Getting strange results for convolution with DFT.

Dear all,

I am trying to determine input with a division of output and impulse response in Fourier domain of a linear system. A minimum regeneration example is below,

Output and impulse are two Guassians with different widths.

Output = y, Fourier Y

Impulse = h, Fourier H

For linear systems y = conv(h,x) or in Fourier domain Y = H*X

I am determining input as x = inverse_fourier(Y/H).

I am getting strange curves, depending on the sampling and scaling. Not sure what I am doing wrong? Many thanks in anticipation.

x = -50:0.1:50;
b1 = 2;
b2 = 40;
sig_1 = exp(-(x./b1).^2); % impulse 
sig_2 = exp(-(x./b2).^2); % output
figure 
plot(x,sig_1);
hold on
plot(x,sig_2);

step_num = size(x,2);
% frequency scale
w_k = (0:step_num-1) * (2*pi/step_num);
w_k = fftshift(w_k);
w_k = unwrap(w_k - 2*pi);

% signal 1
sig1_f = fft(sig_1,step_num);
sig1_f = fftshift(sig1_f);

h0 = figure; % fourier spectrum
plot(w_k,abs(sig1_f),'-*')
hold on

% signal 2
sig2_f = fft(sig_2,step_num);
sig2_f = fftshift(sig2_f);
plot(w_k,abs(sig2_f),'-*k')

input_f = (sig2_f)./(sig1_f);
% truncating higher freq
input_f(sig1_f<0.1) = 0;
plot(w_k,abs(input_f),'-*g')

input1 = ifft(input_f);
input1 = ifftshift(input1);
figure % input
plot(x,abs(input1),'*-k')