Wavelet Toolbox 4 User's Guide
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User's Guide for the Matlab Wavelet Toolbox
Wavelet Toolbox For Use with MATLAB® Michel Misiti Yves Misiti Georges Oppenheim Jean-Michel Poggi Computation Visualization Programming User’s Guide Version 1 How to Contact The MathWorks: ☎ 508-647-7000 Phone 508-647-7001 Fax FAX The MathWorks, Inc. Mail ✉ 24 Prime Park Way Natick, MA 01760-1500 http://www.mathworks.com Web ftp.mathworks.com Anonymous FTP server comp.soft-sys.matlab Newsgroup @ [email protected] Technical support [email protected] Product enhancement suggestions [email protected] Bug reports [email protected] Documentation error reports [email protected] Subscribing user registration [email protected] Order status, license renewals, passcodes [email protected] Sales, pricing, and general information Wavlet Toolbox User’s Guide COPYRIGHT 1996 - 1997 by The MathWorks, Inc. All Rights Reserved. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro- duced in any form without prior written consent from The MathWorks, Inc. U.S. GOVERNMENT: If Licensee is acquiring the software on behalf of any unit or agency of the U. S. Government, the following shall apply: (a) for units of the Department of Defense: RESTRICTED RIGHTS LEGEND: Use, duplication, or disclosure by the Government is subject to restric- tions as set forth in subparagraph (c)(1)(ii) of the Rights in Technical Data and Computer Software Clause at DFARS 252.227-7013. (b) for any other unit or agency: NOTICE - Notwithstanding any other lease or license agreement that may pertain to, or accompany the delivery of, the computer software and accompanying documentation, the rights of the Government regarding its use, reproduction and disclosure are as set forth in Clause 52.227-19(c)(2) of the FAR. -
Lecture 19: Wavelet Compression of Time Series and Images
Lecture 19: Wavelet compression of time series and images c Christopher S. Bretherton Winter 2014 Ref: Matlab Wavelet Toolbox help. 19.1 Wavelet compression of a time series The last section of wavelet leleccum notoolbox.m demonstrates the use of wavelet compression on a time series. The idea is to keep the wavelet coefficients of largest amplitude and zero out the small ones. 19.2 Wavelet analysis/compression of an image Wavelet analysis is easily extended to two-dimensional images or datasets (data matrices), by first doing a wavelet transform of each column of the matrix, then transforming each row of the result (see wavelet image). The wavelet coeffi- cient matrix has the highest level (largest-scale) averages in the first rows/columns, then successively smaller detail scales further down the rows/columns. The ex- ample also shows fine results with 50-fold data compression. 19.3 Continuous Wavelet Transform (CWT) Given a continuous signal u(t) and an analyzing wavelet (x), the CWT has the form Z 1 s − t W (λ, t) = λ−1=2 ( )u(s)ds (19.3.1) −∞ λ Here λ, the scale, is a continuous variable. We insist that have mean zero and that its square integrates to 1. The continuous Haar wavelet is defined: 8 < 1 0 < t < 1=2 (t) = −1 1=2 < t < 1 (19.3.2) : 0 otherwise W (λ, t) is proportional to the difference of running means of u over successive intervals of length λ/2. 1 Amath 482/582 Lecture 19 Bretherton - Winter 2014 2 In practice, for a discrete time series, the integral is evaluated as a Riemann sum using the Matlab wavelet toolbox function cwt. -
Adaptive Wavelet Clustering for Highly Noisy Data
Adaptive Wavelet Clustering for Highly Noisy Data Zengjian Chen Jiayi Liu Yihe Deng Department of Computer Science Department of Computer Science Department of Mathematics Huazhong University of University of Massachusetts Amherst University of California, Los Angeles Science and Technology Massachusetts, USA California, USA Wuhan, China [email protected] [email protected] [email protected] Kun He* John E. Hopcroft Department of Computer Science Department of Computer Science Huazhong University of Science and Technology Cornell University Wuhan, China Ithaca, NY, USA [email protected] [email protected] Abstract—In this paper we make progress on the unsupervised Based on the pioneering