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% Time Series Analysis - A toolbox for the use with Matlab and Octave. % Version 3.32 02-Oct-2003 % % Copyright (C) 1996-2003 by Alois Schloegl <a.schloegl@ieee.org> % WWW: http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/ % $Revision: 1.13 $ % $Id: contents.m,v 1.13 2003/06/24 19:22:37 schloegl Exp $ % % % LICENSE: % This program is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation; either version 2 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program; if not, write to the Free Software % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA % % % Time Series Analysis - a toolbox for the use with Matlab % aar adaptive autoregressive estimator % acovf (*) Autocovariance function % acorf (acf) (*) autocorrelation function % pacf (*) partial autocorrelation function, includes signifcance test and confidence interval % parcor (*) partial autocorrelation function % biacovf biautocovariance function (3rd order cumulant) % bispec Bi-spectrum % durlev (*) solves Yule-Walker equation - converts ACOVF into AR parameters % lattice (*) calcultes AR parameters with lattice method % lpc (*) calculates the prediction coefficients form a given time series % invest0 (*) a prior investigation (used by invest1) % invest1 (*) investigates signal (useful for 1st evaluation of the data) % selmo (*) Select Order of Autoregressive model using different criteria % histo (*) histogram % hup (*) test Hurwitz polynomials % ucp (*) test Unit Circle Polynomials % y2res (*) computes mean, variance, skewness, kurtosis, entropy, etc. from data series % ar_spa (*) spectral analysis based on the autoregressive model % detrend (*) removes trend, can handle missing values, non-equidistant sampled data % flix floating index, interpolates data for non-interger indices % % % Multivariate analysis % adim adaptive information matrix (inverse correlation matrix) % mvar multivariate (vector) autoregressive estimation % mvfilter multivariate filter % mvfreqz multivariate spectra % arfit2 provides compatibility to ARFIT [Schneider and Neumaier, 2001] % % % Conversions between Autocorrelation (AC), Autoregressive parameters (AR), % prediction polynom (POLY) and Reflection coefficient (RC) % ac2poly (*) transforms autocorrelation into prediction polynom % ac2rc (*) transforms autocorrelation into reflexion coefficients % ar2rc (*) transforms autoregressive parameters into reflection coefficients % rc2ar (*) transforms reflection coefficients into autoregressive parameters % poly2ac (*) transforms polynom to autocorrelation % poly2ar (*) transforms polynom to AR % poly2rc (*) % rc2ac (*) % rc2poly (*) % ar2poly (*) % % Utility functions % sinvest1 shows the parameter calculated by INVEST1 % % Test suites % tsademo demonstrates INVEST1 on EEG data % invfdemo demonstration of matched, inverse filtering % bisdemo demonstrates bispectral estimation % % (*) indicates univariate analysis of multiple data series (each in a row) can be processed. % (-) indicates that these functions will be removed in future % % REFERENCES (sources): % http://www.itl.nist.gov/ % http://mathworld.wolfram.com/ % P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991. % O. Foellinger "Lineare Abtastsysteme", Oldenburg Verlag, Muenchen, 1986. % F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993. % M.S. Grewal and A.P. Andrews "Kalman Filtering" Prentice Hall, 1993. % S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996. % E.I. Jury "Theory and Application of the z-Transform Method", Robert E. Krieger Publishing Co., 1973. % M.S. Kay "Modern Spectal Estimation" Prentice Hall, 1988. % Ch. Langraf and G. Schneider "Elemente der Regeltechnik", Springer Verlag, 1970. % S.L. Marple "Digital Spetral Analysis with Applications" Prentice Hall, 1987. % C.L. Nikias and A.P. Petropulu "Higher-Order Spectra Analysis" Prentice Hall, 1993. % M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. % T. Schneider and A. Neumaier "Algorithm 808: ARFIT - a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models" % ACM Transactions on Mathematical software, 27(Mar), 58-65. % C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963). % W.S. Wei "Time Series Analysis" Addison Wesley, 1990. % % % REFERENCES (applications): % [1] A. Schl鰃l, B. Kemp, T. Penzel, D. Kunz, S.-L. Himanen,A. V鋜ri, G. Dorffner, G. Pfurtscheller. % Quality Control of polysomnographic Sleep Data by Histogram and Entropy Analysis. % Clin. Neurophysiol. 1999, Dec; 110(12): 2165 - 2170. % [2] Penzel T, Kemp B, Kl鰏ch G, Schl鰃l A, Hasan J, Varri A, Korhonen I. % Acquisition of biomedical signals databases % IEEE Engineering in Medicine and Biology Magazine 2001, 20(3): 25-32 % % Features: % - Multiple Signal Processing % - Efficient algorithms % - Model order selection tools % - higher (3rd) order analysis % - Maximum entropy spectral estimation % - can deal with missing values (NaN's)