Search results for "DECOMPOSITION"
showing 10 items of 766 documents
Discrete Periodic Spline Wavelets and Wavelet Packets
2014
Similarly to periodic polynomial splines, existence of the set of embedded discrete periodic splines spaces \(\varPi [N]= \fancyscript{S}_{[0]}\supset {}^{2r} \fancyscript{S}_{[1]}\supset \cdots \supset {}^{2r} \fancyscript{S}_{[m]}\cdots \), combined with the DSHA provides flexible tools for design and implementation of wavelet and wavelet packet transforms. As in the polynomial case, all the calculations consist of fast direct and inverse Fourier transforms (FFT and IFFT, respectively) and simple arithmetic operations. Raising the splines order does not increase the computation complexity.
Two-dimensional wavelet transform by wavelength multiplexing
1996
The wavelet transform is a useful tool for data compression, analysis of short transient pulses, optical correlators, etc. This transform was obtained optically by the use of the spatial or temporal multiplexing approaches. A two-dimensional wavelet transform is obtained with only one spatial channel. The information of the different scalings is carried in different wavelengths and summed incoherently at the output plane. Laboratory experimental results are demonstrated.
Biorthogonal Wavelet Transforms
2015
Wavelets in the polynomial and discrete spline spaces were introduced in Chaps. 8 and 10, respectively. In both cases, the wavelets’ design and implementation of the transforms were associated with perfect reconstruction (PR) filter banks. In this chapter, those associations are discussed in more detail. Biorthogonal wavelet bases generated by PR filter banks are investigated and a few examples of compactly supported biorthogonal wavelets are presented. Conditions for filters to restore and annihilate sampled polynomials are established (discrete vanishing moment property). In a sense, the material of this chapter is introductory to Chap. 12, where splines are used as a source for (non-spli…
Periodic Spline Wavelets and Wavelet Packets
2014
This chapter presents wavelets and wavelet packets in the spaces of periodic splines of arbitrary order, which, in essence, are the multiple generators for these spaces. The SHA technique provides explicit representation of the wavelets and wavelet packets and fast implementation of the transforms in one and several dimensions.
Improved color interpolation using discrete wavelet transform
2005
New approaches to Color Interpolation based on Discrete Wavelet Transform are described. The Bayer data are split into the three colour components; for each component the Wavelet Coefficient Interpolation (WCI) algorithm is applied and results are combined to obtain the final colour interpolated image. A further anti-aliasing algorithm can be applied in order to reduce false colours. A first approach consists of interpolating wavelet coefficients starting from a spatial analysis of the input image. It was considered an interpolation step based on threshold levels associated to the spatial correlation of the input image pixel. A second approach consists of interpolating wavelet coefficients …
An improved MSD-based method for PD pattern recognition
2007
In this paper a new method for multi source partial discharge (PD) pattern recognition by discrete wavelet transform, is presented. The proposed method is based on the application of multi-resolution signal decomposition (MSD) technique applied to a 3D PD pattern image. The multi-resolution technique has shown that some detail images (horizontal, vertical and diagonal) at different decomposition levels have frequencial characteristics typical of a single discharge phenomenon. By applying this method to a double-source PD pattern it is observed that one source prevails on the other. Taking advantage from the linearity of the biorthogonal wavelet functions by using a removal and reconstructio…
A General Frame-by-Frame Wavelet Transform Algorithm for a Three-Dimensional Analysis with Reduced Memory Usage
2007
The 3D-DWT is a mathematical tool of increasing importance. However, the huge memory requirement of the algorithms that compute it is one of the main drawbacks in practical implementations. In this paper, we introduce a frame-by-frame algorithm to calculate the 3D-DWT with low memory usage. This algorithm is general, in the sense that it can be employed with any wavelet transform and, contrary to other proposals, it gets the same results as the regular wavelet transform. In addition, there is no need to divide the input video sequence into group of frames, and it can be applied in a continuous manner, so that coding efficiency is increased and no blocking artifacts appear.
172 REAL TIME EDGES DETECTION USING WAVELET TRANSFORM
2000
One of the way to extract edges uses the fast wavelet transform algorithm. This technique allows the detection of multiscale edges and is used to detect all the details, which are in a picture by modifying the scale. The real time application for edge detection involves the implementation of the algorithm on an integrated circuit like a FPGA and the development of an appropriated board. This article deals about the implementation of a wavelet transform algorithm onto a FPGA and development of an electronic board to detect multiscale edges.
Effect of parametric variation of center frequency and bandwidth of morlet wavelet transform on time-frequency analysis of event-related potentials
2017
Time-frequency (TF) analysis of event-related potentials (ERPs) using Complex Morlet Wavelet Transform has been widely applied in cognitive neuroscience research. It has been widely suggested that the center frequency (fc) and bandwidth (σ) should be considered in defining the mother wavelet. However, the issue how parametric variation of fc and σ of Morlet wavelet transform exerts influence on ERPs time-frequency results has not been extensively discussed in previous research. The current study, through adopting the method of Complex Morlet Continuous Wavelet Transform (CMCWT), aims to investigate whether time-frequency results vary with different parametric settings of fc and σ. Besides, …
A contribution to solve the problem of attributing harmonic distortion responsibility
2005
Owing to the proliferation of loads which draw nonsinusoidal currents, the current and voltage distortion in distribution systems is ever increasing. The correct identification of the source of distortion is important for attributing the responsibility of disturbances to utility and customers. In this paper, a new classification of the possible classes of responsibility is proposed, defining some conditions, based on the improvement of the method of decomposition of the current into conforming and nonconforming components, and of the method based on the evaluation of the sign of harmonic active powers, which allows their identification.