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aar


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undocumented function: [a, e, REV, TOC, CPUTIME, ESU] = aar (y, Mode, arg3, arg4, arg5, arg6, arg7, arg8, arg9)


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undocumented function: [a, e, REV, TOC, CPUTIME, ESU] = aar (y, Mode, arg3, a...



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aarmam


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 Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes mean term) 

 !! This function is obsolete and is replaced by AMARMA

 [z,E,REV,ESU,V,Z,SPUR] = aarmam(y, mode, MOP, UC, z0, Z0, V0, W); 
 Estimates AAR parameters with Kalman filter algorithm
 	y(t) = sum_i(a_i(t)*y(t-i)) + m(t) + e(t) + sum_i(b_i(t)*e(t-i))

 State space model
	z(t) = G*z(t-1) + w(t)    w(t)=N(0,W) 
	y(t) = H*z(t)   + v(t)	  v(t)=N(0,V)	

 G = I, 
 z = [m(t),a_1(t-1),..,a_p(t-p),b_1(t-1),...,b_q(t-q)];
 H = [1,y(t-1),..,y(t-p),e(t-1),...,e(t-q)];
 W = E{(z(t)-G*z(t-1))*(z(t)-G*z(t-1))'}
 V = E{(y(t)-H*z(t-1))*(y(t)-H*z(t-1))'}


 Input:
       y	Signal (AR-Process)
       Mode	determines the type of algorithm

       MOP     Model order [m,p,q], default [0,10,0]
			m=1 includes the mean term, m=0 does not. 
			p and q must be positive integers
			it is recommended to set q=0. 
	UC	Update Coefficient, default 0
	z0	Initial state vector
	Z0	Initial Covariance matrix
      
 Output:
	z	AR-Parameter
	E	error process (Adaptively filtered process)
       REV     relative error variance MSE/MSY

 REFERENCE(S): 
 [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications. 
     ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany. 

 More references can be found at 
     http://pub.ist.ac.at/~schloegl/publications/



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 Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes m...



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ac2poly


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 converts the autocorrelation sequence into an AR polynomial
 [A,Efinal] = ac2poly(r)

 see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
 



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 converts the autocorrelation sequence into an AR polynomial
 [A,Efinal] = ac...



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ac2rc


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 converts the autocorrelation function into reflection coefficients 
 [RC,r0] = ac2rc(r)

 see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
 



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 converts the autocorrelation function into reflection coefficients 
 [RC,r0]...



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acorf


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undocumented function: [AUTOCOV, stderr, lpq, qpval] = acorf (Z, N)


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undocumented function: [AUTOCOV, stderr, lpq, qpval] = acorf (Z, N)



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acovf


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 ACOVF estimates autocovariance function (not normalized)
 NaN's are interpreted as missing values. 

 [ACF,NN] = acovf(Z,MAXLAG,Mode);

 Input:
  Z    Signal (one channel per row);
  MAXLAG  maximum lag
  Mode	'biased'  : normalizes with N [default]
	'unbiased': normalizes with N-lag
	'coeff'	  : normalizes such that lag 0 is 1	
        others	  : no normalization

 Output:
  ACF autocovariance function
  NN  number of valid elements 

 REFERENCES:
  A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall, 1975.
  S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
  W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
  J.S. Bendat and A.G.Persol "Random Data: Analysis and Measurement procedures", Wiley, 1986.



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 ACOVF estimates autocovariance function (not normalized)
 NaN's are interpre...



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adim


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undocumented function: [IR, CC, D] = adim (U, UC, IR, CC, arg5)


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undocumented function: [IR, CC, D] = adim (U, UC, IR, CC, arg5)



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amarma


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undocumented function: [z, e, REV, ESU, V, Z, SPUR] = amarma (y, Mode, MOP, UC, z0, Z0, V0, W)


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undocumented function: [z, e, REV, ESU, V, Z, SPUR] = amarma (y, Mode, MOP, U...



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ar2poly


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undocumented function: A = ar2poly (A)


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undocumented function: A = ar2poly (A)



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ar2rc


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undocumented function: [MX, res, arg3] = ar2rc (ar)


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undocumented function: [MX, res, arg3] = ar2rc (ar)



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ar_spa


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undocumented function: [w, A, B, R, P, F, ip] = ar_spa (ARP, nhz, E)


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undocumented function: [w, A, B, R, P, F, ip] = ar_spa (ARP, nhz, E)



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arcext


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undocumented function: [AR, RC] = arcext (MX, P)


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undocumented function: [AR, RC] = arcext (MX, P)



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arfit2


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 ARFIT2 estimates multivariate autoregressive parameters
 of the MVAR process Y

   Y(t,:)' = w' + A1*Y(t-1,:)' + ... + Ap*Y(t-p,:)' + x(t,:)'

 ARFIT2 uses the Nutall-Strand method (multivariate Burg algorithm) 
 which provides better estimates the ARFIT [1], and uses the 
 same arguments. Moreover, ARFIT2 is faster and can deal with 
 missing values encoded as NaNs. 

