Showing papers on "S transform published in 2002"

Power quality analysis using S-transform

Abstract: This paper presents a new approach for power quality analysis using a modified wavelet transform known as the S-transform. The local spectral information of the wavelet transform can, with slight modification, be used to perform local cross spectral analysis with very good time resolution. The "phase correction" absolutely references the phase of the wavelet transform to the zero time point, thus assuring that the amplitude peaks are regions of stationary phase. The excellent time-frequency resolution characteristic of the S-transform makes it an attractive candidate for analysis of power system disturbance signals. Several power quality problems are analyzed using both the S-transform and discrete wavelet transform, showing clearly the advantage of the S-transform in detecting, localizing, and classifying the power quality problems.

Context-based entropy coding of block transform coefficients for image compression

Abstract: It has been well established that state-of-the-art wavelet image coders outperform block transform image coders in the rate-distortion (R-D) sense by a wide margin. Wavelet-based JPEG2000 is emerging as the new high-performance international standard for still image compression. An often asked question is: how much of the coding improvement is due to the transform and how much is due to the encoding strategy? Current block transform coders such as JPEG suffer from poor context modeling and fail to take full advantage of correlation in both space and frequency sense. This paper presents a simple, fast, and efficient adaptive block transform image coding algorithm based on a combination of prefiltering, postfiltering, and high-order space-frequency context modeling of block transform coefficients. Despite the simplicity constraints, coding results show that the proposed coder achieves competitive R-D performance compared to the best wavelet coders in the literature.

Power quality disturbance data compression, detection, and classification using integrated spline wavelet and S-transform

Abstract: In this paper, power quality transient data are compressed and stored for analysis and classification purposes. From the compressed data set, original data are reconstructed and then analyzed using a modified wavelet transform known as S-transform. Compression techniques using splines are performed through signal decomposition, thresholding of wavelet transform coefficients, and signal reconstruction. Finally, the authors present compression results using splines and examine the application of splines compression in power quality monitoring to mitigate against data-communication and data-storage problems. Since S-transform has better time frequency and localization property, power quality disturbances are detected and then classified in a superior way than the recently used wavelet transform.

A fast spherical harmonics transform algorithm

Abstract: The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of O(N3) for cut-off frequency N. In this paper, we propose a fast approximate algorithm for the associated Legendre transform. Our algorithm evaluates the transform by means of polynomial interpolation accelerated by the Fast Multipole Method (FMM). The divide-and-conquer approach with split Legendre functions gives computational complexity O(N2 log N). Experimental results show that our algorithm is stable and is faster than the direct computation for N ≥ 511.

The Bi-Gaussian S-Transform

Abstract: The S-transform kernel is derived from the kernel of the Fourier transform through the introduction of a scalable, translating window. The width of the window is a function of inverse frequency. In effect the S-transform is a method of spectral localization, with some similarities to wavelet transforms but using the concept of frequency rather than the concept of scale. An important property of the S-transform is that it collapses into the Fourier transform when integrated over the time axis; this property requires the window to satisfy a normalizing condition. The window which has been used in the majority of previous S-transform research is the symmetric Gaussian window introduced by Stockwell, Mansinha, and Lowe [IEEE Trans. Signal Process., 44 (1996), pp. 998--1001]. One problem with the use of a Gaussian, however, is degradation of time resolution in the time-frequency spectrum due to the long front taper. In this paper, a bi-Gaussian window is introduced, constructed through the welding of two half Gaussian windows. The asymmetry of the bi-Gaussian introduces asymmetry in the resultant time-frequency spectrum, with time resolution better in the "front" direction, as compared with the "back" direction. The bi-Gaussian S-transform is better at resolving the sharp onset of events in a time series.

Wavelet transform applications in analytical chemistry

Abstract: The wavelet transform has been established with the Fourier transform as a data-processing method in analytical chemistry. The main fields of application in analytical chemistry are related to denoising, compression, variable reduction, and signal suppression. Analytical applications were selected showing prospects and limitations of the wavelet transform. An important aspect consists in showing the advantage of wavelet transform over Fourier transform with respect to dual localization of a signal in both the original and the transformed domain enabling principal new application fields in comparison with Fourier transform.

Overcomplete image coding using iterative projection-based noise shaping

Abstract: Overcomplete transforms, like the dual-tree complex wavelet transform, offer more flexible signal representations than critically-sampled transforms. Large numbers of transform coefficients can be discarded without much reconstruction quality loss by forcing compensatory changes in the remaining coefficients. We develop and demonstrate a new and unique system for achieving these transform coding aims of coefficient elimination and compensation. The system is based on iterative projection of signals between the image domain and transform domain.

Distributed vector processing of the S-transform for medical applications

Abstract: The recently developed Stockwell transform (ST) combines features of the Fourier and Wavelet transforms; it reveals frequency variation over both space and time. It is a potentially powerful tool that can be applied to medical image processing including tissue texture analysis and noise filtering. However, calculation of the ST is computationally intensive, making conventional implementations too slow for medical applications. This problem was addressed with a Fast Fourier transform implementation for Motorola's AltiVec vector processor and a distributed processing system with the goal of creating a flexible system utilizing existing hardware and standards.

