Add white noise with 0 mean and 1 std

Hello,

This is my equations.

w(k) is white noise 0 mean and 0.1 std.

how do i write w(k) ?

syms  x1 x2
for k=1:1:100
    if k==1
        x1(k)=1;
        x2(k)=1;
    end
    x1(k+1)=x1(k)+(exp(-k))*x2(k)+w(k);
    x2(k+1)=0.95*x2(k);
    plot(k,x1(k),'.'); hold on
end

Answer 1

[Walter Roberson]

w = @(k) randn(size(k)) ;

[Image Analyst]

w = @(k) randn(size(k)) ;
% Generate an image
k = ones(15, 20);
noisyImage = w(k)

noisyImage = 15×20

-0.7810 0.1036 0.1450 -0.1242 -0.9082 -1.3220 -0.6045 0.3629 -0.2676 -0.1921 -0.0091 -0.5004 -0.4253 0.9553 0.8836 1.0848 -1.3335 0.2089 -0.7656 0.8363 0.4610 1.0027 0.2731 -2.7784 0.2441 1.4751 -2.4169 1.5512 0.0776 1.2863 -0.2897 0.7990 1.5131 1.0832 0.7598 0.1276 -0.3428 0.4942 0.0207 0.8753 -0.3790 -1.0047 1.2999 -0.2848 0.2502 -1.7495 -1.6437 -0.9650 -0.3198 -1.4467 0.2712 0.4012 0.7655 1.0376 0.3082 1.7186 0.6578 0.8142 2.0475 -0.9921 0.0434 -0.6696 0.7704 1.6930 0.4116 1.7996 -0.6179 2.5044 -0.0524 1.6719 -0.1464 -0.2351 0.2267 0.6188 1.9350 0.2987 -0.4695 0.4348 -1.7675 -0.9463 1.1573 0.4482 -1.1559 -1.6893 -0.7734 0.1444 -0.2741 -0.6408 -0.4387 -2.5542 -0.2029 1.0541 -0.7698 1.3610 -0.3446 0.8400 -0.7967 -2.2869 -0.1228 -1.4366 0.9328 0.8220 2.1294 0.2940 2.2733 2.3510 -0.7355 1.1857 1.6693 0.5286 0.0959 -0.0943 -0.4558 -1.0086 -0.8145 -0.3372 -1.3122 -0.3752 0.5183 0.6015 -1.4857 -1.0335 1.2130 0.0601 1.2628 -0.3752 1.0815 1.0309 -0.4806 0.0364 0.1153 -0.4294 0.1245 -0.5647 0.2229 0.9447 -1.2427 0.7314 1.0757 0.1191 0.4880 -1.6522 -1.5705 -2.2672 -0.8059 0.4782 -0.8197 -1.1855 -1.4402 0.9377 -0.1491 1.8360 -0.0808 0.8838 -0.1365 1.2182 -0.5812 -1.4240 1.6505 0.7840 1.0893 0.5928 -0.5563 -0.2506 0.4924 1.2383 0.5349 0.7785 0.2878 2.0619 0.6695 -1.3376 -0.3346 0.3277 0.6791 0.3253 -1.6830 -0.1535 -0.7157 -0.1444 0.7894 -1.6131 -0.1647 -0.4107 2.8196 -0.1712 1.3158 0.2098 -1.7310 0.3945 -0.0196 -0.1790 -0.7076 0.9815 -1.1711 -0.1627 -0.2817 0.6665 -1.0187 -0.2875

imshow(noisyImage, []);
axis('on', 'image');

fprintf('Mean = %g, StdDev = %g.\n', mean2(noisyImage), std2(noisyImage))

Mean = 0.00566259, StdDev = 1.01108.

[Walter Roberson]

w = @(k) randn(size(k)) ;
syms  x1 x2
for k=1:1:100
    if k==1
        x1(k)=1;
        x2(k)=1;
    end
    x1(k+1)=x1(k)+(exp(-k))*x2(k)+w(k);
    x2(k+1)=0.95*x2(k);
    plot(k,x1(k),'.'); hold on
end