Showing papers on "Harmonic wavelet transform published in 2017"

A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models

Abstract: This chapter aims to incorporate the wavelet transform and auditory nerve-based models into a tool that could be used for speaker identification, in the hope that the results would be more robust to noise than the standard methods. It utilizes the continuous wavelet transform to extract reliably the different components of the modulation model and the parameters characterizing them. The chapter shows that results of a first test of the use of the synchro-squeezed representation for speaker identification. It also shows that some results: the “untreated” wavelet transform of a speech segment, its squeezed and synchrosqueezed versions, and the extraction of the parameters used for speaker identification. The whole construction is based on a continuous wavelet transform. In practice, this is of course a discrete but very redundant transform, heavily oversampled both in time and in scale. The chapter concludes with some pointers to and comparisons with similar work in the literature, and with sketching possible future directions.

Forensics feature analysis in quaternion wavelet domain for distinguishing photographic images and computer graphics

Abstract: In this paper, a novel set of features based on Quaternion Wavelet Transform (QWT) is proposed for digital image forensics. Compared with Discrete Wavelet Transform (DWT) and Contourlet Wavelet Transform (CWT), QWT produces the parameters, i.e., one magnitude and three angles, which provide more valuable information to distinguish photographic (PG) images and computer generated (CG) images. Some theoretical analysis are done and comparative experiments are made. The corresponding results show that the proposed scheme achieves 18 percents’ improvements on the detection accuracy than Farid’s scheme and 12 percents than Ozparlak’s scheme. It may be the first time to introduce QWT to image forensics, but the improvements are encouraging.

Fourier Phase Retrieval: Uniqueness and Algorithms

Abstract: The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science Fourier phase retrieval poses fundamental theoretical and algorithmic challenges In general, there is no unique mapping between a one-dimensional signal and its Fourier magnitude, and therefore the problem is ill-posed Additionally, while almost all multidimensional signals are uniquely mapped to their Fourier magnitude, the performance of existing algorithms is generally not well-understood In this chapter we survey methods to guarantee uniqueness in Fourier phase retrieval We then present different algorithmic approaches to retrieve the signal in practice We conclude by outlining some of the main open questions in this field

Short-Frequency Fourier Transform for Fault Diagnosis of Induction Machines Working in Transient Regime

Abstract: Transient-based methods for fault diagnosis of induction machines (IMs) are attracting a rising interest, due to their reliability and ability to adapt to a wide range of IM’s working conditions. These methods compute the time–frequency (TF) distribution of the stator current, where the patterns of the related fault components can be detected. A significant amount of recent proposals in this field have focused on improving the resolution of the TF distributions, allowing a better discrimination and identification of fault harmonic components. Nevertheless, as the resolution improves, computational requirements (power computing and memory) greatly increase, restricting its implementation in low-cost devices for performing on-line fault diagnosis. To address these drawbacks, in this paper, the use of the short-frequency Fourier transform (SFFT) for fault diagnosis of induction machines working under transient regimes is proposed. The SFFT not only keeps the resolution of traditional techniques, such as the short-time Fourier transform, but also achieves a drastic reduction of computing time and memory resources, making this proposal suitable for on-line fault diagnosis. This method is theoretically introduced and experimentally validated using a laboratory test bench.

A Novel Decision Tree Regression-Based Fault Distance Estimation Scheme for Transmission Lines

Abstract: In this paper, a decision tree regression (DTR)-based fault distance estimation scheme for double-circuit transmission lines is presented. Fault location is estimated using the information obtained from fault events data. The DTR was chosen because it requires less training time, offers greater accuracy with a large data set, and robustness than all other techniques like artificial neural networks, support vector machines, adaptive neurofuzzy inference systems, etc. Hitherto, DT has been used for fault detection/classification, but it has not been used for fault location. Three-phase current and voltage signals measured at one end of the line are used as inputs to a fault-location network. The proposed method does not require a communication link as it uses only one-end measurements. Signals are processed with two signal-processing techniques-discrete Fourier transforms and discrete wavelet transform. A comparative study of both techniques has been carried out to observe the effect of signal processing on the fault-location estimation method. The proposed method is tested on three test systems, namely: 1) the 2-bus; 2) the WSCC-9-bus; and 3) the IEEE 14-bus test systems. The test results confirm that the proposed DTR-based algorithm is not affected by the variation in fault type, fault location, fault inception angle, fault resistance, prefault load angle, SCC, load variation, and line parameters. The proposed scheme is relatively simple and easy in comparison with complex equation-based fault-location estimation methods.

