Tools Of Harmonic Analysis Research Articles

Modeling, Analysis and Comparative of Down Sampling based Clamping SV PWM for Cascaded and Diode Clamped Multilevel Inverter fed Induction Motor Drive

This paper presents investigation and performance analysis of novel down sampling based clamping SV PWM technique for diode and cascaded Multi-level Invereter fed to Induction motor drive. A novel down sampling based clamping SVPWM has developed by adding triangular off set to sinusoidal fundamental waveform is modified by down sampling the reference wave by order of 10 so this technique is called clamping space vector pulse width modulation techniques such as PD, POD and APOD. so as to shift the lower order harmonics to higher order side. This novel carrier is compared with the offset injected space vector reference waveform to generate the required PWM pulses to the inverter. To analyze the performance of the proposed PWM technique it is implemented on seven level diode and cascaded Multi-level Inverter using Matlab/Simulink software tool for output line, phase voltage, currents, speed, torque and Total harmonic distortion analysis.

Strichartz estimate of the solutions for the free fractional Schrödinger equation with spatial variable coefficient

This paper studies the Strichartz estimate of the solutions for the free fractional Schrödinger equation with spatial variable coefficient, which arises from the integrable model of the inhomogeneous spherically symmetric HFSS. It is different from the classical fractional Schrödinger equation in which the Strichartz estimates have been proved. We establish some harmonic analysis tools such as the equivalence of the Sobolev type spaces W ˙ σ , 2 and H ˙ σ and Hankel type Littlewood–Paley theory. By utilizing these ingredients, we prove the Strichartz estimate.

Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces

We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time existence and uniqueness of solution to a stochastic magnetohydrodynamics equation. The existence result holds with a positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools such as Littlewood–Paley decomposition, Jean–Micheal Bony paradifferential calculus and stochastic calculus. The law of large numbers is a key tool in our investigation. Our global existence result is new in three-dimensional spaces.

New Inversion Formulas for the Horospherical Transform

The following two inversion methods for totally geodesic Radon transforms on constant curvature spaces are well known in integral geometry. The first method employs mean value operators in accordance with the classical Funk–Radon–Helgason scheme. The second one relies on the properties of potentials that can be inverted by polynomials of the Beltrami–Laplace operator. Using tools of harmonic analysis, we show that both methods are also applicable to the horospherical transform on the real hyperbolic space.

Riesz Transforms Outside a Convex Obstacle

The goal of this paper is to develop some basic harmonic analysis tools for the Dirichlet Laplacian in the exterior domain associated to a smooth convex obstacle in dimensions $d\geq 3$. Specifically, we will discuss analogues of the Mikhlin Multiplier Theorem, Littlewood-Paley Theory, and Hardy inequalities, culminating in a proof that homogeneous Sobolev norms defined with respect to the Dirichlet and whole-space Laplacians are equivalent for the sharp ranges of integrability exponent $p$ and regularity $s$. Counterexamples are included to show that these results are indeed sharp. In particular, we precisely settle the question of boundedness of Riesz transforms on $L^p$, including the endpoint. The utility of such results in the study of nonlinear PDE is that they allow us to deduce important results, such as the fractional product and chain rules for the Dirichlet Laplacian, directly from the classical Euclidean setting. As an application, we discuss the local well-posedness and stability problems for energy-critical NLS. All the results of this paper play an essential role in the authors' proof of large-data global well-posedness and scattering for the energy-critical NLS in three dimensional exterior domains; see arXiv:1208:4904.

Tidal Analysis and Prediction for the Gangra Location, Hooghly Estuary in the Bay of Bengal

The Hooghly estuary located in the head Bay of Bengal region is a part of the highly dynamic deltaic environment. Tidal variations are pre-dominant in this estuary, and tides propagate considerable distance through a complex network of various riverine systems, inlets, bays and creeks having vital implications on water mass exchange, reworking of deltaic sediments and the mixing process. The Hooghly River houses two major ports of national importance, viz. Kolkata Dock System and Haldia Dock Complex. Tidal forcing is primarily semi-diurnal in nature and with the presence of complex riverine morphology, the tidal characteristics are substantially modified causing various tidal constituents of compound tides. The present study performs location-specific tidal analysis and prediction utilizing one-hourly tide data with SLPR2 harmonic tidal analysis tool for Gangra situated upstream of the Hooghly River. In a geomorphologic perspective, the water-level elevation at Gangra results from natural tidal flow, as well as refracted effects from cross-flow due to the presence of two natural island barriers, namely Sagar Island situated southward off Gangra and Nayachara in the east. The Hooghly channel comprises of complex bathymetric features and tidal analysis at Gangra reveals the presence of Msf (luni-solar synodic fortnightly) tidal constituent. Very few locations in India have reported on the existence of the Msf tides, and Gangra is one among them. This study also performs a comprehensive validation between the computed monthly tidal prediction from SLPR2 and measured water level at Gangra. The skill level of prediction exhibits a good match. This study also investigates the influence of atmospheric effects on sea-level pressure variations and the resultant water-level elevation from extreme weather events such as depressions and severe cyclonic storms that occurred during 2013. The study signifies the importance of tidal analysis and prediction for operational needs.

Time‐dependent operators on some non‐orientable projective orbifolds

G. R. Franssens In this paper, we present an explicit construction for the fundamental solution of the heat operator, the Schrödinger operator, and related first‐order parabolic Dirac operators on a class of some conformally flat non‐orientable orbifolds. More concretely, we treat a class of projective cylinders and tori where we can study parabolic monogenic sections with values in different pin bundles. We present integral representation formulas together with some elementary tools of harmonic analysis that enable us to solve boundary value problems on these orbifolds. Copyright © 2015 John Wiley & Sons, Ltd.

Using spectral analysis to evaluate flute tone quality

Many skilled flutists place a high priority on “good” tone quality, or timbre. Unlike pitch and rhythm, timbre is difficult to objectively quantify. This project explores (1) how tone quality is described by skilled flutists, (2) whether the harmonic spectrum has some correlation with tone quality, (3) whether certain harmonic spectra are preferred, or considered “good.” Thirty-one flutists ranging from high school students to professionals were recorded. A set of samples was used in surveys and interviews to capture descriptors and ratings of tone quality. All of the recorded samples were analyzed using application programs, Harmonic Analysis Tools (HAT), created for this study. HAT uses digital signal processing techniques to produce “spectral signatures”. The signatures consist of the harmonic content, pitch, and amplitude of a sample. The outcome of this research is a baseline set of some often used descriptors. In addition, results showed some correlation between harmonic spectra and descriptors. There were also trends in preferences with respect to certain spectral characteristics. An unexpected finding was that University students showed divergent timbre preferences compared to highly experienced flutists.

Dirac and Laplace operators on some non-orientable conformally flat orbifolds

In this paper we present an explicit construction of the fundamental solution to the Dirac and Laplace operator on some non-orientable conformally flat manifolds and special orbifolds. We first treat a class of projective cylinders and tori where we can study monogenic sections with values in different pin bundles. Then we discuss the Möbius strip, the Klein bottle and higher dimensional generalizations of them. We present integral representation formulas together with some elementary tools of harmonic analysis on these manifolds resp. orbifolds.

Modes of asymmetry: The application of harmonic analysis to symmetric quantum dynamics and quantum reference frames

Finding the consequences of symmetry for open system quantum dynamics is a problem with broad applications, including describing thermal relaxation, deriving quantum limits on the performance of amplifiers, and exploring quantum metrology in the presence of noise. The symmetry of the dynamics may reflect a symmetry of the fundamental laws of nature, a symmetry of a low-energy effective theory, or it may describe a practical restriction such as the lack of a reference frame. In this paper, we apply some tools of harmonic analysis together with ideas from quantum information theory to this problem. The central idea is to study the decomposition of quantum operations---in particular, states, measurements and channels---into different modes, which we call modes of asymmetry. Under symmetric processing, a given mode of the input is mapped to the corresponding mode of the output, implying that one can only generate a given output if the input contains all of the necessary modes. By defining monotones that quantify the asymmetry in a particular mode, we also derive quantitative constraints on the resources of asymmetry that are required to simulate a given asymmetric operation. We present applications of our results for deriving bounds on the probability of success in nondeterministic state transitions, such as quantum amplification, and a simplified formalism for studying the degradation of quantum reference frames.

Harmonic analysis and research on channel coding and decoding

The channel coding is one of the key technologies in communication systems and its traditional theory is based on algebra and the nite eld GF ( p ). This paper rstly establishes the mathematical model of the channel coding in noisy cases, then introduces the novel channel coding theory based on harmonic analysis and applies important tools of harmonic analysis including compressed sensing and Walsh-Hadamard transform to achieve the decoding and blind recognition of channel coding. Some elementary results and newly progress of channel coding based on harmonic analysis are surveyed including Gilbert-Varshamov bound theorem, l1 decoding, RIP condition, Walsh-Hadamard transform.

The central limit theorem for monotone convolution with applications to free Levy processes and infinite ergodic theory

In this paper free harmonic analysis tools are used to study parabolic iteration in the complex upper half-plane. The main result here is a complete characterization for the norming constants in the monotonic central limit theorem. This allows us to construct a new class of conservative and ergodic measure-preserving transformations on the real line with Lebesgue measure. Among all, we mention that the generalized Boole transformation with infinitely many poles is shown to be conservative, as long as its residues are summable.

The Continuous Wavelet Transform for A Bessel Type Operator on the Half Line

We consider a singular differential oper- ator ∆ on the half line which generalizes the Bessel operator. Using harmonic analysis tools corresponding to ∆, we construct and investigate a new continuous wavelet transform on (0, ∞( tied to ∆. We apply this wavelet transform to invert an intertwining operator between ∆ and the second derivative operator d 2 /dx 2 .

