How i can evaluate characteristic function for a random normal vector

I want to numerically evaluate characteristic functions (ChF) of PDF

For example, the ChF of the Multi-Normal distribution is

where is the ChF variable (vector), is the distribution mean (vector), is its variance-covariance matrix and i is the imaginary unit.

If I numerically construct a normal distribution and the ChF as below, how could I numerically estimate its characteristic function and then plot in a 3d plot the real part and the imaginary part?

I think i have to pass to the anonymous function a matrix if I want to evaluate the vector

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ChF of X(w) K-dimensional normal(MU,SIGMA)
%
% X real stochastic vector
%
% MU = [ mu_1 ]
%      [ mu_2 ]
%
% SIGMA = [ sigma_1*sigma_1           rho*sigma_1*sigma_2 ]
%         [ rho*sigma_1*sigma_2       sigma_2*sigma_2     ]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear variables
close all
clc

i = complex(0,1);

% mean vector
mu_1 = 10;
mu_2 = 5;
MU = [mu_1; mu_2];

% var-covar matrix
rho = 0.3;
sigma_1 = 1;
sigma_2 = 0.5;
SIGMA = [sigma_1*sigma_1, rho*sigma_1*sigma_2;...
        rho*sigma_1*sigma_2, sigma_2*sigma_2];


% ChF function
chf = @(t) exp(i * transpose(t) * MU - 0.5 * transpose(T) * SIGMA * t );


% plot ChF
figure(1)
t = linspace(0,5,250);
chfVAL = chf(t);
plot3(t,real(chfVAL),imag(chfVAL),'linewidth',2)
grid on
title('Characteristic function')
xlabel('t')
ylabel('real(ChF)')
zlabel('imag(ChF)')

Answer 1

[Torsten]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ChF of X(w) K-dimensional normal(MU,SIGMA)
%
% X real stochastic vector
%
% MU = [ mu_1 ]
%      [ mu_2 ]
%
% SIGMA = [ sigma_1*sigma_1           rho*sigma_1*sigma_2 ]
%         [ rho*sigma_1*sigma_2       sigma_2*sigma_2     ]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear variables
close all
clc

i = complex(0,1);

% mean vector
mu_1 = 10;
mu_2 = 5;
MU = [mu_1; mu_2];

% var-covar matrix
rho = 0.3;
sigma_1 = 1;
sigma_2 = 0.5;
SIGMA = [sigma_1*sigma_1, rho*sigma_1*sigma_2;...
        rho*sigma_1*sigma_2, sigma_2*sigma_2];


% ChF function
chf = @(t) exp(i * transpose(t) * MU - 0.5 * transpose(t) * SIGMA * t );


% plot ChF
figure(1)
[X,Y] = ndgrid(linspace(-10,20,2500),linspace(-10,20,2500));
chfVAL = arrayfun(@(X,Y)chf([X;Y]),X,Y);
surf(X,Y,real(chfVAL))
shading interp
colorbar

[Simone Perotti]

Torsten, thanks so much for your answer. Not only it solved my problem, it also deepened my knowledge of programming and "plotting" in 3d.