Generalized S transform

Abstract: The generalized S transform (GST), a family of reversible integer-to-integer transforms inspired by the S transform, is proposed. This family of transforms is then studied in detail by considering topics such as GST parameter calculation, the effects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some examples of specific transforms in the GST family are also given. In particular, a new transform in this family is introduced, and its practical utility is demonstrated.

Examples of Wavelet Transform Time-frequency Analysis In Direct Hydrocarbon Detection

Abstract: Windowing problems limit the resolution of conventional time-frequency analysis using the Short Time Fourier Transform (STFT) and interfere with valid measurement of seismic attenuation. Wavelet transform time-frequency spectral analysis eliminates windowing and consequently has very high temporal resolution. Synthetic studies show that the technique can be used to generate useful spectral attributes. Case studies indicate that the method allows anomalies to be seen on spectrally decomposed sections that may not be apparent on a broad-band stack. Application to various gas reservoirs indicates that wavelet transform time-frequency analysis can potentially be used for direct hydrocarbon detection using seismic attenuation in thick reservoirs, tuning-related peak frequency anomalies in thin reservoirs and low frequency shadows associated with hydrocarbons.

Spline Mojette transform. Applications in tomography and communications

Abstract: The Mojette transform is a fast and exact discrete Radon transform. Its inverse also share the same order of complexity properties. Spline functional spaces are here used to derive a class of new Mojette transforms. Algorithms with linear complexity (in terms of projections and pixels number) are derived. The transform capabilities are shown first to model the discrete tomographic acquisition process. This efficient transform is also exemplified in the area of real-time packet network transmissions where it is able to fight against losses and noise degradations.

A new complex-directional wavelet transform and its application to image denoising

Abstract: This paper describes a new complex-directional expansive perfect reconstruction two-dimensional wavelet transform. Each complex wavelet is oriented along one of six possible directions, and the magnitude of each complex wavelet has a smooth bell-shape. The transform is based both on the complex dual-tree wavelet transform introduced by Kingsbury (see Phil. Trans. Royal Society London, A, September 1999 and Applied and Computational Harmonic Analysis, vol.10, no.3, p.234-53, 2001) and on the double-density DWT. It is designed so as to possess simultaneously the properties of the complex dual-tree DWT and the double-density DWT. The paper also describes a simple subband-dependent data-driven denoising algorithm for use with this transform. An example is shown to illustrate the performance of the denoising algorithm and the transform.

High-resolution surface feature evaluation using multiwavelength optical transforms

Abstract: Surface feature evaluation with resolution beyond the classical diffraction limit can be achieved by a combined space--frequency representation of the scattered field. This was demonstrated in a measuring procedure where the surface was consecutively illuminated by a collection of focused beams and the diffracted data was measured in the far field. Mathematically, if the focused beam has a Gaussian profile, the optical system implements a Gabor transform. Other transformations, such as wavelet transforms can be obtained by properly structuring the illuminating beam. This work presents an approach where structured beams at several wavelengths are used. This additional information gathered by this procedure allows an increased resolution and the reduction of ambiguities that may occur in the analysis of single wavelength measurements.

A Configurable Architecture for the Wavelet Packet Transform

Abstract: The standard Wavelet Transform (WT) has a wide range of applications, from signal analysis to image or video compression and communications. Most of these applications would be benefited if the transform provided good spectral and temporal resolution in arbitrary regions of the time-frequency plane. This flexible choice of the time-frequency tiling is provided by the Wavelet Packet Transform (WPT). Though many VLSI architectures have been proposed for the WT in the literature, it is not the case for the WPT. We present both word-serial and word-parallel real-time pipelined architectures capable of computing a complete WPT binary tree, but which are easily configurable to compute any required WPT subtree.

Multi-scale auto-convolution for affine invariant pattern recognition

Abstract: This paper describes a novel image transform, called the multi-scale auto-convolution, which is invariant with respect to affine transformations of the spatial image coordinates. The transform can be applied directly to image patches without segmentation. Algebraically, the transform is simple requiring only rescaling of the image and computation of two-dimensional convolutions that can be performed efficiently in the frequency domain. Similar transforms can also be derived for other linear distortions of the image. The experiments performed show that classification of complex patterns can be carried out reliably with only a small set of transform coefficients.

Tomography time-frequency transform

Abstract: The paper shows that the fractional Fourier transform (FRFT) of a signal is the Radon transform of the time-frequency distribution of the same signal. Therefore, a time-frequency distribution known as the tomography time-frequency transform (TTFT) is defined as the inverse Radon transform of the FRFT of the signal. Because the computation of the TTFT does not explicitly require any window or kernel function, high resolutions in both the frequency and time domains can be achieved. When the signal contains multiple components, the cross terms can be effectively removed by an adaptive filtering process that is applied on the FRFT rather than the final result. Therefore, distortions made by the filtering process on the desired signal components can be minimized.

