How can I evaluate this Fourier-transform?

I am trying to evaluate the Fourier-transform of a complex function. I have tried using fourier(_):

    b=30;
    c=1;

    syms t;

    A=exp(-t.^2/(2*c^2)+i*b*(exp(-t.^2/(2*c^2))).^2)

ft_A=fourier(A)

which just gives me the result:

    A =

exp(exp(-t^2)*30i - t^2/2)

ft_A =

fourier(exp(exp(-t^2)*30i - t^2/2), t, w)

Instead, I think i need to go with integral(_) since i suspect that the Fourier transform does not have an analytic solution:

b=30;
c=1;
A=exp(-t.^2/(2*c^2)+i*b*(exp(-t.^2/(2*c^2))).^2)
fun=@(t,w) A.*exp(i*w*t)
q=integral(@(t)fun(t,w),-Inf,Inf)

This dosent work. The resulting error is:

Undefined function or variable 'w'.

Error in ft>@(t)fun(t,w)

Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 103)
        [q,errbnd] = vadapt(@minusInfToInfInvTransform,interval);

Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

Error in ft (line 5)
  q=integral(@(t)fun(t,w),-Inf,Inf)

I guess I need to define w as a vector and then make a new vector where each entry is the integral "q" for a given entry of the w-vector, but how do I do that?

Answer 1

[Abhishek Ballaney]

https://www.mathworks.com/help/matlab/ref/fft.html

Answer 2

[Torsten]

b=30;
c=1;
fun=@(t,w)exp(-t.^2/(2*c^2)+1I*b*exp(-t.^2/c^2)).*exp(1I*w.*t);
q=@(w)integral(@(t)fun(t,w),-Inf,Inf,'ArrayValued',true);
q(1)

Best wishes

Torsten.