A Real Time Adaptive Monitoring Method for Power Signal Harmonic Analysis

With wider deployments of smart meters, smart grids, and distributed generation, power quality monitoring has become increasingly important. It is well known that fast Fourier transform (FFT) is a powerful tools for power signal harmonic analysis, but leakage effect, picket fence effect, and aliasing effect make FFT suffer from specific restrictions. In this paper, we proposed a new method for power signal harmonic analysis. The major components of this method are a frequency and phasor estimating algorithm, a real time procedure and an adaptive monitoring. To verify this method, we provided the comparisons of this method with FFT.

The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line

We consider a singular differential-difference operator Λ on R which includes as a particular case the one-dimensional Dunkl operator. By using harmonic analysis tools corresponding to Λ, we introduce and study a new continuous wavelet transform on R tied to Λ. Such a wavelet transform is exploited to invert an intertwining operator between Λ and the first derivative operator d/dx.

TWO CURVELETS VARIATIONAL MODELS DEPEND ON DECOMPOSITION SPACES

Wavelet has become an appealing image processing technique, due to the fact that the sparseness of wavelet expansion is equivalent to smoothness measure in Besov spaces so that the regularization of image can be performed by manipulating its wavelet coefficients. Unfortunately, wavelets have good performance especially at representing point singularities, but they fail to efficiently represent object edges. As one of computational harmonic analysis tools, curvelets have an essentially optimal representation of objects which is C2 away from a C2 edge. In this paper, we first apply constraint of curvelet-type decomposition spaces as a regularizing term to variational model for image denoising. Based on the equivalent relationship between semi-norm of curvelet-type decomposition spaces and the weighted curvelet coefficients, solution to the proposed model approximately equals to different curvelet shrinkages. As a second contribution, we also propose another image restoration model from image decomposition point of view. Furthermore, an equivalent theorem of two proposed models is given. Finally, the experiment results show the superiority of proposed models over traditional wavelet-based ones.

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class Λ*. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps. Kovalev was supported by the NSF grant DMS-0968756.

The Performance of PCM Quantization Under Tight Frame Representations

In this paper, we study the performance of the PCM scheme for quantizing finite unit-norm tight frame expansions for $\mathbb{R}^d$ and derive the PCM quantization error without the white noise hypothesis. We prove that for the class of unit norm tight frames derived from uniform frame paths the quantization error has an upper bound of $O(\delta^{3/2})$ regardless of the frame redundancy. This is achieved using some of the techniques developed by Güntürk in his study of Sigma-Delta quantization. Using tools of harmonic analysis we show that this upper bound is sharp for $d=2$. A consequence of this result is that unlike with Sigma-Delta quantization, the error for PCM quantization in general does not diminish to zero as one increases the frame redundancy. We extend the result to high dimension and show that the PCM quantization error has an upper bound $O(\delta^{(d+1)/2})$ for asymptotically equidistributed unit-norm tight frame of $\mathbb{R}^{d}$.

A new proof of Branson’s classification of elliptic generalized gradients

We give a representation theoretical proof of Branson’s classification (J Funct Anal 151(2):334–383, 1997), of minimal elliptic sums of generalized gradients. The original proof uses tools of harmonic analysis, which as powerful as they are, seem to be specific for the structure groups SO(n) and Spin(n). The different approach we propose is a local one, based on the relationship between ellipticity and optimal Kato constants and on the representation theory of \({\mathfrak{so}(n)}\). Optimal Kato constants for elliptic operators were computed by Calderbank et al. (J Funct Anal 173(1):214–255, 2000). We extend their method to all generalized gradients (not necessarily elliptic) and recover Branson’s result, up to one special case. The interest of this method is that it is better suited to be applied for classifying elliptic sums of generalized gradients of G-structures, for other subgroups G of the special orthogonal group.

Nonlinear Aspects of Calderón-Zygmund Theory

Calderon-Zygmund theory is classically a linear fact and amounts to get sharp integrability and differentiability properties of solutions of linear equations depending on those of the given data. A typical question is for instance: Given the Poisson equation −∆u=μ, in which Lebesgue space do Du or D 2 u lie if we assume that μ∈L γ for some γ≥1? Questions of this type have been traditionally answered using the theory of singular integrals and using Harmonic Analysis methods, which perfectly fit in the case of linear equations. The related results lie at the core of nowadays analysis of partial differential equations (pde) as they often provide the first regularity information after which further qualitative properties of solutions can be established. In the last years there has anyway been an ever growing number of results concerning nonlinear equations: put together, they start shaping what we may call a nonlinear Calderon-Zygmund theory. This means a theory which reproduces for non-linear equations the results and phenomena known for linear ones, without necessarily appealing to linear techniques and tools. The approaches are in this case suited to the special equations under consideration. Yet, although bypassing general Harmonic Analysis tools, in some way they preserve the general spirit of some the basic Harmonic Analysis ideas, applying them directly at a pde level. This is a report on some of the main results available in this context.