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Author: Gottlieb Publisher: ISBN: Category : Languages : en Pages : 4
Book Description
The investigators pursued research on the use of spectral methods in computational fluid dynamics. The implementation is examined for the solution of time dependent partial differential equations. Other topics pursued included the adaptation of spectral methods for compressible flow problems involving shocks, and the exploration of information content in spectral calculations. Papers produced during this effort included such titles as Spectral methods for time dependent partial differential equations, recovering pointwise values of discontinuous data within spectral accuracy, and Information content in spectral calculations.
Author: Gottlieb Publisher: ISBN: Category : Languages : en Pages : 4
Book Description
The investigators pursued research on the use of spectral methods in computational fluid dynamics. The implementation is examined for the solution of time dependent partial differential equations. Other topics pursued included the adaptation of spectral methods for compressible flow problems involving shocks, and the exploration of information content in spectral calculations. Papers produced during this effort included such titles as Spectral methods for time dependent partial differential equations, recovering pointwise values of discontinuous data within spectral accuracy, and Information content in spectral calculations.
Author: Baris Bozkurt Publisher: Presses univ. de Louvain ISBN: 2874630136 Category : Computers Languages : en Pages : 125
Book Description
This study proposes a new spectral representation called the Zeros of Z-Transform (ZZT), which is an all-zero representation of the z-transform of the signal. In addition, new chirp group delay processing techniques are developed for analysis of resonances of a signal. The combination of the ZZT representation with the chirp group delay processing algorithms provides a useful domain to study resonance characteristics of source and filter components of speech. Using the two representations, effective algorithms are developed for: source-tract decomposition of speech, glottal flow parameter estimation, formant tracking and feature extraction for speech recognition. The ZZT representation is mainly important for theoretical studies. Studying the ZZT of a signal is essential to be able to develop effective chirp group delay processing methods. Therefore, first the ZZT representation of the source-filter model of speech is studied for providing a theoretical background. We confirm through ZZT representation that anti-causality of the glottal flow signal introduces mixed-phase characteristics in speech signals. The ZZT of windowed speech signals is also studied since windowing cannot be avoided in practical signal processing algorithms and the effect of windowing on ZZT representation is drastic. We show that separate patterns exist in ZZT representations of windowed speech signals for the glottal flow and the vocal tract contributions. A decomposition method for source-tract separation is developed based on these patterns in ZZT. We define chirp group delay as group delay calculated on a circle other than the unit circle in z-plane. The need to compute group delay on a circle other than the unit circle comes from the fact that group delay spectra are often very noisy and cannot be easily processed for formant tracking purposes (the reasons are explained through ZZT representation). In this thesis, we propose methods to avoid such problems by modifying the ZZT of a signal and further computing the chirp group delay spectrum. New algorithms based on processing of the chirp group delay spectrum are developed for formant tracking and feature estimation for speech recognition. The proposed algorithms are compared to state-of-the-art techniques. Equivalent or higher efficiency is obtained for all proposed algorithms. The theoretical parts of the thesis further discuss a mixed-phase model for speech and phase processing problems in detail. Index Terms—spectral representation, source-filter separation, glottal flow estimation, formant tracking, zeros of z-transform, group delay processing, phase processing.
Author: David Gottlieb Publisher: SIAM ISBN: 9781611970425 Category : Technology & Engineering Languages : en Pages : 175
Book Description
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Author: Jan S. Hesthaven Publisher: Cambridge University Press ISBN: 113945952X Category : Mathematics Languages : en Pages : 4
Book Description
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Author: Claudio Canuto Publisher: Springer Science & Business Media ISBN: 3540307281 Category : Mathematics Languages : en Pages : 616
Book Description
Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Author: William H. Press Publisher: Cambridge University Press ISBN: 0521880688 Category : Computers Languages : en Pages : 1195
Book Description
Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in colour for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support, or to subscribe to an online version, please visit www.nr.com.
Author: Gottlieb
Author: Gottlieb
Author: George Kvernadze
Author: S. Abarbanel
Author: Baris Bozkurt
Author: David Gottlieb
Author: Jan S. Hesthaven
Author: Alex Leonard Solomonoff
Author: Lloyd N. Trefethen
Author: Claudio Canuto
Author: William H. Press