Showing papers on "Harmonic wavelet transform published in 1999"

Efficient time series matching by wavelets

Abstract: Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases.

Feature extraction from wavelet coefficients for pattern recognition tasks

Abstract: An efficient feature extraction method based on the fast wavelet transform is presented. The paper especially deals with the assessment of process parameters or states in a given application using the features extracted from the wavelet coefficients of measured process signals. Since the parameter assessment using all wavelet coefficients will often turn out to be tedious or leads to inaccurate results, a preprocessing routine that computes robust features correlated to the process parameters of interest is highly desirable. The method presented divides the matrix of computed wavelet coefficients into clusters equal to row vectors. The rows that represent important frequency ranges (for signal interpretation) have a larger number of clusters than the rows that represent less important frequency ranges. The features of a process signal are eventually calculated by the Euclidean norms of the clusters. The effectiveness of this new method has been verified on a flank wear estimation problem in turning processes and on a problem of recognizing different kinds of lung sounds for diagnosis of pulmonary diseases.

Discrete fractional Fourier transform based on orthogonal projections

Abstract: The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been developed by Santhanam and McClellan (see ibid., vol.42, p.994-98, 1996) but its results do not match those of the corresponding continuous fractional Fourier transforms. We propose a new discrete fractional Fourier transform (DFRFT). The new DFRFT has DFT Hermite eigenvectors and retains the eigenvalue-eigenfunction relation as a continous FRFT. To obtain DFT Hermite eigenvectors, two orthogonal projection methods are introduced. Thus, the new DFRFT will provide similar transform and rotational properties as those of continuous fractional Fourier transforms. Moreover, the relationship between FRFT and the proposed DFRFT has been established in the same way as the conventional DFT-to-continuous-Fourier transform.

Two denoising methods by wavelet transform

Abstract: To wavelet-based noise reduction methods are discussed. First, we improve the traditional spatially selective noise filtration technique proposed by Xu et al. (1994). Second, we introduce a new threshold-based denoising algorithm based on undecimated discrete wavelet transform. Simulations and comparisons are given.

Applications of the windowed FFT to electric power quality assessment

Abstract: This paper discusses the application of the windowed fast Fourier transform to electric power quality assessment. The windowed FFT is a time windowed version of the discrete time Fourier transform. The window width may be adjusted and shifted to scan through large volumes of power quality data. Narrow window widths are used for detailed analyses, and wide window widths are used to move rapidly across archived power quality data measurements. The mathematics of the method are discussed and applications are illustrated.

Template based recovery of Fourier-based watermarks using log-polar and log-log maps

Abstract: Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyrighted material. The paper describes a method for the secure and robust copyright protection of digital images. We present an approach for embedding a digital watermark into an image using the fast Fourier transform. To this watermark is added a template in the Fourier transform domain, to render the method robust against rotations and scaling, or aspect ratio changes. We detail an algorithm based on the log-polar or log-log maps for the accurate and efficient recovery of the template in a rotated and scaled image. We also present results which demonstrate the robustness of the method against some common image processing operations such as compression, rotation, scaling and aspect ratio changes.

Shift invariant properties of the dual-tree complex wavelet transform

Abstract: We discuss the shift invariant properties of a new implementation of the discrete wavelet transform, which employs a dual-tree of wavelet filters to obtain the real and imaginary parts of complex wavelet coefficients. This introduces limited redundancy (2/sup m/:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses.

Adaptive Wavelet Transforms via Lifting

Abstract: This paper develops two new adaptive wavelet transforms based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performances of the new transforms are compared to existing wavelet transforms, and applications to signal denoising are investigated.

Wavelet-transform-based algorithm for harmonic analysis of power system waveforms

Abstract: This paper develops an approach based on wavelet transform for the evaluation of harmonic contents of power system waveforms. The new algorithm can simultaneously identify all harmonics including integer, noninteger and subharmonics. In the first step of the approach, the frequency spectrum of the waveform is decomposed into subbands using discrete wavelet packet transform filter banks. In the second step, continuous wavelet transform is applied to nonzero subbands to evaluate the harmonic contents. In the first step, there is the problem of images due to down samplings and up samplings of the waveform. A method for alleviating this image problem is developed in the paper. Methods are developed to accurately quantify harmonics frequency amplitude and phase. The approach is validated by its application to synthesised waveforms and to power system waveforms measured in the Western Australia system. It is found to be powerful and suitable for practical use.

