peak to average power ratio (PAPR) performance is improved over those of DFT OFDM and Haar WTOFDM.
Abstract: The present wireless implementation needs efficient modulation methods and signal processing at physical layer to enhance system performance. Orthogonal Frequency Division Multiplexing (OFDM) is one such modulation and multiplexing method preferred for such implementation. OFDM implementation using harmonic wavelets has better performance and implementation simplicity. In this paper denoising is applied to Analytic Discrete Cosine Harmonic Wavelet Transform OFDM (ADCHWT OFDM) which is implemented in harmonic wavelet domain. An ADCHWT is simple and shift invariant as it does not involve explicit decimation, interpolation and associated filtering and delay compensation. The reduced leakage and computational simplicity offered by ADCHWT provide an interesting opportunity to explore its application for OFDM system. By application of denoising BER, the performance is further improved in shift invariant ADCHWT OFDM compared to its earlier version Discrete Cosine Harmonic Wavelet Transform (DCHWT OFDM). Further its peak to average power ratio (PAPR) performance is also improved over those of DFT OFDM and Haar WTOFDM.
01 Oct 2018
TL;DR: Improvement of transfer entropy was applied to the analysis of synchronous EEG and EMG signal to evaluate the performance of cortical muscle coupling and significant area curves showed the corresponding strength of cortex muscle coupling.
Abstract: Synchronous analysis of Electroencephalogram (EEG) and Electromyography (EMG) signals can reflect the information transport function of the motor nerve. Symbol phase transfer entropy was a further improvement of transfer entropy. It was applied to the analysis of synchronous EEG and EMG signal to evaluate the performance of cortical muscle coupling. The EEG/EMG signals recorded synchronously at different muscle strength were decomposed into uniform narrow band oscillations using harmonic wavelet transform. The corresponding SPTEs of EEG and EMG narrow band oscillations were calculated and summed, and the significant areas were obtained. By moving the analysis window, time varying significant areas were obtained and significant area curves showed the corresponding strength of cortical muscle coupling.
01 Jan 2018
TL;DR: The Fourier transform has arguably had the most significant impact over the course of the 20th century as discussed by the authors, and it is the most widely used numerical method in the world today.
Abstract: Of all the numerical methods we have seen so far, the Fourier transform has arguably had the most significant impact over the course of the 20th century.
TL;DR: This work proposes a simple transform based on extrema points of the signal that can be applied to noise-corrupted synthetic signals and to sleep studies detecting delta wave in brain EEG signal.
Abstract: Signal transforms are very important tools to extract useful information from scientific, engineering, or medical raw data. Unfortunately, traditional transform techniques impose unrealistic assumptions on the signal, often producing erroneous interpretation of results. Well-known integral transforms, such as short-time Fourier transform, though have fast implementation algorithms (e.g., FFT), are still computationally expensive. They have multiple parameters that should be tuned, and it is not readily clear how to tune them for long-duration non-stationary signals. To solve these problems, one needs a computationally inexpensive transform with no parameters that will highlight important data aspects. We propose a simple transform based on extrema points of the signal. The transform value at a given point is calculated based on the distance and magnitude difference of two extrema points it lies between, rather than considering every point around it. We discuss implementation of the developed algorithm and show examples of successfully applying the transform to noise-corrupted synthetic signals and to sleep studies detecting delta wave in brain EEG signal. Ideas for improvement and further research are discussed.
TL;DR: In this article, a pipelined architecture was proposed to statically scale the resolution of the processor to suite adequate trade-off constraints, and the proposed FFT makes use of programmable fixed-point/floating-point to realize higher precision FFT.
Abstract: The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application However, the high-performance DSP processor is the important method of electrical harmonic analysis Hence, in this research work, the effort was taken to design a novel high-resolution single 1024-point fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) processors for improvement of the harmonic measurement techniques Meanwhile, the project is started with design and simulation to demonstrate the benefit that is achieved by the proposed 1024-point FFT/IFFT processor The pipelined structure is incorporated in order to enhance the system efficiency As such, a pipelined architecture was proposed to statically scale the resolution of the processor to suite adequate trade-off constraints The proposed FFT makes use of programmable fixed-point/floating-point to realize higher precision FFT