The sampling theorem based methodology for harmonics analysis

This paper investigates the validity of the sampling theorem in the analysis of supply side line current harmonics as applied to 6-pulse AC-DC thyristor converters. The common pattern of the percentage harmonic factor, for the converter characteristic harmonic current, per incremental change of the thyristor firing angle is used as the basis of the study. The RMS values of the peak amplitudes of the characteristic harmonic currents induced in the input-phase of the converter supplying a DC motor are described in terms of the sampling theorem equations and further evaluated in terms of their respective individual harmonic contributions as the thyristor firing angle is changed. The MatLab/Simulink package is also employed to simulate the forward drive speed control operation of a DC motor using the 6-pulse AC-DC thyristor converter. However the percentage harmonic factor trends observed in the sampling theorem method appear to be generally increasing which is in contradiction to the MatLab/Simulink produced trends

The sampling theorem based methodology for harmonics analysis

This paper investigates the validity of the sampling theorem in the analysis of supply side line current harmonics as applied to 6-pulse AC-DC thyristor converters. The common pattern of the percentage harmonic factor, for the converter characteristic harmonic current, per incremental change of the thyristor firing angle is used as the basis of the study. The RMS values of the peak amplitudes of the characteristic harmonic currents induced in the input-phase of the converter supplying a DC motor are described in terms of the sampling theorem equations and further evaluated in terms of their respective individual harmonic contributions as the thyristor firing angle is changed. The MatLab/Simulink package is also employed to simulate the forward drive speed control operation of a DC motor using the 6-pulse AC-DC thyristor converter. However the percentage harmonic factor trends observed in the sampling theorem method appear to be generally increasing which is in contradiction to the MatLab/Simulink produced trends

Robust Image Watermarking Using QR Factorization In Wavelet Domain

A robust blind image watermarking algorithm in wavelet transform domain (WT) based on QR factorization, and quantization index modulation (QIM) technique is presented for legal protection of digital images. The host image is decomposed into wavelet subbands, and then the approximation subband is QR factorized. The secret watermark bit is embedded into the R vector in QR using QIM. The experimental results show that the proposed algorithm preserves the high perceptual quality. It also sustains against JPEG compression, and other image processing attacks. The comparison analysis demonstrates the proposed scheme has better performance in imperceptibility and robustness than the previously reported watermarking algorithms

Multivariate orthonormal interpolating scaling vectors

AbstractIn this paper we introduce an algorithm for the construction of interpolating scaling vectors on Rd with compact support and orthonormal integer translates. Our method is substantiated by constructing several examples of bivariate scaling vectors for quincunx and box–spline dilation matrices. As the main ingredients of our recipe we derive some implementable conditions for accuracy and orthonormality of an interpolating scaling vector in terms of its mask

High-order balanced multiwavelets: theory, factorization, and design

This correspondence deals with multiwavelets, which are a recent generalization of wavelets in the context of time-varying filter banks and with their applications to signal processing and especially com- pression. By their inherent structure, multiwavelets are fit for processing multichannel signals. This is the main issue in which we will be interested here. The outline of the correspondence is as follows. First, we will review material on multiwavelets and their links with multifilter banks and, especially, time-varying filter banks. Then, we will have a close look at the problems encountered when using multiwavelets in applications, and we will propose new solutions for the design of multiwavelets filter banks by introducing the so-called balanced multiwavelets

Regular generalized sampling in T-invariant subspaces of a Hilbert space

A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases which generalize the usual sampling settings.Comment: 23 page

Gröbner bases and wavelet design

AbstractIn this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases

MULTIRIDGELETS FOR TEXTURE ANALYSIS

Directional wavelets have orientation selectivity and thus are able to efficiently represent highly anisotropic elements such as line segments and edges. Ridgelet transform is a kind of directional multi-resolution transform and has been successful in many image processing and texture analysis applications. The objective of this research is to develop multi-ridgelet transform by applying multiwavelet transform to the Radon transform so as to attain attractive improvements. By adapting the cardinal orthogonal multiwavelets to the ridgelet transform, it is shown that the proposed cardinal multiridgelet transform (CMRT) possesses cardinality, approximate translation invariance, and approximate rotation invariance simultaneously, whereas no single ridgelet transform can hold all these properties at the same time. These properties are beneficial to image texture analysis. This is demonstrated in three studies of texture analysis applications. Firstly a texture database retrieval study taking a portion of the Brodatz texture album as an example has demonstrated that the CMRT-based texture representation for database retrieval performed better than other directional wavelet methods. Secondly the study of the LCD mura defect detection was based upon the classification of simulated abnormalities with a linear support vector machine classifier, the CMRT-based analysis of defects were shown to provide efficient features for superior detection performance than other competitive methods. Lastly and the most importantly, a study on the prostate cancer tissue image classification was conducted. With the CMRT-based texture extraction, Gaussian kernel support vector machines have been developed to discriminate prostate cancer Gleason grade 3 versus grade 4. Based on a limited database of prostate specimens, one classifier was trained to have remarkable test performance. This approach is unquestionably promising and is worthy to be fully developed