Real-Time Identification of Flutter Boundaries Using the Discrete Wavelet Transform

Abstract: Real-time analysis of an airframe’s eutter boundaries during eight testing can help ensure safety and reduce costs. One method of identiecation is to performcorrelation elteringusing a set of singlet functions. The method is abletoidentifyaccuratelythefrequencyand dampingcoefe cientof thesystemtoexcitation, but the computational time required can be too signiecant to implement in real-time. An alternative method is presented for correlation e ltering that employs amultiple-level discretewavelet transform. The wavelet transform decomposes theresponse signal into a set of subsignals that correspond to different frequency bands. The same operation is applied to each entry in a dictionary of singlet functions. The transform results in a considerable reduction in the data and, thus, to a reduction in the computational time needed to calculate the correlation. We demonstrate that our approach is able to identify accurately frequency and damping characteristics of the impulse response of both a synthetically generated test signal and actual eight-test data. As a result, real-time identie cation of eutter boundaries during e ight testing may be possible with relatively low-cost computational resources.

The Hartley transform applied to particle image velocimetry

Abstract: The measurement principle of particle image velocimetry (PIV) is based on cross-correlation analysis of flow images. By using the cross-correlation property and fast algorithm of the Fourier transform, the analysis in PIV can be implemented easily and quickly. The Hartley transform is an integral transform similar to the Fourier transform and has most of the characteristics of the Fourier transform. The Hartley transform also has some better properties and a faster algorithm than the Fourier transform. The cross-correlation property of the Hartley transform based on separable kernels is presented in detail and the application to PIV analysis is introduced. The advantage of the Hartley transform can be shown from the comparison of numbers of operations in theory and computation time in practice.

Signal-dependent wavelet transform and application to lossless image compression

Abstract: A signal-dependent wavelet transform based on the lifting scheme is proposed. The transform can be made reversible (i.e. an integer-to-integer transform). The reversible transform, followed by arithmetic coding, is applied to lossless image compression. Simulation results indicate that the proposed method is superior to the S+P method.

The time-frequency analysis of the harmonics with wavelet transform for the power electronics systems

Abstract: The time frequency analysis technique using wavelet transform is proposed to overcome EMC (electromagnetic compatibility) problems. The proposed technique takes into consideration the change in amplitude of the harmonics during the observation. By applying it to harmonics analysis, we can analyze the harmonics from not only the frequency but also the time point of view. Therefore, it enables us to obtain the effective solution for harmonics problems. In this paper, a wavelet transform is carried out against the actual measured data. Based on obtained results, it is shown that the features and high validity of the proposed technique for the power electronics field by comparing with the previous approach using FFT (fast Fourier transform).

An efficient computational scheme for the two-dimensional overcomplete wavelet transform

Abstract: We have studied the computational complexity associated with the overcomplete wavelet transform for the commonly used spline wavelet family. By deriving general expressions for the computational complexity using the conventional filtering implementation, we show that the inverse transform is significantly more costly in computation than the forward transform. To reduce this computational complexity, we propose a new spatial implementation based on the exploitation of the correlation between the lowpass and the bandpass outputs that is inherent in the overcomplete representation. Both theoretical studies and experimental findings show that the proposed spatial implementation can greatly simplify the computations associated with the inverse transform. In particular, the complexity of the inverse transform using the proposed implementation can be reduced to slightly less than that of the forward transform using the conventional filtering implementation. We also demonstrate that the proposed scheme allows the use of an arbitrary boundary extension method while maintaining the ease of the inverse transform.

Power quality analysis and classification using a generalized phase corrected wavelet transform

Abstract: One of the attempts to localize the spectrum of a nonstationary time series has been the wavelet transform. Although the wavelet transform is an excellent tool for detecting and localizing power quality disturbance events, it fails to classify them. This paper therefore, presents a newer approach by phase correcting the wavelet transform known as S-transform. The S-transform separates the localizing-in-time aspect of the real valued Gaussian window with the modulation (selection of frequency), so that the window translates and not the modulation. By not translating the oscillatory exponential kernel, the S-transform localizes the real and imaginary components of the spectrum independently, localizing both the phase and amplitude spectrum. This aspect of the S-transform is an improvement on the wavelet transform in that the average of all the local spectra does indeed give the same result as the Fourier transform. Further, the S-transform is generalized and used to detect, localize and classify the power quality disturbance events using the extracted features and a simple rule base.

An S-transform based neural pattern classifier for non-stationary signals

Abstract: The paper presents a new approach for the classification of non-stationary signal patterns in an electric power network using a modified wavelet transform and neural network. The wavelet transform is phase corrected to yield a new transform known as the S-transform, which has an excellent time-frequency resolution characteristic. The phase correction absolutely references the phase of the wavelet transform to the zero time point, thus assuring that the amplitude peaks are regions of stationary phase. Once the features of a noisy time varying signal during steady state or transient conditions are extracted using the S-transform, they are passed through either a feedforward neural network or a probabilistic neural network for pattern classification. The average classification accuracy of the noisy signals due to disturbances in the power network is of the order 98%.