%
%?Author:?Stilian?Stoev?（C）?sstoev@math.bu.edu
%
%?Generates?paths?of?fractional?Gaussian?noise.??The?algorithm?exploits
%?the?efficiency?of?the?FFT?algorithm.?
%
%?*?Written?by:?Stilian?Stoev?.??
%?*?Latest?revision:?October?5?2003.
%
%?*?When?0%????The?generated?paths?have?“exact?distributions“?discarding
%??the?effect?of?the?random?number?generator.??The?code?uses
%??the?“corrected“?algorithm?of?Steven?B.?Lowen?1999?
%??“Efficient?Generation?of?Fractional?Brownian?Motion?for
%???Simulation?of?Infrared?Focal-plane?Array?Calibration?Drift“
%
%?*?When?1/2%???The?paths?are?generated?by?using?a?truncated?symmetric?moving?average
%?filter.??The?filter?coefficients?are?computed?via?IFFT?of?the?square
%?root?of?the?FFT?of?the?covariances?of?the?FGN.
%???The?moving?average?is?also?computed?by?using?the?FFT?algorithm.
%
%??*Remark*?This?method?is?simple?and?probably?similar?to?“circulant?
%?embedding?techniques“?numerically.??It?is?however?more?general?and
%?easier?to?extend?for?arbitrary?covariance?strucures.??It?is?originally
%?due?to?Stilian?Stoev?.?Please?email?if?you?know
%?of?other?similar?algorithms.
%
%?Input:
%???sigma?<-?the?variance
%???????H?<-?Hurst
%???????n?<-?number?of?independent?samples?to?be?generated.
%???????N?<-?the?size?of?the?sample?
%???????M?<-?1/2?of?the?length?of?the?filter?to?be?used
%????????????（used?only?for?1/2%???force?<-?if?force?==?1?then?the?FFT‘s?in?the?case?1/2?%????????????are?forced?to?be?of?dyadi