Plotting random signal on circle

Question

I have some random signal (for example sin signal) with the time scale.

t=0:0.1:2*pi
y=sin(t)
plot(t,y)

Now I want to draw this signal on this circle. So the time vector actually becomes an envelope of the circle. Envelope of the circle represents "y = 0" in cartesian coordinate system.

Here is an example of what I expect the output to look like:

_{(source: slikomat.com)}

Thank in advanced!

Answer 1

A simpler way is to use polar:

t = linspace(0,2*pi,1000);
y = .1*sin(t*30); %// amplitude .1 and frequency 30, relative to circle
polar(t, 1+y);

If you want to remove the text generated by polar, use

delete(findall(gca, 'type', 'text'))

Answer 2

Based on my previous answer to How to plot a circle?:

%// radius
r = 2;

%// center
c = [3 3];

%// number of points
n = 1000;

%// running variable
t = linspace(0,2*pi,n);

%// noise
noise_frequency_factor = 20;
noise_amplification = 0.1*r;
noise_function = @(a,b,x) a*(sin(b*x) + 1);
noise = noise_function(noise_amplification,noise_frequency_factor,t);

%// circle with noise
x = c(1) + (r+noise).*sin(t);
y = c(2) + (r+noise).*cos(t);

%// draw line
line(x,y)

%// envelope circle
x = c(1) + (r).*sin(t);
y = c(2) + (r).*cos(t);

%// draw line
line(x,y,'color','r')

%// or draw polygon if you want to fill it with color
%// fill(x,y,[1,1,1])
axis equal

Answer 3

You need to add "noise" to the radius of the circle, roughly around r=1:

th = linspace( 0, 2*pi, N ); %// N samples
noise = rand( 1, N ) * .1; %// random noise in range [0..0.1]
r = 1+noise; %// add noise to r=1
figure;
plot( r.*cos(th), r.*sin(th) ); title('noise on circle');

An example plot would look like: