非等距数据的1D高斯滤波器

Question

I have a data distributed in non-equidistant 1D space and I need to convolve this with a Gaussian filter,

gaussFilter = sqrt(6.0/pi*delta**2)*exp(-6.0*x**2 /delta**2);

where delta is a constant and x corresponds to space.

Can anyone hint how to perform a good integration (2nd order) as the data is not equally spaced taking care of the finite end? I intend to write the code in Fortran, but a Matlab example is also welcome.

Answer 1

use this:

function yy = smooth1D(x,y,delta)
    n = length(y);
    yy = zeros(n,1);
    for i=1:n;
        ker = sqrt(6.0/pi*delta^2)*exp(-6.0*(x-x(i)).^2 /delta^2);
        %the gaussian should be normalized (don't forget dx), but if you don't want to lose     (signal) energy, uncomment the next line
        %ker = ker/sum(ker); 
        yy(i) = y'*ker;
    end
end

Answer 2

Found something which works. Though not sure if this is very accurate way as the integration (trapz) is of first order.

function [fbar] = gaussf(f,x,delta )


n = length(f);
fbar = zeros(n,1);

for i=1:n;
    kernel =  sqrt(6/(pi*delta^2))*exp(-6*((x - x(k))/delta).^2);

    kernel = kernel/trapz(x,kernel);
    fbar(i) = trapz(x,f.*kernel);
end

end