Construction of interpolating and orthonormal multigenerators and multiwavelets on the interval

In den letzten Jahren haben sich Wavelets zu einem hochwertigen Hilfsmittel in der angewandten Mathematik entwickelt. Eine Waveletbasis ist im Allgemeinen ein System von Funktionen, das durch die Skalierung, Translation und Dilatation einer endlichen Menge von Funktionen, den sogenannten Mutterwavelets, entsteht. Wavelets wurden sehr erfolgreich in der digitalen Signal- und Bildanalyse, z. B. zur Datenkompression verwendet. Ein weiteres wichtiges Anwendungsfeld ist die Analyse und die numerische Behandlung von Operatorgleichungen. Insbesondere ist es gelungen, adaptive numerische Algorithmen basierend auf Wavelets für eine riesige Klasse von Operatorgleichungen, einschließlich Operatoren mit negativer Ordnung, zu entwickeln. Der Erfolg der Wavelet- Algorithmen ergibt sich als Konsequenz der folgenden Fakten: - Gewichtete Folgennormen von Wavelet-Expansionskoeffizienten sind in einem bestimmten Bereich (abhängig von der Regularität der Wavelets) äquivalent zu Glättungsnormen wie Besov- oder Sobolev-Normen. - Für eine breite Klasse von Operatoren ist ihre Darstellung in Wavelet-Koordinaten nahezu diagonal. - Die verschwindenden Momente von Wavelets entfernen den glatten Teil einer Funktion und führen zu sehr effizienten Komprimierungsstrategien. Diese Fakten können z. B. verwendet werden, um adaptive numerische Strategien mit optimaler Konvergenzgeschwindigkeit zu konstruieren, in dem Sinne, dass diese Algorithmen die Konvergenzordnung der besten N-Term-Approximationsschemata realisieren. Die maßgeblichen Ergebnisse lassen sich für lineare, symmetrische, elliptische Operatorgleichungen erzielen. Es existiert auch eine Verallgemeinerung für nichtlineare elliptische Gleichungen. Hier verbirgt sich jedoch eine ernste Schwierigkeit: Jeder numerische Algorithmus für diese Gleichungen erfordert die Auswertung eines nichtlinearen Funktionals, welches auf eine Wavelet-Reihe angewendet wird. Obwohl einige sehr ausgefeilte Algorithmen existieren, erweisen sie sich als ziemlich langsam in der Praxis. In neueren Studien wurde gezeigt, dass dieses Problem durch sogenannte Interpolanten verbessert werden kann. Dabei stellt sich heraus, dass die meisten bekannten Basen der Interpolanten keine stabilen Basen in L2[a,b] bilden. In der vorliegenden Arbeit leisten wir einen wesentlichen Beitrag zu diesem Problem und konstruieren neue Familien von Interpolanten auf beschränkten Gebieten, die nicht nur interpolierend, sondern auch stabil in L2[a,b] sind. Da dies mit nur einem Generator schwer (oder vielleicht sogar unmöglich) zu erreichen ist, werden wir mit Multigeneratoren und Multiwavelets arbeiten.In recent years, wavelets have become a very powerful tools in applied mathematics. In general, a wavelet basis is a system of functions that is generated by scaling, translating and dilating a finite set of functions, the so-called mother wavelets. Wavelets have been very successfully applied in image/signal analysis, e.g., for denoising and compression purposes. Another important field of applications is the analysis and the numerical treatment of operator equations. In particular, it has been possible to design adaptive numerical algorithms based on wavelets for a huge class of operator equations including operators of negative order. The success of wavelet algorithms is an ultimative consequence of the following facts: - Weighted sequence norms of wavelet expansion coefficients are equivalent in a certain range (depending on the regularity of the wavelets) to smoothness norms such as Besov or Sobolev norms. - For a wide class of operators their representation in wavelet coordinates is nearly diagonal. -The vanishing moments of wavelets remove the smooth part of a function. These facts can, e.g., be used to construct adaptive numerical strategies that are guaranteed to converge with optimal order, in the sense that these algorithms realize the convergence order of best N-term approximation schemes. The most far-reaching results have been obtained for linear, symmetric elliptic operator equations. Generalization to nonlinear elliptic equations also exist. However, then one is faced with a serious bottleneck: every numerical algorithm for these equations requires the evaluation of a nonlinear functional applied to a wavelet series. Although some very sophisticated algorithms exist, they turn out to perform quite slowly in practice. In recent studies, it has been shown that this problem can be ameliorated by means of so called interpolants. However, then the problem occurs that most of the known bases of interpolants do not form stable bases in L2[a,b]. In this PhD project, we intend to provide a significant contribution to this problem. We want to construct new families of interpolants on domains that are not only interpolating, but also stable in L2[a,b]or even orthogonal. Since this is hard to achieve (or maybe even impossible) with just one generator, we worked with multigenerators and multiwavelets