work of Sheikholeslami that applies task of mining arbitrarily shaped clusters in highly noisy datasets, wavelet transform, originally used for signal processing, on which is a task present in many real-world applications. Based spatial data clustering [12], we propose a new wavelet based on the fundamental work that first applies a wavelet transform to data clustering, we propose an adaptive clustering algorithm, algorithm called AdaWave that can adaptively and effectively denoted as AdaWave, which exhibits favorable characteristics for uncover clusters in highly noisy data. To tackle general appli- clustering. By a self-adaptive thresholding technique, AdaWave cations, we assume that the clusters in a dataset do not follow is parameter free and can handle data in various situations. any specific distribution and can be arbitrarily shaped. It is deterministic, fast in linear time, order-insensitive, shape- To show the hardness of the clustering task, we first design insensitive, robust to highly noisy data, and requires no pre- knowledge on data models. -
A Fourier-Wavelet Monte Carlo Method for Fractal Random Fields
JOURNAL OF COMPUTATIONAL PHYSICS 132, 384±408 (1997) ARTICLE NO. CP965647 A Fourier±Wavelet Monte Carlo Method for Fractal Random Fields Frank W. Elliott Jr., David J. Horntrop, and Andrew J. Majda Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012 Received August 2, 1996; revised December 23, 1996 2 2H k[v(x) 2 v(y)] l 5 CHux 2 yu , (1.1) A new hierarchical method for the Monte Carlo simulation of random ®elds called the Fourier±wavelet method is developed and where 0 , H , 1 is the Hurst exponent and k?l denotes applied to isotropic Gaussian random ®elds with power law spectral the expected value. density functions. This technique is based upon the orthogonal Here we develop a new Monte Carlo method based upon decomposition of the Fourier stochastic integral representation of the ®eld using wavelets. The Meyer wavelet is used here because a wavelet expansion of the Fourier space representation of its rapid decay properties allow for a very compact representation the fractal random ®elds in (1.1). This method is capable of the ®eld. The Fourier±wavelet method is shown to be straightfor- of generating a velocity ®eld with the Kolmogoroff spec- ward to implement, given the nature of the necessary precomputa- trum (H 5 Ad in (1.1)) over many (10 to 15) decades of tions and the run-time calculations, and yields comparable results scaling behavior comparable to the physical space multi- with scaling behavior over as many decades as the physical space multiwavelet methods developed recently by two of the authors. -
A Practical Guide to Wavelet Analysis
A Practical Guide to Wavelet Analysis Christopher Torrence and Gilbert P. Compo Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado ABSTRACT A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Niño– Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theo- retical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of changes in ENSO variance on interdecadal timescales. Using new datasets that extend back to 1871, the Niño3 sea surface temperature and the Southern Oscilla- tion index show significantly higher power during 1880–1920 and 1960–90, and lower power during 1920–60, as well as a possible 15-yr modulation of variance. The power Hovmöller of sea level pressure shows significant variations in 2–8-yr wavelet power in both longitude and time. 1. Introduction complete description of geophysical applications can be found in Foufoula-Georgiou and Kumar (1995), Wavelet analysis is becoming a common tool for while a theoretical treatment of wavelet analysis is analyzing localized variations of power within a time given in Daubechies (1992). -
An Overview of Wavelet Transform Concepts and Applications