 [w, A, C, sbc, fpe] = arfit2(v, pmin, pmax, selector, no_const)

 INPUT: 
  v		data - each channel in a column
  pmin, pmax 	minimum and maximum model order
  selector	'fpe' or 'sbc' [default] 
  no_const	'zero' indicates no bias/offset need to be estimated 
		in this case is w = [0, 0, ..., 0]'; 

 OUTPUT: 
  w		mean of innovation noise
  A		[A1,A2,...,Ap] MVAR estimates	
  C		covariance matrix of innovation noise
  sbc, fpe	criteria for model order selection 

 see also: ARFIT, MVAR

 REFERENCES:
  [1] A. Schloegl, 2006, Comparison of Multivariate Autoregressive Estimators.
       Signal processing, p. 2426-9.
  [2] T. Schneider and A. Neumaier, 2001. 
	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.



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 ARFIT2 estimates multivariate autoregressive parameters
 of the MVAR process Y



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biacovf


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 BiAutoCovariance function 
 [BiACF] = biacovf(Z,N);

 Input:	Z    Signal
		N  # of coefficients
 Output:	BIACF bi-autocorrelation function (joint cumulant 3rd order
 Output:	ACF   covariance function (joint cumulant 2nd order)



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 BiAutoCovariance function 
 [BiACF] = biacovf(Z,N);



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bisdemo


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 BISDEMO (script) Shows BISPECTRUM of eeg8s.mat



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 BISDEMO (script) Shows BISPECTRUM of eeg8s.mat




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bispec


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 Calculates Bispectrum 
 [BISPEC] = bispec(Z,N);

 Input:	Z    Signal
		N  # of coefficients
 Output:	BiACF  bi-autocorrelation function = 3rd order cumulant
		BISPEC Bi-spectrum 

 Reference(s):
 C.L. Nikias and A.P. Petropulu "Higher-Order Spectra Analysis" Prentice Hall, 1993.
 M.B. Priestley, "Non-linear and Non-stationary Time series Analysis", Academic Press, London, 1988.



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 Calculates Bispectrum 
 [BISPEC] = bispec(Z,N);



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 Time Series Analysis (Ver 3.10)
 Schloegl A. (1996-2019) Time Series Analysis - A Toolbox for the use with Matlab.
 WWW: http://pub.ist.ac.at/~schloegl/matlab/tsa/

	Copyright (C) 1996-2003,2008 by Alois Schloegl <alois.schloegl@gmail.com>

  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]



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 Time Series Analysis (Ver 3.10)
 Schloegl A. (1996-2019) Time Series Analysi...



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 Time Series Analysis - A toolbox for the use with Matlab and Octave. 

 Copyright (C) 1996-2004,2008,2019 by Alois Schloegl <alois.schloegl@gmail.com>
 WWW: http://pub.ist.ac.at/~schloegl/matlab/tsa/

    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 3 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, see <http://www.gnu.org/licenses/>.


  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)
   rmle        AR estimation using recursive maximum likelihood function 
   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 
   mvaar       multivariate adaptvie autoregressive estimation using Kalman filtering
   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. 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
 [3] Alois Schlögl (2000)
     The electroencephalogram and the adaptive autoregressive model: theory and applications
     Shaker Verlag, Aachen, Germany,(ISBN3-8265-7640-3). 

 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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 Time Series Analysis - A toolbox for the use with Matlab and Octave.



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durlev


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undocumented function: [MX, res, arg3] = durlev (AutoCov)


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undocumented function: [MX, res, arg3] = durlev (AutoCov)



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flag_implicit_samplerate


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undocumented function: DIM = flag_implicit_samplerate (i)


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undocumented function: DIM = flag_implicit_samplerate (i)



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flix


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 floating point index - interpolates data in case of non-integer indices

 Y=flix(D,x)
   FLIX returns Y=D(x) if x is an integer 
   otherwise D(x) is interpolated from the neighbors D(ceil(x)) and D(floor(x)) 
 
 Applications: 
 (1)  discrete Dataseries can be upsampled to higher sampling rate   
 (2)  transformation of non-equidistant samples to equidistant samples
 (3)  [Q]=flix(sort(D),q*(length(D)+1)) calculates the q-quantile of data series D   

 FLIX(D,x) is the same as INTERP1(D,X,'linear'); Therefore, FLIX might
 become obsolete in future. 

 see also: HIST2RES, Y2RES, PLOTCDF, INTERP1



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 floating point index - interpolates data in case of non-integer indices



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hup


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undocumented function: b = hup (C)


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undocumented function: b = hup (C)



