Showing papers on "Harmonic wavelet transform published in 2006"

Wavelet Methods for Time Series Analysis

Abstract: 1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.

Research progress of the fractional Fourier transform in signal processing

Abstract: The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.

Wavelets, ridgelets and curvelets on the sphere

Abstract: We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be inverted i.e. we can exactly reconstruct the original data from its coefficients in either representation. Several applications are described. We show how these transforms can be used in denoising and especially in a Combined Filtering Method, which uses both the wavelet and the curvelet transforms, thus benefiting from the advantages of both transforms. An application to component separation from multichannel data mapped to the sphere is also described in which we take advantage of moving to a wavelet representation.

The Theory and Use of the Quaternion Wavelet Transform

Abstract: This paper presents the theory and practicalities of the quaternion wavelet transform (QWT). The major contribution of this work is that it generalizes the real and complex wavelet transforms and derives a quaternionic wavelet pyramid for multi-resolution analysis using the quaternionic phase concept. As a illustration we present an application of the discrete QWT for optical flow estimation. For the estimation of motion through different resolution levels we use a similarity distance evaluated by means of the quaternionic phase concept and a confidence mask. We show that this linear approach is amenable to be extended to a kind of quadratic interpolation.

Signal processing for neuroscientists : introduction to the analysis of physiological signals

Abstract: Introduction Data Acquisition Noise Signal Averaging Real and Complex Fourier Series Continuous, Discrete, and Fast Fourier Transform Fourier Transform Applications LTI systems, Convolution, Correlation, and Coherence Laplace and z-Transform Introduction to Filters: the RC-Circuit Filters: Analysis Filters: Specification, Bode plot, Nyquist plot Filters: Digital Filters Spike Train Analysis Wavelet Analysis: Time Domain Properties Wavelet Analysis: Frequency Domain Properties Nonlinear Techniques

Unsupervised Feature Extraction for Time Series Clustering Using Orthogonal Wavelet Transform

Abstract: Unsupervised Feature Extraction for Time Series Clustering Using Orthogonal Wavelet Transform

Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing

Abstract: An advanced continuous wavelet transform algorithm for digital interferogram analysis and processing is proposed. The algorithm is an extension of the traditional wavelet transform; the mother wavelet and normalization parameter are selected based on the characteristics of optical interferograms. To reduce the processing time, a fast Fourier transform scheme is employed to implement the wavelet transform calculation. The algorithm is simple and is a robust tool for interferogram filtering and for whole-field fringe and phase information detection. The concept is verified by computer simulation and actual experimental interferogram analysis.

Oriented Wavelet Transform for Image Compression and Denoising

Abstract: In this paper, we introduce a new transform for image processing, based on wavelets and the lifting paradigm. The lifting steps of a unidimensional wavelet are applied along a local orientation defined on a quincunx sampling grid. To maximize energy compaction, the orientation minimizing the prediction error is chosen adaptively. A fine-grained multiscale analysis is provided by iterating the decomposition on the low-frequency band. In the context of image compression, the multiresolution orientation map is coded using a quad tree. The rate allocation between the orientation map and wavelet coefficients is jointly optimized in a rate-distortion sense. For image denoising, a Markov model is used to extract the orientations from the noisy image. As long as the map is sufficiently homogeneous, interesting properties of the original wavelet are preserved such as regularity and orthogonality. Perfect reconstruction is ensured by the reversibility of the lifting scheme. The mutual information between the wavelet coefficients is studied and compared to the one observed with a separable wavelet transform. The rate-distortion performance of this new transform is evaluated for image coding using state-of-the-art subband coders. Its performance in a denoising application is also assessed against the performance obtained with other transforms or denoising methods

Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines

Abstract: Gotz, Druckmuller, and, independently, Brady have defined a discrete Radon transform (DRT) that sums an image9s pixel values along a set of aptly chosen discrete lines, complete in slope and intercept. The transform is fast, O ( N 2 log N ) for an N × N image; it uses only addition, not multiplication or interpolation, and it admits a fast, exact algorithm for the adjoint operation, namely backprojection. This paper shows that the transform additionally has a fast, exact (although iterative) inverse. The inverse reproduces to machine accuracy the pixel-by-pixel values of the original image from its DRT, without artifacts or a finite point-spread function. Fourier or fast Fourier transform methods are not used. The inverse can also be calculated from sampled sinograms and is well conditioned in the presence of noise. Also introduced are generalizations of the DRT that combine pixel values along lines by operations other than addition. For example, there is a fast transform that calculates median values along all discrete lines and is able to detect linear features at low signal-to-noise ratios in the presence of pointlike clutter features of arbitrarily large amplitude.

