Inverse Fourier Transform Using ifourier command

Hi! I have a quick question on the ifourier command. I am currently trying to take the inverse fourier transform of the following function.

I can get the following answer but I am having trouble with plotting.

ifourier gives me -> -(2*pi*t*sign(t) + 2*fourier(cos(w)/w^2, w, -t))/(2*pi)

I would greatly apprecaite any help on trying to get this to plot. The graph for the original function should look something like this.

Thanks again

Answer 1

[Paul]

Sometimes simplify is needed:

syms w t
X(w) = 4*sin(w/2)^2/w^2;
x(t) = ifourier(X(w),w,t)

x(t) = 

x(t) = simplify(x(t),100)

x(t) = 

fplot(x(t),[-2 2])

[William Trace Lacour]

When can you tell that you need a simplify? Otherwise that fixed it. Awesome!

[William Trace Lacour]

and I guess why is it needed?

[Paul]

Don't know why it was needed. I suppose in this case it might have to do with whatever rules and tansforms the Symbolic Math Toolbox uses for fourier()/ifourier(). Sometimes one just has to try things. simplify() is usually a good place to start. In other cases, rewrite(), expand(), etc. can be helpful.