How to find local “means” from noisy signal with Matlab?

Question

I have 2-D data from a measurement that looks as below:

The noise causes the Y data to be in the range from [4.03, 4.1]. How can I obtain a mean value (x, y) for each group of points, eg for the graphic this would be around (0.3, 4.07), (1.6, 4.08), (2.3, 4.05), (3, 4.07)?

I saw something about nlfilter, but most example about that represent a 2-D image. Thanks for your help!

EDIT:

I generate the plot below with:

plot(t, y);

The t data looks as:

t(some_condition(1:40))

ans =

   1.0e-04 *

  Columns 1 through 6

    0.0216    0.0216    0.0216    0.0216    0.0216    0.0217

  Columns 7 through 12

    0.0217    0.0217    0.0217    0.0217    0.0218    0.0928

  Columns 13 through 18

    0.0928    0.0928    0.0928


  >> mean(t(some_condition))

  ans =

   1.6686e-05

So, I only get one value for the mean in t, while I want to have 4 means (actually, the 2 dots around 0.8) are noise too.

Answer 1

You can try the following:

x_filter = [0.03  0.16 0.23 0.30]*1e-5; % Insert value you want to filter here and exluce those which not

for i = 1:numel(x_filter)
    ind = abs(t-x_filter(i))<0.01e-5; % Or any other offset
    x_m = mean(t(ind));
    y_m = mean(y(ind));
    plot(x_m,y_m,'x','MarkerSize',20);
end

Answer 2

In MATLAB the mean function operates column-wise, so using mean(ydata) would give you an array containing the mean for each x-position. If I got you right, here is a sample code which does what you are after (I think):

clear
clc

%// Generate dummy data
x = repmat(1:4,10,1);
y = rand(10,4);

My = mean(y)

My looks like this:

My =

0.5854    0.6799    0.5431    0.2933

Then plot the points using scatter:

hold on

for k = 1:size(y,2)
scatter(x(:,k),y(:,k))
markerarea = 200;
scatter(k,My(k),markerarea,'filled','d') %// Represent the mean as a diamond.
end
hold off

axis([0 5 0 1])

which looks like this:

Is this what you had in mind? If not please tell me I'll edit/remove my answer :)