An overview of wavelet transform concepts and applications Christopher Liner, University of Houston February 26, 2010 Abstract The continuous wavelet transform utilizing a complex Morlet analyzing wavelet has a close connection to the Fourier transform and is a powerful analysis tool for decomposing broadband wavefield data. A wide range of seismic wavelet applications have been reported over the last three decades, and the free Seismic Unix processing system now contains a code (succwt) based on the work reported here. Introduction The continuous wavelet transform (CWT) is one method of investigating the time-frequency details of data whose spectral content varies with time (non-stationary time series). Moti- vation for the CWT can be found in Goupillaud et al. [12], along with a discussion of its relationship to the Fourier and Gabor transforms. As a brief overview, we note that French geophysicist J. Morlet worked with non- stationary time series in the late 1970's to find an alternative to the short-time Fourier transform (STFT). The STFT was known to have poor localization in both time and fre- quency, although it was a first step beyond the standard Fourier transform in the analysis of such data. Morlet's original wavelet transform idea was developed in collaboration with the- oretical physicist A. Grossmann, whose contributions included an exact inversion formula. A series of fundamental papers flowed from this collaboration [16, 12, 13], and connections were soon recognized between Morlet's wavelet transform and earlier methods, including harmonic analysis, scale-space representations, and conjugated quadrature filters. For fur- ther details, the interested reader is referred to Daubechies' [7] account of the early history of the wavelet transform. -
Fourier, Wavelet and Monte Carlo Methods in Computational Finance
Fourier, Wavelet and Monte Carlo Methods in Computational Finance Kees Oosterlee1;2 1CWI, Amsterdam 2Delft University of Technology, the Netherlands AANMPDE-9-16, 7/7/2016 Kees Oosterlee (CWI, TU Delft) Comp. Finance AANMPDE-9-16 1 / 51 Joint work with Fang Fang, Marjon Ruijter, Luis Ortiz, Shashi Jain, Alvaro Leitao, Fei Cong, Qian Feng Agenda Derivatives pricing, Feynman-Kac Theorem Fourier methods Basics of COS method; Basics of SWIFT method; Options with early-exercise features COS method for Bermudan options Monte Carlo method BSDEs, BCOS method (very briefly) Kees Oosterlee (CWI, TU Delft) Comp. Finance AANMPDE-9-16 1 / 51 Agenda Derivatives pricing, Feynman-Kac Theorem Fourier methods Basics of COS method; Basics of SWIFT method; Options with early-exercise features COS method for Bermudan options Monte Carlo method BSDEs, BCOS method (very briefly) Joint work with Fang Fang, Marjon Ruijter, Luis Ortiz, Shashi Jain, Alvaro Leitao, Fei Cong, Qian Feng Kees Oosterlee (CWI, TU Delft) Comp. Finance AANMPDE-9-16 1 / 51 Feynman-Kac theorem: Z T v(t; x) = E g(s; Xs )ds + h(XT ) ; t where Xs is the solution to the FSDE dXs = µ(Xs )ds + σ(Xs )d!s ; Xt = x: Feynman-Kac Theorem The linear partial differential equation: @v(t; x) + Lv(t; x) + g(t; x) = 0; v(T ; x) = h(x); @t with operator 1 Lv(t; x) = µ(x)Dv(t; x) + σ2(x)D2v(t; x): 2 Kees Oosterlee (CWI, TU Delft) Comp. Finance AANMPDE-9-16 2 / 51 Feynman-Kac Theorem The linear partial differential equation: @v(t; x) + Lv(t; x) + g(t; x) = 0; v(T ; x) = h(x); @t with operator 1 Lv(t; x) = µ(x)Dv(t; x) + σ2(x)D2v(t; x): 2 Feynman-Kac theorem: Z T v(t; x) = E g(s; Xs )ds + h(XT ) ; t where Xs is the solution to the FSDE dXs = µ(Xs )ds + σ(Xs )d!s ; Xt = x: Kees Oosterlee (CWI, TU Delft) Comp. -
Ulla Saari Eco-Friendliness in the Brand Experience of High-Tech Products
Ulla Saari Eco-friendliness in the Brand Experience of High-Tech Products Julkaisu 1363 • Publication 1363 Tampere 2016 Tampereen teknillinen yliopisto. Julkaisu 1363 Tampere University of Technology. Publication 1363 Ulla Saari Eco-Friendliness in the Brand Experience of High-Tech Products Thesis for the degree of Doctor of Science in Technology to be presented with due permission for public examination and criticism in Festia Building, Auditorium Pieni Sali 1, at Tampere University of Technology, on the 10th of February 2016, at 12 noon. Tampereen teknillinen yliopisto - Tampere University of Technology Tampere 2016 ISBN 978-952-15-3670-0 (printed) ISBN 978-952-15-3690-8 (PDF) ISSN 1459-2045 i ABSTRACT The focus in this research is to develop a brand measurement scale for measuring how consumers experience eco-friendliness when reflecting on global high-tech brands. The aim is to examine can the eco-friendliness dimension in the brand experience of a high- tech brand be measured with a brand experience measurement scale by extending the research of Brakus et al. (2009). This research topic was selected because also high-tech companies are facing the need to analyze how consumers view the eco-friendliness of their brands in order to create greener products that could also benefit the financial performance of the company (Siegel, 2009). Eco-friendliness can be seen as an important factor for consumers when they are purchasing e.g. fast-moving consumer goods (McDonald et al., 2009) and automobiles (Kim, 2011). However, it is not still considered to be so relevant when buying consumer electronics or high-tech products and this is an area that has not been researched as extensively (McDonald et al., 2009). -
Early Outcomes of Native and Graft-Related Abdominal Aortic Infection Managed with Orthotopic Xenopericardial Grafts
Early outcomes of native and graft-related abdominal aortic infection managed with orthotopic xenopericardial grafts William Alonso, MD, Baris Ozdemir, FRCS, PhD, Lucien Chassin-Trubert, MD, Vicent Ziza, MD, Pierre Alric, MD, PhD, and Ludovic Canaud, MD, PhD, Montpellier, France ABSTRACT Objective: Reconstruction of infected aortic cases has shifted from extra-anatomic to in situ. This study reports the surgical strategy and early outcomes of abdominal aortic reconstruction in both native and graft-related aortic infection with in situ xenopericardial grafts. Methods: Included in the analysis are 21 consecutive patients (mean age, 69 years; 20 male) who underwent abdominal xenopericardial in situ reconstruction of native aortic infection (4) and endovascular (4) or open (13) graft aortic infection between July 2017 and September 2019. All repairs were performed on an urgent basis, but none were ruptured. All patients were followed up with clinical and biologic evaluation, ultrasound at 3 months, and computed tomography scan at 6 months and 1 year. Results: Technical success was 100%; 8 patients were treated with xenopericardial tubes and 13 with bifurcated grafts. Thirty-day mortality was 4.7% (one death due to pneumonia with respiratory hypoxic failure in critical care.). Six patients (28%) developed acute kidney injury, four (19%) requiring temporary dialysis; five fully recovered and one died. Four patients (19%) required a return to the operating room. After a median follow-up of 14 months (range, 1-26 months), overall mortality was 19% (n ¼ 4). Two patients presented with recurrent sepsis after reconstruction, leading to death due to multiorgan failure. Other patients (17/21) have discontinued antibiotics with no evidence of recurrence of infection clinically, radiologically, or on blood tests. -
HHS Public Access Author Manuscript Crit Care Med
Peripherally Inserted Central Catheters in the ICU: A Retrospective Study of Adult Medical Patients in 52 Hospitals Author Govindan, S, Snyder, A, Flanders, SA, Chopra, V Published 2018 Journal Title Critical care medicine Version Accepted Manuscript (AM) DOI https://doi.org/10.1097/CCM.0000000000003423 Copyright Statement © 2018 LWW. This is a non-final version of an article published in final form in Critical Care Medicine, 2018, 46 (12), pp. e1136-e1144. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal link for access to the definitive, published version. Downloaded from http://hdl.handle.net/10072/392253 Griffith Research Online https://research-repository.griffith.edu.au HHS Public Access Author manuscript Crit Care Med. Author manuscript; available in PMC 2019 December 01. Published in final edited form as: Crit Care Med. 2018 December ; 46(12): e1136–e1144. doi:10.1097/CCM.0000000000003423. Peripherally Inserted Central Catheters (PICCs) in the ICU: A Retrospective Study of Adult Medical Patients in 52 Hospitals Sushant Govindan, MD MSc1,4, Ashley Snyder2, Scott A. Flanders, MD2, and Vineet Chopra, MD MSc2,3,4 1.Division of Pulmonary and Critical Care, Department of Medicine, University of Michigan Health System 2.Division of Hospital Medicine, Department of Medicine, University of Michigan Health System 3.Center for Clinical Management Research, Ann Arbor VA Healthcare System 4.Patient Safety Enhancement Program, Ann Arbor VA Medical Center all in Ann Arbor, MI Abstract Objective: To quantify variation in use and complications from PICCs placed in the intensive care unit vs. PICCs placed on the general ward. -
