MATERNOISE is the jMatern module of jLab.

 MATERNOISE  Realizations of the Matern process and variations, including fBm. [with A. Sykulski]
 
    Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA) simulates a length N complex-
    valued Matern random process Z having variance SIGMA^2, slope parameter
    ALPHA, and damping parameter LAMBDA.
 
    DT is the sample interval.  Note that LAMBDA is understood to have the
    same units as the inverse sample interval 1/DT.  For values of LAMBDA
    greater than about 1/DT, the process becomes essentially white noise. 
    Thus typical values will have LAMBDA<(1/DT).
 
    Z=MATERNOISE(DT,N,A,ALPHA,0) generates realizations of fractional
    Brownian motion.  In this case, the third input argument is the 
    spectral amplitude A, not the standard deviation SIGMA.
 
    Z=MATERNOISE(DT,[N,M],SIGMA,ALPHA,LAMBDA) generate M realizations of  
    the process, so that Z is of size N x M.
 
    For details, including the fast generation method described below, see:
 
      Lilly, Sykulski, Early, and Olhede, (2017).  Fractional Brownian
         motion, the Matern process, and stochastic modeling of turbulent 
         dispersion.  Nonlinear Processes in Geophysics, 24: 481--514.
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    Extensions
 
    Several extensions of the basic Matern form are supported, all of which
    are discussed in more detail in MATERNSPEC.
 
    Oscillatory Matern
        Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA,NU)
    Generalized Matern (+ optional oscillations)
        Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA,GAMMA,'general') 
        Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA,GAMMA,NU,'general') 
    Extended Matern  (+ optional oscillations)
        Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA,MU,'extended')
        Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA,MU,NU,'extended')
    Composite Matern 
        Z=MATERNOISE(DT,N,SIGMA,ALPHA,LAMBDA,MU,NU,'composite')
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    Real-valued processes
 
    By default MATERNOISE generates a complex-valued process. 
 
    X=MATERNOISE(...,'real') instead generates a real-valued Matern 
    process. This also works with any of extended versions described above.
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    Multiple parameter values
 
    The input arguments SIGMA, ALPHA, etc. may all be either scalars, or
    arrays of the same length, say K.  
 
    Z=MATERNOISE(DT,N,SIGMA,ALPHA,...), with at least one of SIGMA, ALPHA,
    etc. being an array of length K, returns a matrix Z that is N x K. 
 
    Z=MATERNOISE(DT,[N M],SIGMA,ALPHA,...) then gives Z of size N x M x K.
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    Algorithm
 
    MATERNOISE uses a Cholesky matrix decomposition method which makes the
    autocovariance matrix of the generated process Z have exactly the form 
    of a sampled Matern autocovariance function, for nonzero LAMBDA, or of 
    fractional Brownian motion for LAMBDA=0. 
 
    Note that since the Cholesky decomposition requires O(N^3) operations,
    generating very long time series (>2000 points or so) may be slow.
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    Fast algorithm 
 
    MATERNOISE(...,'fast') uses a fast approximate generation algorithm 
    described in Lilly et al. (2017).  This method works by making use of 
    the known analytic form for the Matern impulse response function.
 
    In the fast algorithm, oversampling is used to ensure that the 
    structure of the Green's function is accurately resolved. 
 
    [Z,ERR]=MATERNOISE(...,'fast') also returns the fractinal error ERR 
    involved in the fast algorithm's approximation of the autocovariance 
    sequence.  This is the total squared error between the actual and 
    approximated autocovariance sequences, divided by the summed squared
    magnitude of the actual autocovariance sequence.  Note that this is for
    testing purposes only, as it substantially slows down the algorithm. 
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    See also MATERNSPEC, MATERNCOV, MATERNIMP, MATERNFIT.
 
    'maternoise --t' runs some tests.
    'maternoise --f' generates a sample figure.
 
    Usage: z=maternoise(dt,N,sigma,alpha,lambda);
           z=maternoise(dt,N,sigma,alpha,lambda,'fast');
           [z,err]=maternoise(dt,N,sigma,alpha,lambda,'fast');
           z=maternoise(dt,[N,M],sigma,alpha,lambda,mu,nu);
           z=maternoise(dt,N,A,alpha,0);
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    This is part of JLAB --- type 'help jlab' for more information
    (C) 2013--2020  A.M. Sykulski and J.M. Lilly
                                  --- type 'help jlab_license' for details