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invest0


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 First Investigation of a signal (time series) - automated part
 [AutoCov,AutoCorr,ARPMX,E,ACFsd,NC]=invest0(Y,Pmax);

 [AutoCov,AutoCorr,ARPMX,E,ACFsd,NC]=invest0(AutoCov,Pmax,Mode);
 

 Y	time series
 Pmax	maximal order (optional)

 AutoCov	Autocorrelation 
 AutoCorr	normalized Autocorrelation
 PartACF	Partial Autocorrelation
 ARPMX     Autoregressive Parameter for order Pmax-1
 E	        Error function E(p)
 NC            Number of values (length-missing values)

 REFERENCES:
  P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
  M.S. Grewal and A.P. Andrews "Kalman Filtering" Prentice Hall, 1993. 
  S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
  W.S. Wei "Time Series Analysis" Addison Wesley, 1990.



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 First Investigation of a signal (time series) - automated part
 [AutoCov,Aut...



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invest1


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 First Investigation of a signal (time series) - interactive
 [AutoCov,AutoCorr,ARPMX,E,CRITERIA,MOPS]=invest1(Y,Pmax,show);

 Y	time series
 Pmax	maximal order (optional)
 show  optional; if given the parameters are shown

 AutoCov	Autocorrelation 
 AutoCorr	normalized Autocorrelation
 PartACF	Partial Autocorrelation
 E	Error function E(p)
 CRITERIA curves of the various (see below) criteria, 
 MOPS=[optFPE optAIC optBIC optSBC optMDL optCAT optPHI];
      optimal model order according to various criteria

 FPE	Final Prediction Error (Kay, 1987)
 AIC	Akaike Information Criterion (Marple, 1987)
 BIC	Bayesian Akaike Information Criterion (Wei, 1994)
 SBC	Schwartz's Bayesian Criterion (Wei, 1994)
 MDL	Minimal Description length Criterion (Marple, 1987)
 CAT	Parzen's CAT Criterion (Wei, 1994)
 PHI	Phi criterion (Pukkila et al. 1988)
 minE		order where E is minimal

 REFERENCES:
  P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
  S.   Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
  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.



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 First Investigation of a signal (time series) - interactive
 [AutoCov,AutoCo...



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invfdemo


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 invfdemo	demonstrates Inverse Filtering



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 invfdemo	demonstrates Inverse Filtering




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lattice


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 Estimates AR(p) model parameter with lattice algorithm (Burg 1968) 
 for multiple channels. 
 If you have the NaN-tools, LATTICE.M can handle missing values (NaN), 

 [...] = lattice(y [,Pmax [,Mode]]);

 [AR,RC,PE] = lattice(...);
 [MX,PE] = lattice(...);

  INPUT:
 y	signal (one per row), can contain missing values (encoded as NaN)
 Pmax	max. model order (default size(y,2)-1))
 Mode  'BURG' (default) Burg algorithm
	'GEOL' geometric lattice

  OUTPUT
 AR    autoregressive model parameter	
 RC    reflection coefficients (= -PARCOR coefficients)
 PE    remaining error variance
 MX    transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
        AR(:,K) = MX(:, K*(K-1)/2+(1:K)); = MX(:,sum(1:K-1)+(1:K)); 
        RC(:,K) = MX(:,cumsum(1:K));      = MX(:,(1:K).*(2:K+1)/2);

 All input and output parameters are organized in rows, one row 
 corresponds to the parameters of one channel

 see also ACOVF ACORF AR2RC RC2AR DURLEV SUMSKIPNAN 
 
 REFERENCE(S):
  J.P. Burg, "Maximum Entropy Spectral Analysis" Proc. 37th Meeting of the Society of Exp. Geophysiscists, Oklahoma City, OK 1967
  J.P. Burg, "Maximum Entropy Spectral Analysis" PhD-thesis, Dept. of Geophysics, Stanford University, Stanford, CA. 1975.
  P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
  S.   Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
  W.S. Wei "Time Series Analysis" Addison Wesley, 1990.



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 Estimates AR(p) model parameter with lattice algorithm (Burg 1968) 
 for mul...



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lpc


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undocumented function: A = lpc (Y, P, mode)


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undocumented function: A = lpc (Y, P, mode)



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mvaar


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 Multivariate (Vector) adaptive AR estimation base on a multidimensional
 Kalman filer algorithm. A standard VAR model (A0=I) is implemented. The 
 state vector is defined as X=(A1|A2...|Ap) and x=vec(X')

 [x,e,Kalman,Q2] = mvaar(y,p,UC,mode,Kalman)

 The standard MVAR model is defined as:

		y(n)-A1(n)*y(n-1)-...-Ap(n)*y(n-p)=e(n)

	The dimension of y(n) equals s 
	
	Input Parameters:

 		y			Observed data or signal 
 		p			prescribed maximum model order (default 1)
		UC			update coefficient	(default 0.001)
		mode	 	update method of the process noise covariance matrix 0...4 ^
					correspond to S0...S4 (default 0)

	Output Parameters

		e			prediction error of dimension s
		x			state vector of dimension s*s*p
		Q2			measurement noise covariance matrix of dimension s x s




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 Multivariate (Vector) adaptive AR estimation base on a multidimensional
 Kal...