National Conference on Science and the Law Proceedings
U.S. Department of Justice Office of Justice Programs National Institute of Justice National Conference on Science and the Law Proceedings Research Forum Sponsored by In Collaboration With National Institute of Justice Federal Judicial Center American Academy of Forensic Sciences National Academy of Sciences American Bar Association National Center for State Courts NATIONAL CONFERENCE ON SCIENCE AND THE LAW Proceedings San Diego, California April 15–16, 1999 Sponsored by: National Institute of Justice American Academy of Forensic Sciences American Bar Association National Center for State Courts In Collaboration With: Federal Judicial Center National Academy of Sciences July 2000 NCJ 179630 Julie E. Samuels Acting Director National Institute of Justice David Boyd, Ph.D. Deputy Director National Institute of Justice Richard M. Rau, Ph.D. Project Monitor Opinions or points of view expressed in this document are those of the authors and do not necessarily reflect the official position of the U.S. Department of Justice. The National Institute of Justice is a component of the Office of Justice Programs, which also includes the Bureau of Justice Assistance, Bureau of Justice Statistics, Office of Juvenile Justice and Delinquency Prevention, and Office for Victims of Crime. Preface Preface The intersections of science and law occur from crime scene to crime lab to criminal prosecution and defense. Although detectives, forensic scientists, and attorneys may have different vocabularies and perspectives, from a cognitive perspective, they share a way of thinking that is essential to scientific knowledge. A good detective, a well-trained forensic analyst, and a seasoned attorney all exhibit “what-if” thinking. This kind of thinking in hypotheticals keeps a detective open-minded: it prevents a detective from ignoring or not collecting data that may result in exculpatory evidence. -
Market Segmentation & Competitive Analysis Handy People
Market Segmentation & Handy People Competitive Analysis Because Time is Money Prepared by: Armin Ausejo University of Washington Jennifer Davies Masters of Communication in Digital Media Joe Hallock Digital Media Branding & Marketing Kate Roemer Lori Dugdale, Instructor Chia-Fang Tsai November 6, 2005 Handy People Market Segmentation and Competitive Analysis Market Need Over the past two years, home improvement has been on the rise and continues to be a booming industry, both for consumers and new job growth. According to the Home Improvement Research Institute (HIRI), which began tracking home improvement product sales in 1984, “total home improvement product sales reached a record $271 billion in 2004, a 12.6 percent increase over 2003 sales” and “raised its estimate for home improvement product purchasing in 2005 to $287 billion, from a prior estimate of $281 billion” (Home Channel News Newsfax, Vol. 16, No. 26; Pg. 2). This statistic is corroborated by the National Association of the Remodeling Industry (NARI), who found that in 2003, “Americans spent 214 billion dollars on home improvement products and services” and had “projected revenues of $224 billion in 2004.1” No doubt, this rise in product sales affects both consumers and contractors alike. It shows that the market for home improvement is strong, and thus promising for new entrants like Handy People. While many consumers would like to join the DIY (do-it-yourself) movement and handle their home upgrades and repairs themselves, many people find themselves short on time and expertise to complete those jobs to their liking. Margeau Gilbert of Coldwell Banker Residential Brokerage in Laurel, Maryland told The Washington Times, “I can't tell you the number of clients I've had who have started a DIY project and promised to finish it by the time their home is sold.