lab2 вроде / fract23

% main_fbm
clc
close all
clear all
N = 2^15 % 32768
sig = 1;
H = 0.9; %Hurst parameter
sigma(1) = sig;
for k = 1:N
sigma(k+1) = 0.5*sig*((k+1)^(2*H) - 2*k^(2*H) + (k-1)^(2*H));
end
c = [sigma sigma((end-1):-1:2)]';
Szc = size(c) % 65536 1
lambda = fft(c) ; % eigenvalues
eta = sqrt(lambda./(2*N));
Z = randn(2*N,1)+sqrt(-1).*randn(2*N,1); %complex normal vectors
Zeta = Z.*eta;
X2n = fft(Zeta) ;
A = X2n(1:(N+1));
X = real(A);
c = 1/N;
figure(200), plot(1:128,X(1:128)), grid
title('Fract Gauss Noise X'), xlabel('k')
[C,lgs] = xcorr(X,40); size(C) % 65537
CMAX = max(C(:));
figure(201), plot(lgs,C(:)/CMAX), grid
title('Coeff Correl X'), xlabel('k')
X1 = c^H*cumsum(X) ; %scaled process
[C1,lgs1] = xcorr(X1); size(C1) % 65537
C1MAX = max(C1(:));
figure(300), plot(1:128,X1(1:128)), grid
title('Fract Brown Motion X'), xlabel('k')
figure(301), plot(lgs1,C1(:)/C1MAX), grid
title('Coeff Correl X1'), xlabel('k')
END = 0