Introduction to the Fractional Fourier Transform and Its Applications

Abstract: Publisher Summary This chapter is an introduction to the fractional Fourier transform and its applications. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a . Mathematically, the a th order fractional Fourier transform is the a th power of the Fourier transform operator. The a = 1st order fractional transform is the ordinary Fourier transform. In essence, the a th order fractional Fourier transform interpolates between a function f(u) and its Fourier transform F(μ) . The 0th order transform is simply the function itself, whereas the 1st order transform is its Fourier transform. The 0.5th transform is something in between, such that the same operation that takes us from the original function to its 0.5 th transform will take us from its 0.5th transform to its ordinary Fourier transform. More generally, index additivity is satisfied: The a 2 th transform of the a 1 th transform is equal to the ( a 2 + a 1 )th transform. The –1th transform is the inverse Fourier transform, and the – a th transform is the inverse of the a th transform.

High-impedance fault detection utilizing a Morlet wavelet transform approach

Abstract: An application of Morlet wavelets to the analysis of high-impedance fault generated signals is proposed in this paper. With the time-frequency localization characteristics embedded in wavelets, the time and frequency information of a waveform can be presented as a visualized scheme. Different from the fast Fourier transform, the wavelet transform approach is more efficient in monitoring fault signals as time varies. The proposed method has been applied to discriminate the high-impedance faults from the normal switching events, and to examine the faults under various grounds including Portland cement, wet soil and grass. Testing results have demonstrated the practicality and advantages of the proposed method for the applications.

Power system transient and harmonic studies using wavelet transform

Abstract: This paper presents the application of wavelet transforms in power system transient and harmonic analyses. Based on the discrete time domain approximation, the system components such as resistors, inductors and capacitor are modeled respectively in the discrete wavelet domain for the purpose of transient and steady state analyses. Since the power system is described by a set of ordinary differential equations, an initial value of the state variable is considered for the transient analysis, while a periodic condition is applied to the state variable for the steady state analysis. The wavelet domain impedance is set up, and the equivalent circuit is thus built for system simulation. This method can be implemented by any kind of orthogonal wavelet transform. Numerical results from an arc furnace system are also presented for the transient, harmonic and time-frequency analyses.

Image compression using wavelets

Abstract: The discrete wavelet transform (DWT) represents images as a sum of wavelet functions (wavelets) on different resolution levels. The basis for the wavelet transform can be composed of any function that satisfies requirements of multiresolution analysis. It means that there exists a large selection of wavelet families depending on the choice of wavelet function. The choice of wavelet family depends on the application. In image compression application this choice depends on image content. This paper provides fundamentals of wavelet based image compression. The options for wavelet image representations are tested. The results of image quality measurements for different wavelet functions, image contents, compression ratios and resolutions are given.

Short-time Fourier transforms and Wigner-Ville distributions applied to the calibration of power frequency harmonic analyzers

Abstract: This paper is concerned with the measurement of nonsinusoidal waveforms, in particular the use of waveform transforms in the calibration of power frequency harmonic analyzer instruments designed to make harmonic measurements under nonstationary conditions. The suitability of the Fourier transform (FT) for the analysis of nonstationary waveforms is discussed. A method involving windowing of the waveform data known as the short-time Fourier transform (STFT) and its application to harmonic amplitude measurements is considered. Limitations in time and frequency resolution inherent in the STFT lead to the development and investigation of the Wigner-Ville Distribution for use in this application. The performance of the various transforms are compared by simulation. Results using a test signal, typical of a practical signal encountered by harmonic analyzers, are presented for each transform.

Denoising by singularity detection

Abstract: A new algorithm for noise reduction using the wavelet transform is proposed. Similar to Mallat's (1992) wavelet transform modulus maxima denoising approach, we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales. However, we do not perform maxima detection and processing; therefore, complicated reconstruction is avoided. Instead, the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding "cone of influence", and the coefficients that correspond to the regular part of the signal for reconstruction are selected. The algorithm gives an improved denoising result, as compared with the previous approaches, in terms of mean squared error and visual quality. The new denoising algorithm is also invariant to translation. It does not introduce spurious oscillations and requires very little a priori information of the signal or noise. Besides, we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so-called "directional cone of influence". The denoising technique is applied to tomographic image reconstruction, where the improved performance of the new approach can clearly be observed.

Three-dimensional object recognition by Fourier transform profilometry

Abstract: An automatic method for three-dimensional (3-D) shape recognition is proposed. It combines the Fourier transform profilometry technique with a real-time recognition setup such as the joint transform correlator (JTC). A grating is projected onto the object surface resulting in a distorted grating pattern. Since this pattern carries information about the depth and the shape of the object, their comparison provides a method for recognizing 3-D objects in real time. A two-cycle JTC is used for this purpose. Experimental results demonstrate the theory and show the utility of the new proposed method.

The wavelet transform in aeromagnetic processing

Abstract: The discrete wavelet transform (DWT) provides an effective and efficient alternative to traditional Fourier and spatial-convolution processing techniques in the enhancement of aeromagnetic data. Standard operators such as horizontal and vertical derivatives, integrals of any order, and the Hilbert transform can be diagonalized in the wavelet domain, leading to an efficient algorithm. The DWT preserves the spatial localization of the components of the signal, allowing for intelligent discrimination between noise and signal in a given frequency range. This, for example, allows for more accurate calculation of higher order derivatives from noisy signals than is possible with conventional techniques. Additional accuracy can be gained by using a cycle-spinning algorithm to minimize local artifacts from the DWT denoising procedure.

Fast solution of electromagnetic integral equations using adaptive wavelet packet transform

Abstract: The adaptive wavelet packet transform is applied to sparsify the moment matrices for the fast solution of electromagnetic integral equations. In the algorithm, a cost function is employed to adaptively select the optimal wavelet packet expansion/testing functions to achieve the maximum sparsity possible in the resulting transformed system. The search for the best wavelet packet basis and the moment matrix transformation are implemented by repeated two-channel filtering of the original moment matrix with a pair of quadrature filters. It is found that the sparsified matrix has above-threshold elements that grow only as O(N/sup 1.4/) for typical scatterers. Consequently the operations to solve the transformed moment equation using the conjugate gradient method scales as O(N/sup 1.4/). The additional computational cost for carrying out the adaptive wavelet packet transform is evaluated and discussed.

Texture classification using dual-tree complex wavelet transform

Abstract: A new texture feature extraction method utilizing the dual-tree complex wavelet transform (DT-CWT) is introduced. The complex wavelet transform is a tool that uses a dual tree of wavelet filters to find the real and imaginary parts of complex wavelet coefficients. The approximate shift invariance, good directional selectivity, and computational efficiency properties of the DT-CWT make it a good candidate for representing the texture features. We propose a method for efficiently using the properties of the DT-CWT in finding the directional and spatial/frequency characteristics of the patterns and classifying different texture patterns in terms of these characteristics. Experimental results show that the proposed feature extraction and classification method is efficient in terms of the computational speed and retrieval accuracy.

Instantaneous parameters extraction via wavelet transform

Abstract: A novel theorem on the wavelet transform and Hilbert transform (HT) is proposed and applied to extract the instantaneous parameters of energy-limited, real signals. Numerical simulations shows advantages of the presented method in both precision and antinoise performance.

Motion field modeling and estimation using motion transformation

Abstract: This paper presents the concept of using a motion transform for finding the motion field between two images. A motion transform is a representation for modeling the motion field in the transform domain. Compared to other parametric motion models, e.g., affine, projective, etc., a motion transform offers a considerable advantage by its capability to model any motion field, including one with motion discontinuities. It also offers the flexibility of dynamically choosing the significant time-frequency components used to model the underlying motion. Simulation results on motion estimation using the DCT/DFT for motion modeling are presented. These results are comparable to the results from a wavelet-based approach.

Two-dimensional matched filtering for motion estimation

Abstract: In this work, we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence. The least-squares optimum approach involves the computation of the three-dimensional (3-D) Fourier transform of the sequence, followed by the detection of one or more planes in this domain with high energy concentration. We present a more efficient algorithm, based on the properties of the Radon transform and the two-dimensional (2-D) fast Fourier transform, which can sacrifice little performance for significant computational savings. We accomplish the motion detection and estimation by designing appropriate matched filters. The performance is demonstrated on two image sequences.