graphing a fourier transform function

I have a function: f=gaussmf(x,[3,10]), and wanting to plot the magnitude if its fourier transform. I am defining the frequency, s, to be s= x*(1/N). x is my independent variable vector for the original function and goes from 0:250. N is my number of x points being input into the original function, which in this case is 251. I am wanting to plot the magnitude of my FT as a function of s.

When I do this I am using the fftshift(FT(f)) but I want to be able to see my plot in its original location along s, not shifted along the s-axis, where the peak is not in the 'correct' location along the s-axis.

What I am trying to say is when I plot fft(FT(f)), I am only seeing the tails of the FT plot. I simply want to 'shift' the plot so I can see the entire curve along its original location, however I don't want to shift the function along the s-axis.

Answer 1

[Matt J]

I don't quite understand what you want, but if you are using f=gaussmf(0:250,[3,10]) to construct f,then the left tail of the Gaussian looks like it would be highly under-sampled. That may be why the shape of the FFT is not as you expect.

If f is centered at 10, you probably want to sample symmetrically around 10

f=gaussmf(10+(-126:126), [3,10])

although why you don't simply just center the gaussian at zero is unclear to me.

 f=gaussmf(-126:126, [3,0])

Since you only want the magnitude spectrum, shifting the peak to x=10 has no effect and just complicates things.

[richard]

The function f is basically zero everywhere except around x=10. So I can plug in basically x=0:20 to plot out my f just fine.

But are you saying the x=0:20 wont cut it for my Fourier transform plot? I am using frequency,s, for my FT plot, which involves using x.

The left tail of my f looks ok, but are you referring to the FT plot when you say 'left tail'?

I think you're instructions are getting the results I want, but I'm a little confused on what you meant by undersampling. Are you saying my f is undersampled or my FT is undersampled?

[Matt J]

Never mind what I said about undersampling, although I do think sampling x more finely gives a noticeably smoother plot of gaussmf(x,[3,10]). But anyway, when I run the code below, I get a nice Gaussian-looking magnitude spectrum centered at s=0 ... all as expected. If this is not what you're after, you can use this is as basis for explaining what you're doing differently.

    %Axes

    x=linspace(0,250,501);  %x-axis

      N=length(x);
      dx=x(2)-x(1);
      ds=1/N/dx;

    s=( (0:N-1) -ceil((N-1)/2) )*ds;  %freq axis

    %Signals

      G=@(x,sig,c)exp(-(x-c).^2/2/sig^2);    

    f=G(x,3,10);
    F=fftshift(abs(fft(f)*dx));

    %Plots

    figure(1);
    plot(x,f);

    figure(2);
    plot(s,F)