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% Time Series Analysis (Ver 3.10)
% Schloegl A. (1996-2003) Time Series Analysis - A Toolbox for the use with Matlab. 
% WWW: http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/
%
%     Version 3.10    Date: 25. Feb 2003
%     Copyright (C) 1996-2003 by Alois Schloegl <a.schloegl@ieee.org>
%
%  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
%   quantiles   calculates quantiles 
%
% Multivariate analysis (planned in future)
%   mvar    multivariate (vector) autoregressive estimation 
%   mvfilter      multivariate filter
%   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. Schlögl, B. Kemp, T. Penzel, D. Kunz, S.-L. Himanen,A. Värri, 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, Klösch G, Schlögl 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)

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