plot of inverse fourier transform

I am trying to plot the inverse fourier transform of a function and I want this plot to be centered at zero. This is the following code that I have:

clear
dx=1;
x=(-45:355)*dx;        %'x' position
N=length(x);

ds=(1)/(N*dx);
s=(0:400)*ds;           %freq position

h1=normpdf(x,0,2);
HS=abs(fft(h1));
MTF=HS;
M=(1-(1-MTF.^2).^244.9)./(MTF);     %function
M1=ifftshift(ifft(M));

plot(x,M1)

I am trying to plot M1 (the inverse fourier transform of my filter, M) vs x. I am converting my filter, M, from frequency space to 'space' space. The problem is when I plot M1 vs x, the function is all the way down at 150 but I want it centered at zero and do not know how to fix it.

Any help will be appreciated

[sixwwwwww]

Do you need just simple manipulation of x-axis? mean you just want to shift x = 0 according to the maximum value in Inverse Fourier Transform?

Answer 1

[sixwwwwww]

If you just need shift the x-axis with respect to maximum amplitude position in your Inverse Fourier Transform spectrum then you can do it as follows:

clear
dx=1;
x=(-45:355)*dx;        %'x' position
N=length(x);

ds=(1)/(N*dx);
s=(0:400)*ds;           %freq position

h1=normpdf(x,0,2);
HS=abs(fft(h1));
MTF=HS;
M=(1-(1-MTF.^2).^244.9)./(MTF);     %function
M1=ifftshift(ifft(M));
[Max, Max_ind] = max(M1);
x_shift = Max_ind - abs(min(x));
x = x - x_shift;
plot(x,M1), xlim([min(x) max(x)])

This shift in space domain corresponds to a constant phase multiplication in Frequency domain