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mvar


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undocumented function: [ARF, RCF, PE, DC, varargout] = mvar (Y, Pmax, Mode)


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undocumented function: [ARF, RCF, PE, DC, varargout] = mvar (Y, Pmax, Mode)



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mvfilter


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undocumented function: [x, z] = mvfilter (B, A, x, z)


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undocumented function: [x, z] = mvfilter (B, A, x, z)



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mvfreqz


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undocumented function: [S, h, PDC, COH, DTF, DC, pCOH, dDTF, ffDTF, pCOH2, PDCF, coh, GGC, Af, GPDC, GGC2, DCOH] = mvfreqz (B, A, C, N, Fs)


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undocumented function: [S, h, PDC, COH, DTF, DC, pCOH, dDTF, ffDTF, pCOH2, PD...



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pacf


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undocumented function: [PARCOR, sig, cil, ciu] = pacf (Z, KMAX)


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undocumented function: [PARCOR, sig, cil, ciu] = pacf (Z, KMAX)



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parcor


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undocumented function: [PARCOR, ARP, PE] = parcor (AutoCov)


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undocumented function: [PARCOR, ARP, PE] = parcor (AutoCov)



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poly2ac


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 converts an AR polynomial into an autocorrelation sequence
 [R] = poly2ac(a [,efinal] );

 see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
 



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 converts an AR polynomial into an autocorrelation sequence
 [R] = poly2ac(a ...



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poly2ar


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undocumented function: A = poly2ar (A)


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undocumented function: A = poly2ar (A)



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poly2rc


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 converts AR-polynomial into reflection coefficients
 [RC,R0] = poly2rc(A [,Efinal])

  INPUT:
 A     AR polynomial, each row represents one polynomial
 Efinal    is the final prediction error variance (default value 1)

  OUTPUT
 RC    reflection coefficients
 R0    is the variance (autocovariance at lag=0) based on the 
	prediction error


 see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC



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 converts AR-polynomial into reflection coefficients
 [RC,R0] = poly2rc(A [,E...



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rc2ac


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 converts reflection coefficients to autocorrelation sequence
 [R] = rc2ac(RC,R0);

 see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
 



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 converts reflection coefficients to autocorrelation sequence
 [R] = rc2ac(RC...



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rc2ar


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undocumented function: [MX, res, arg3, acf] = rc2ar (rc)


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undocumented function: [MX, res, arg3, acf] = rc2ar (rc)



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rc2poly


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 converts reflection coefficients into an AR-polynomial
 [a,efinal] = rc2poly(K)

 see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
 



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 converts reflection coefficients into an AR-polynomial
 [a,efinal] = rc2poly...



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rmle


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 RMLE estimates AR Parameters using the Recursive Maximum Likelihood 
 Estimator according to [1]
 
 Use: [a,VAR]=rmle(x,p)
 Input: 
 x is a column vector of data
 p is the model order
 Output:
 a is a vector with the AR parameters of the recursive MLE
 VAR is the excitation white noise variance estimate

 Reference(s):
 [1] Kay S.M., Modern Spectral Analysis - Theory and Applications. 
       Prentice Hall, p. 232-233, 1988. 




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 RMLE estimates AR Parameters using the Recursive Maximum Likelihood 
 Estima...



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sbispec


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undocumented function: [] = sbispec (BISPEC)


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undocumented function: [] = sbispec (BISPEC)



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selmo


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undocumented function: [FPE, AIC, BIC, SBC, MDL, CATcrit, PHI, optFPE, optAIC, optBIC, optSBC, optMDL, optCAT, optPHI, p, C] = selmo (e, NC)


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undocumented function: [FPE, AIC, BIC, SBC, MDL, CATcrit, PHI, optFPE, optAIC...



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selmo2


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undocumented function: X = selmo2 (y, Pmax)


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undocumented function: X = selmo2 (y, Pmax)



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sinvest1


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SINVEST1 shows the parameters of a time series calculated by INVEST1
 only called by INVEST1



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SINVEST1 shows the parameters of a time series calculated by INVEST1
 only ca...



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tsademo


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 TSADEMO	demonstrates INVEST1 on EEG data



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 TSADEMO	demonstrates INVEST1 on EEG data




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ucp


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undocumented function: b = ucp (c)


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undocumented function: b = ucp (c)



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y2res


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undocumented function: R = y2res (Y)


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undocumented function: R = y2res (Y)





