System frequency response via fft

Dear all,

I am trying to determine system response with given input and output and using the system response to determine an other pair of input for a given output.

Mathematically,

System frequency response F(h)=(F(y1))/(F(x1))

where F Fourier transform

h system response

x1 top hat input

y1 system output, assumed guassian

y2 required output, top hat

x2 input to be determined

F(x2)=(F(y2))/(F(h))=(F(y2).F(x1))/(F(y1))

x2=ifft((F(y2).F(x1))/(F(y1)))

I am doing fourier transform using fft and getting strange x2 curve. Not sure what I am doing wrong.I am using the following code. Many thanks for the anticipated response.

close all

% sampling size
step_num = 100;

% x range to define the curves
x_max = 50;
x_margin = 20;

% sampling frequency
fs = step_num/(x_max+x_margin);
fx = (0:step_num-1)/step_num*fs;

% x linespace
x = linspace(0,x_max+x_margin,step_num);
% x1 top hat profile
x1 = x<=x_max; % x1 is one for Ex less than x_max and zero afterwards
x1_f = (fft(x1,step_num)/step_num);

% y1 guassian
y1 = exp(-(0.05*x).^2);
% fourier conversion
y1_f = (fft(y1,step_num)/step_num);

% y2 req: top hat profile
y2 = x<=x_max; % x1 is one for Ex less than x_max and zero afterwards
y2_f = (fft(y2,step_num)/step_num);

% determining fourier of required input
x2_f = (y2_f).*(x1_f)./(y1_f);
x2 = real(ifft(x2_f));

% curve plot
figure
plot(x,x2,'Color','green','LineWidth',2);
hold on
plot(x,x1,'Color','black','LineWidth',2);
plot(x,y1,'Color','blue','LineWidth',2);
xlabel('Radial coordinate','fontsize',12);
ylabel('Intensity','fontsize',12);
legend('Required input x2','Input x1','Output y1')
axis([0 70 0 1.1])