FFT inside a specific interval

Hello

I have a frequency and temporal domain.

And a vector linked to frequency domain.

I would like to FFt this vector but inside a specific frequency interval. And I don't know how to reconstruct the temporal vector...

FWHM=140e-15/1.76; 
Tduration=FWHM./(2.*log(1+sqrt(2)))
phy.Tcav =1/Trep;

num.n=1*2^17; 
num.tspan =10000*FWHM*1.76 
num.dt=num.tspan/(num.n-1); 

T = zeros(1, num.n);
for k=1:1:num.n
    T(k)=(k-1)*num.dt-num.tspan/2;
end

DeltaT=T(2)-T(1); 
fmax=1./(DeltaT); 
fmin=1./(T(num.n)-T(1));
num.fspan=(fmax-fmin);
F=linspace(-num.fspan/2,num.fspan/2-num.fspan/num.n,num.n);
num.f=fftshift(F);

wabs=2.*pi.*fftshift(num.f);

A=0.1.*sin(10e-12.*(wabs))

Lim=1500:3500

A2=0.1.*sin(10e-12.*(wabs(Lim)))

plot(wabs(Lim),A2)
figure
plot(T(Lim),abs(fftshift(fft(A2))))

I know that i need to recreat T, from wabs(ini) and wabs(final) but can't found the tricks

If someone has an idea

Regards

[William Rose]

@MartinM, YOur code does not run because Trep is not defined.

Answer 1

[MartinM]

FF=F+phy.fo;
df=FF(1500)-FF(1499);
dt=1/df/length(Lim);
t=dt*linspace(-(length(Lim)-1)/2,length(Lim)/2,length(Lim))

plot(t,abs(fftshift(fft(A2))))

Not perfect,

but looks ok

Is it better if length(Lim) is a nextpow2?