Matlab - Signal Noise Removal

Question

I have a vector of data, which contains integers in the range -20 20.

Bellow is a plot with the values:

Answer 1

One approach to detect outliers is to use the three standard deviation rule. An example:

%# some random data resembling yours
x = randn(100,1);
x(75) = -14;
subplot(211), plot(x)

%# tone down the noisy points
mu = mean(x); sd = std(x); Z = 3;
idx = ( abs(x-mu) > Z*sd );         %# outliers
x(idx) = Z*sd .* sign(x(idx));      %# cap values at 3*STD(X)
subplot(212), plot(x)

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EDIT:

It seems I misunderstood the goal here. If you want to do the opposite, maybe something like this instead:

%# some random data resembling yours
x = randn(100,1);
x(75) = -14; x(25) = 20;
subplot(211), plot(x)

%# zero out everything but the high peaks
mu = mean(x); sd = std(x); Z = 3;
x( abs(x-mu) < Z*sd ) = 0;
subplot(212), plot(x)