A comparison of Fourier transform and wavelet transform methods for detection and classification of faults on transmission lines

Abstract: This paper presents a comparative study of the performance of Fourier transform and wavelet transform based methods for detection, classification and location of faults on high voltage transmission lines. The algorithms devised are based on Fourier transform analysis of transient current signals recorded in the event of a short circuit on a transmission line. Similar analysis is performed using multi-resolution Daubchies-8 wavelet transform and comparative merits of the two methods are discussed.

Constrained surrogate time series with preservation of the mean and variance structure.

Abstract: A method is presented for generating surrogates that are constrained realizations of a time series but which preserve the local mean and variance of the original signal. The method is based on the popular iterated amplitude adjusted Fourier transform method but makes use of a wavelet transform to constrain behavior in the time domain. Using this method it is possible to test for local changes in the nonlinear properties of the signal. We present an example for a change in Hurst exponent in a time series produced by fractional Brownian motion.

Optimally Sparse Image Representations using Shearlets

Abstract: It is now widely acknowledged that traditional wavelets are not very effective in dealing with multidimensional signals containing distributed discontinuities This paper presents a new discrete multiscale directional representation called the discrete shearlet transform This approach, which is based on the shearlet transform previously developed by the authors and their colaborators, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges Numerical experiments demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency

ECG Denoising with Adaptive Bionic Wavelet Transform

Abstract: In this paper a new ECG denoising scheme is proposed using a novel adaptive wavelet transform, named bionic wavelet transform (BWT), which had been first developed based on a model of the active auditory system. There has been some outstanding features with the BWT such as nonlinearity, high sensitivity and frequency selectivity, concentrated energy distribution and its ability to reconstruct signal via inverse transform but the most distinguishing characteristic of BWT is that its resolution in the time-frequency domain can be adaptively adjusted not only by the signal frequency but also by the signal instantaneous amplitude and its first-order differential. Besides by optimizing the BWT parameters parallel to modifying a new threshold value, one can handle ECG denoising with results comparing to those of wavelet transform (WT). Preliminary tests of BWT application to ECG denoising were constructed on the signals of MIT-BIH database which showed high performance of noise reduction.

Classification of surface EMG signals using harmonic wavelet packet transform.

Abstract: In this paper, an efficient method based on the discrete harmonic wavelet packet transform (DHWPT) is presented to classify surface electromyographic (SEMG) signals. After the relative energy of SEMG signals in each frequency band had been extracted by the DHWPT, a genetic algorithm was utilized to select appropriate features in order to reduce the feature dimensionality. Then, the selected features were used as the input vectors to a neural network classifier to discriminate four types of prosthesis movements. Compared with other classification methods, the proposed method provided high classification accuracy in experimental research. In addition, this method could also save a lot of computational time because the DHWPT has a fast algorithm based on the fast Fourier transform for numerical implementation.

Pseudo-log-polar Fourier transform for image registration

Abstract: A new registration algorithm based on pseudo-log-polar Fourier transform (PLPFT) for estimating large translations, rotations, and scalings in images is developed. The PLPFT, which is calculated at points distributed at nonlinear increased concentric squares, approximates log-polar Fourier representations of images accurately. In addition, it can be calculated quickly by utilizing the Fourier separability property and the fractional fast Fourier transform. Using the log-polar Fourier representations and cross-power spectrum method, we can estimate the rotations and scalings in images and obtain translations later. Experimental results have verified the robustness and high accuracy of this algorithm.

Sensorless speed measurement of induction motor using Hilbert transform and interpolated fast Fourier transform

Abstract: A new scheme based on the Hilbert transform and the interpolated fast Fourier transform (IFFT) is proposed to improve the estimation accuracy of induction motor speed from motor current signals. The phase and amplitude fluctuation associated with the eccentricity harmonics is first demodulated by the Hilbert transform. IFFT is then performed to estimate the speed of induction motors running under constant speed and transient conditions. Simulations have shown considerable improvement in estimation accuracy using IFFT as compared to the FFT technique. An experimental study has further confirmed good agreement between the estimated motor speed using the proposed scheme and the measured speed using an encoder.

