分数维Brownian运动之Matlab程序

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1. function fBr = MakeBrownian(n,H,par)
   
2. % MakeBrownian -- Create Fractional Brownian Signal
   
3. % Usage
   
4. % fBr = MakeBrownian(n,H,par)
   
5. % Inputs
   
6. % n signal length
   
7. % H base of digits in expansion
   
8. % par optional, degree of extension in algorithm, default =8.
   
9. % Outputs
   
10. % fBr (pseudo) Fractional Brownian signal
    
11. %
    
12. % Description
    
13. % Uses a Frequency Domain algorithm to get a pseudo Brownian Motion
    
14. % The law is NOT normalized to give unit variance to unit increments.
    
15. %
    
16. if nargin < 3,
    
17. par = 8;
    
18. end
    
19. N = n .*par;
    
20. % generate the FT of a real white noise
    
21. w = WhiteNoise(zeros(1,N));
    
22. what = fft(w);
    
23. % formal fractional integral
    
24. eta = 2 * pi * [0 : (N/2) (-(N/2)+1) : (-1)] ./ N;
    
25. eta(1) = 1;
    
26. bhat = (abs(eta) .^ (-2*H)) .* what;
    
27. bhat(1) = 0.;
    
28. fBr = ifft(bhat);
    
29. % extract a segment that is well away from the edges
    
30. start = floor(par/2 .* n);
    
31. stop = start+n-1;
    
32. fBr = real(fBr(start:stop));
    
33. %
    
34. % Part of WaveLab Version 802
    
35. % Built Sunday, October 3, 1999 8:52:27 AM
    
36. % This is Copyrighted Material
    
37. % For Copying permissions see COPYING.m
    
38. % Comments? e-mail wavelab@stat.stanford.edu
    
39. %

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