Early detection of tooth crack damage in gearbox using empirical wavelet transform combined by Hilbert transform

Abstract: Hilbert-Huang Transform (HHT) has been renowned for its capacity to reveal fault indicating information issue from vibration signals. It uses Empirical Mode Decomposition (EMD) to decompose a signal accordingly to its contained information into a set of Intrinsic Mode Functions (IMFs). Then, the instantaneous frequencies are performed of each IMF using Hilbert Transform (HT). However, the HHT has some disadvantages which are caused by the EMD technique. The EMD has the mode mixing problem that may occur between IMFs, it causes the End Effect phenomenon, which leads to a wrong instantaneous values at both sides of the signal. Furthermore, its lack of mathematical basis. To overcome the HHT inherent problems, we propose the use of the Empirical Wavelet Transform (EWT) which designs an appropriate wavelet filter bank fully depends on the processed signal with HT in the early detection and condition monitoring of tooth crack fault. In this paper, we develop a dynamic model describing a single stage spur gear ...

Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications

Abstract: Least-squares spectral analysis, an alternative to the classical Fourier transform, is a method of analyzing unequally spaced and non-stationary time series in their first and second statistical moments. However, when a time series has components with low or high amplitude and frequency variability over time, it is not appropriate to use either the least-squares spectral analysis or Fourier transform. On the other hand, the classical short-time Fourier transform and the continuous wavelet transform do not consider the covariance matrix associated with a time series nor do they consider trends or datum shifts. Moreover, they are not defined for unequally spaced time series. A new method of analyzing time series, namely, the least-squares wavelet analysis is introduced, which is a natural extension of the least-squares spectral analysis. This method decomposes a time series to the time–frequency domain and obtains its spectrogram. In addition, the probability distribution function of the spectrogram is derived that identifies statistically significant peaks. The least-squares wavelet analysis can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability, including datum shifts, trends, and constituents of known forms, by taking into account the covariance matrix associated with the time series. The outstanding performance of the proposed method on synthetic time series and a very long baseline interferometry series is demonstrated, and the results are compared with the weighted wavelet Z-transform.

Application of signal analysis for diagnostics

Abstract: Signals are usually described in two domains: time and frequency. The Fourier transform is used for signal transformation from time domain to frequency domain and vice versa and that is enough to analyse the stationary signal. If a signal is non-stationary, the Fourier transform can be utilized to determine frequencies in signal but it can't be applied to determine the moment when a particular signal exists. For the analysis of non-stationary signals the wavelet transform can be used as well as a continuous or discrete wavelet transform. If the signal has a large number of samples, a discrete wavelet transform should be applicable preferably. If the signal is a discrete dynamic series, fast algorithms of discrete wavelet transforms can be used. The article presents 4 types of wavelets that can be applied to carry out fast discrete wavelet transforms. Based on the performed calculations the most appropriate wavelet is chosen.

The Wavelet Transforms

Abstract: Historically, the concept of wavelets started to appear more frequently only in the early 1980s. This new concept can be viewed as a synthesis of various ideas originating from different disciplines including mathematics, physics, and engineering. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean Morlet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. Wavelet transforms are relatively recent developments that have fascinated the scientific, engineering, and mathematics community with their versatile applicability. The application areas for wavelets have been growing for the last 20 years at a very rapid rate. They have been applied in a number of fields including signal and image processing, sampling theory, turbulence, differential equations, statistics, quality control, computer graphics, economics and finance, medicine, neural networks, geophysics, astrophysics, quantum mechanics, neuroscience, and chemistry. For more information about the history and applications of wavelet transforms, the reader is referred to Daubechies (1992), Chui (l992), Meyer (1993a,b), Kaiser (1994), Cohen (1995), Hubbard (1996), Strang and Nguyen (1996), Burrus et al. (1997), Wojtaszczyk (1997), Debnath (1998a,b,c), Mallat (1998), Pinsky (2001), Ali et al. (2015), Gomes and Velho (2015), and Debnath and Shah (2015).

The linear canonical wavelet transform on some function spaces

Abstract: It is well known that the domain of Fourier transform (FT) can be extended to the Schwartz space 𝒮(R) for convenience. As a generation of FT, it is necessary to detect the linear canonical transform (LCT) on a new space for obtaining the similar properties like FT on 𝒮(R). Therefore, a space 𝒮A1(R) generalized from 𝒮(R) is introduced firstly, and further we prove that LCT is a homeomorphism from 𝒮A1(R) onto itself. The linear canonical wavelet transform (LCWT) is a newly proposed transform based on the convolution theorem in LCT domain. Moreover, we propose an equivalent definition of LCWT associated with LCT and further study some properties of LCWT on 𝒮A1(R). Based on these properties, we finally prove that LCWT is a linear continuous operator on the spaces of Lp,A1 and HA1s,p.

High-speed all-optical Haar wavelet transform for real-time image compression.

