How to control the variation speed of a generated random signal ?

Hello:

I want to generate a random signal that 1) follows a Normal distribution 2) has slow variations. So I have did this:

pd_lp = makedist('Normal','mu',2,'sigma',1);

R_lp_base = random(pd_lp,5000,1);

figure

plot(R_lp_base)

The variation of this signal is rapid and I need it to be slow. Does anyone knows how to control the variation´s speed of the random generated signals in matlab ?

[Jan]

How slow is "slow"? Would this solve your needs:

x =  sort(R_lp_base);

This is the slowest possible version.

[youcha]

Hello:

I want something similar to the effect of creating a signal with 50 points and then interpolate the signal to expand the points and get 5000 points.

The idea of interpolation is not correct for my case because it modify the statistical distribution of the original signal (R_lp_base is Gaussian but R_lp is not Gaussian)

pd_lp = makedist('Normal','mu',2,'sigma',1);
R_lp_base = random(pd_lp,50,1);
figure()
plot(R_lp_base)
R_lp=interp1(1:50,R_lp_base,linspace(1,50,5000)','spline');
figure
plot(R_lp)

Answer 1

[Jan]

Start with sorting the random values. Then mix the result partially:

x = rand(1, 500);
y = sort(x);
z1 = [y(1:2:500),  flip(y(2:2:500))];
z2 = [z1(1:2:500), flip(z1(2:2:500))];

t = 1:500;
plot(t, x, 'b', t, y+1.1, 'g', t, z1+2.2, 'c', t, z2+3.3, 'r')

This has the wanted distribution and you can increase the "speed" with applying [zi(1:2:500), flip(zi(2:2:500))] repeatedly.

Alternative:

x = rand(1, 500);

y = x;
s = 0.01;
for k = 2:500
    match = find(abs(y(k:500) - y(k-1)) < s);
    if ~isempty(match)
        r = match(randi([1, numel(match)])) + k - 1;
        [y(k), y(r)] = swap(y(k), y(r));
    end
end
t = 1:500;
plot(t, x, 'b', t, y+1, 'c')

mean(abs(diff(x)))

ans = 0.3521

mean(abs(diff(y)))

ans = 0.0432

function [b,a] = swap(a,b)
end

What an ugly hack. Call it "mudsort".

[youcha]

I did not understand your code.

If you have ploted the code I added in the last comment you will be able to see the meaning of slow variation that I want.

My question is there anyway to adjust the argumento or the parameters of the makedist function to control the speed variation of the signal?