Convolution of two Matrices without changing the density function.

I was working with a code to generate a 2D-surface. My goal is to create a surface where the density function (height distribution) looks like the one produced by the following code:

 N=1000;                                 %Number of Points
m = [-0.3; 1.3];                         %Means                
sigma = cat(3,0.5,0.04);                 %Standard deviation         
w = [5; 1];                              %Weights for the two means   
gmd = gmdistribution(m,sigma,w);         %Gaussian mixture model
vec = random(gmd,N^2);                   %Draw random numbers from gmd
Z = reshape(vec,[N,N]);                  %Reshape vec into a Matrix

Plotting the histogram of Z shows a Gaussian distribution with two peaks (bimodal gaussian distribution). Now I want to convolute this set of numbers Z to get a 2D-surface with correlating points:

 rL=60;                                              %Surface Length
clx=0.4;                                             %Correlation length
x = linspace(-rL/2,rL/2,N);                          %Create x-Coordinate Vector
y = linspace(-rL/2,rL/2,N);                          %Create y-Coordinate Vector
[X,Y] = meshgrid(x,y);                               %Create Coordinate System
F = exp(-((X.^2+Y.^2)/(clx^2/2)));                   %Gaussian filter
f = 2/sqrt(pi)*rL/N/clx*ifft2(fft2(Z).*fft2(F));     %Correlation of surface including convolution, inverse Fourier transform and normalizing prefactors

Now here is my problem: The density function of f looses the bimodal characteristics and has just one peak. I would like to know if there is a way to keep this bimodal characteristics, or is it impossible because of how the convolution and the fourier transformations work? Could I solve this problem by changing the filter F? Or does anyone know an alternative method?

Thanks in advance,

David

(As orientation I used the code from the Random surface generator from this website: http://www.mysimlabs.com/surface_generation.html )