Abstract: We present a high-speed single pixel flow imager based on an all-optical Haar wavelet transform of moving objects. Spectrally-encoded wavelet measurement patterns are produced by chirp processing of broad-bandwidth mode-locked laser pulses. A complete wavelet pattern set serially illuminates the object via a spectral disperser. This high-rate structured illumination transforms the scene into a set of sparse coefficients. We show that complex scenes can be compressed to less than 30% of their Nyquist rate by thresholding and storing the most significant wavelet coefficients. Moreover by employing temporal multiplexing of the patterns we are able to achieve pixel rates in excess of 360 MPixels/s.

An open-source full 3D electromagnetic modeler for 1D VTI media in Python: empymod

Abstract: The Python-code empymod computes the 3D electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal. The bottleneck in frequency- and time-domain calculations of electromagnetic responses derived in the wavenumber-frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain, the so-called Hankel and Fourier transforms. Three different Hankel transform methods (quadrature, quadrature-with-extrapolation [QWE], and filters) and four different Fourier transform methods (fast Fourier transform [FFT], FFTLog, QWE, and filters) are included in empymod, which allows us to compare these different methods in terms of speed and precision. The best transform in terms of speed and precision depends on the modeled frequencies. Published digital filters for the Hankel transform are very fast and precise for frequencies in the range of controlled-source electromag...

The Robust Sparse Fourier Transform (RSFT) and Its Application in Radar Signal Processing

Abstract: The Sparse Fourier Transform (SFT), designed for signals that contain a small number of frequencies, enjoys low complexity, and thus is ideally suited for big data applications. In this paper, we propose Robust Sparse Fourier Transform, (RSFT), which is a modification of SFT that extends the SFT advantages to real world, noisy settings. RSFT can accommodate off-grid frequencies in the data. Furthermore, by incorporating Neyman–Pearson detection in the SFT stages, frequency detection does not require knowledge of the exact sparsity of the signal, and is robust to noise. We analyze the asymptotic performance of RSFT, and study the computational complexity versus detection performance tradeoff. We show that, by appropriately choosing the detection thresholds, the optimal tradeoff can be achieved. We discuss the application of RSFT on short-range ubiquitous radar signal processing and demonstrate its feasibility via simulations.

Effectively Interpreting Discrete Wavelet Transformed Signals [Lecture Notes]

Abstract: Following two decades of research focusing on the discrete wavelet transform (DWT) and driven by students' high level of questioning, I decided to write this essay on one of the most significant tools for time-frequency signal analysis. As it is widely applicable in a variety of fields, I invite readers to follow this lecture note, which is specially dedicated to show a practical strategy for the interpretation of DWT-based transformed signals while extracting useful information from them. The particular focus resides on the procedure used to find the time support of frequencies and how it is influenced by the wavelet family and the support size of corresponding filters.

A Sampling Theorem for Fractional Wavelet Transform With Error Estimates

Abstract: As a generalization of the ordinary wavelet transform, the fractional wavelet transform (FRWT) is a very promising tool for signal analysis and processing. Many of its fundamental properties are already known; however, little attention has been paid to its sampling theory. In this paper, we first introduce the concept of multiresolution analysis associated with the FRWT, and then propose a sampling theorem for signals in FRWT-based multiresolution subspaces. The necessary and sufficient condition for the sampling theorem is derived. Moreover, sampling errors due to truncation and aliasing are discussed. The validity of the theoretical derivations is demonstrated via simulations.

Infrared and Visible Images Fusion Method Based On Discrete Wavelet Transform

Abstract: For infrared images, the performance of texture details in the target scene is not good, and for visible images, the performance is constrained by illumination and environment. In this paper, an image fusion method based on Discrete Wavelet Transform (DWT) is proposed. First, the infrared and visible images are decomposed by DWT, the low frequency and high frequency components will be obtained. For the low frequency component, the fusion method is based on the regional energy. For the high frequency components, the fusion method is based on the weighted sum of the difference between the neighboring coefficients. Finally, the fusion image is obtained by the inverse DWT. The results prove that, compared with the similar research methods, the performance of the proposed method is better.

Envelope detection using generalized analytic signal in 2D QLCT domains

Abstract: The hypercomplex 2D analytic signal has been proposed by several authors with applications in color image processing. The analytic signal enables to extract local features from images. It has the fundamental property of splitting the identity, meaning that it separates qualitative and quantitative information of an image in form of the local phase and the local amplitude. The extension of analytic signal of linear canonical transform domain from 1D to 2D, covering also intrinsic 2D structures, has been proposed. We use this improved concept on envelope detector. The quaternion Fourier transform plays a vital role in the representation of multidimensional signals. The quaternion linear canonical transform (QLCT) is a well-known generalization of the quaternion Fourier transform. Some valuable properties of the two-sided QLCT are studied. Different approaches to the 2D quaternion Hilbert transforms are proposed that allow the calculation of the associated analytic signals, which can suppress the negative frequency components in the QLCT domains. As an application, examples of envelope detection demonstrate the effectiveness of our approach.

An Exact and Fast Computation of Discrete Fourier Transform for Polar and Spherical Grid

Abstract: Numerous applied problems of two-dimensional (2-D) and 3-D imaging are formulated in continuous domain. They place great emphasis on obtaining and manipulating the Fourier transform in polar and spherical coordinates. However, the translation of continuum ideas with the discrete sampled data on a Cartesian grid is problematic. There exists no exact and fast solution to the problem of obtaining discrete Fourier transform for polar and spherical grids in the literature. In this paper, we develop exact algorithms to the above problem for 2-D and 3-D, which involve only 1-D equispaced fast Fourier transform with no interpolation or approximation at any stage. The result of the proposed approach leads to a fast solution with very high accuracy. We describe the computational procedure to obtain the solution in both 2-D and 3-D, which includes fast forward and inverse transforms. We find the nested multilevel matrix structure of the inverse process, and we propose a hybrid grid and use a preconditioned conjugate gradient method that exhibits a drastic improvement in the condition number.

Anisotropic Discrete Dual-Tree Wavelet Transform for Improved Classification of Trabecular Bone

Abstract: This paper deals with a new anisotropic discrete dual-tree wavelet transform (ADDTWT) to characterize the anisotropy of bone texture More specifically, we propose to extend the conventional discrete dual-tree wavelet transform (DDTWT) by using the anisotropic basis functions associated with the hyperbolic wavelet transform instead of isotropic spectrum supports A texture classification framework is adopted to assess the performance of the proposed transform The generalized Gaussian distribution is used to model the distribution of the sub-band coefficients The estimated vector of parameters for each image is then used as input for the support vector machine classifier Experiments were conducted on synthesized anisotropic fractional Brownian motion fields and on a real database composed of osteoporotic patients and control cases Results show that the ADDTWT outperforms most of the competing anisotropic transforms with an area under curve rate of 93%

Image fusion based on simultaneous empirical wavelet transform

Abstract: In this paper, a new multi-scale image fusion algorithm for multi-sensor images is proposed based on Empirical Wavelet Transform (EWT). Different from traditional wavelet transform, the wavelets of EWT are not fixed, but the ones generated according to the processed signals themselves, which ensures that these wavelets are optimal for processed signals. In order to make EWT can be used in image fusion, Simultaneous Empirical Wavelet Transform (SEWT) for 1D and 2D signals are proposed, by which different signals can be projected into the same wavelet set generated according to all the signals. The fusion algorithm constructed on the 2D SEWT contains three steps: source images are decomposed into a coarse layer and a detail layer first; then, the algorithm fuses detail layers using maximum absolute values, and fuses coarse layers using the maximum global contrast selection; finally, coefficients in all the fused layers are combined to obtain the final fused image using 2D inverse SEWT. Experiments on various images are conducted to examine the performance of the proposed algorithm. The experimental results have shown that the fused images obtained by the proposed algorithm achieve satisfying visual perception; meanwhile, the algorithm is superior to other traditional algorithms in terms of objective measures.

Fast and Stabilized Algorithm for Analyzing Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Abstract: To quickly and stably analyze electromagnetic scattering of electrically large bodies of revolution (BORs), compressive sensing is effectively applied to solve sparse matrix equation obtained by wavelet transform In wavelet domain, only several important rows of sparse impedance matrix were extracted to construct an underdetermined equation by prior knowledge that provided from excitation vectors after wavelet matrix transform Finally, the unknown current on the surface of BOR is reconstructed by orthogonal matching pursuit Numerical results of differently shaped BORs were presented to the show the efficiency of the proposed method

Load Characterization and Low-Order Approximation for Smart Metering Data in the Spectral Domain

Abstract: Smart metering data are providing new opportunities for various energy analyses at household level. However, traditional load analyses based on time-series techniques are challenged due to the irregular patterns and large volume from smart metering data. This paper proposes a promising alternative to decompose smart metering data in the spectral domain, where 1) the irregular load profiles can be characterized by the underlying spectral components, and 2) massive amount of load data can be represented by a small number of coefficients extracted from spectral components. This paper assesses the performances of load characterization at different aggregated levels by two spectral analysis techniques, using the discrete Fourier transform (DFT) and discrete wavelet transform (DWT). Results show that DWT significantly outperforms DFT for individual smart metering data, while DFT could be effective at a highly aggregated level.