Efficient computation of quadratic-phase integrals in optics

Abstract: We present a fast NlogN time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one need not choose N much larger than the space-bandwidth product of the signals, despite the highly oscillatory integral kernel. The only deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus the algorithm computes quadratic-phase integrals with a performance similar to that of the fast-Fourier-transform algorithm in computing the Fourier transform, in terms of both speed and accuracy.

Characterization of polarization attributes of seismic waves using continuous wavelet transforms

Abstract: Complex-trace analysis is the method of choice for analyzing polarized data. Because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics, it can be used to separate and characterize these waves. Traditional methods of complex-trace analysis only give the instantaneous attributes as a function of time or frequency. However, for transient wave types or seismic events that overlap in time, an estimate of the polarization parameters requires analysis of the time-frequency dependence of these attributes. We propose a method to map instantaneous polarization attributes of seismic signals in the wavelet domain and explicitly relate these attributes with the wavelet-transform coefficients of the analyzed signal. We compare our method with traditional complex-trace analysis using numerical examples. An advantage of our method is its possibility of performing the complete wave-mode separation/filtering process in the wavelet ...

Why is the Linear Canonical Transform so little known

Abstract: The linear canonical transform (LCT), is the name of a parameterized continuum of transforms which include, as particular cases, the most widely used linear transforms and operators in engineering and physics such as the Fourier transform, fractional Fourier transform (FRFT), Fresnel transform (FRST), time scaling, chirping, and others. Therefore the LCT provides a unified framework for studying the behavior of many practical transforms and system responses in optics and engineering in general. From the system‐engineering point of view the LCT provides a powerful tool for design and analysis of the characteristics of optical systems. Despite this fact only few authors take advantage of the powerful and general LCT theory for analysis and design of optical systems. In this paper we review some important properties about the continuous LCT and we present some new results regarding the discretization and computation of the LCT.

Application of wavelet transform technique to detect tool failure in turning operations

Abstract: In this study, discrete wavelet decomposition is used to detect tool failure and to conduct the de-noising of the cutting force signal in a turning process. As a result of de-noising, the wavelet de-noising method is more effective than the FFT filtering technique that is typically used. An analysis of the approximation and the detail coefficients of the cutting force signal confirmed that the onset time of tool failure and chatter vibration was successfully detected.

Direction-Adaptive Discrete Wavelet Transform via Directional Lifting and Bandeletization

Abstract: We propose an adaptive lifted discrete wavelet transform to locally adapt the filtering direction to the geometric flow in the image. The proposed approach refines previous directional lifting approaches to achieve superior compression performance with less demand for computation. Additionally, a bandeletization procedure is combined with directional lifting in a unified framework to further remove the correlation in the wavelet coefficients. Up to 2.8 dB improvement in PSNR over the conventional 2-D CDF 9/7 wavelet transform for natural images is reported. Significant improvement in subjective quality is also observed.

Comparisons of discrete wavelet transform, wavelet packet transform and stationary wavelet transform in denoising PD measurement data

Abstract: Noise has been a major limitation to partial discharge (PD) measurement. It is crucial to suppress noise prior to any PD data analysis. Recent research shows that the discrete wavelet transform, wavelet packet transform and stationary wavelet transform techniques have all achieved good effect in noise rejection in PD measurement. This paper compares the effectiveness and computing time required of the three types of wavelet transform methods when applied to simulated PD data in presence of white noise and sinusoidal interference.

Letter to the Editor: Stockwell and Wavelet Transforms

Abstract: Recent applied literature introduces the Stockwell transform (S-transform) as a new approach to time-frequency analysis. It is the purpose of this letter to encourage the interaction between the wavelet and the Stockwell communities by demonstrating that—up to minor modifications—the S-transform is a special case of the well-known continuous wavelet transform via a Morlet-type mother wavelet, with the features of a linear frequency scale, and an amplitude and modulation adjustment in phase space. The extensive research and applications obtained for the continuous wavelet transform can therefore be directly applied to the Stockwell domain.

Linear Canonical Transform and Its Implication

Abstract: As an emerging tool for signal processing,the linear canonical transform(LCT) proves itself to be more general and flexible than the Fourier transform as well as the fractional Fourier transform.So it can slove problems that can't be dealt with well by the latter.In this paper,the definition of LCT and some special cases are given at first,followed by its properties as listed.Besides,the discrete linear canonical transform is introduced.The implication of LCT is illustrated finally,displaying(LCT's) potentials and capabilities in the field of signal processing.