- #1

- 4

- 0

Find the Fourier transform F(w)=integral from -infinity to infinity of f(t)e^(i*w*t)dt

f(t)=e^(-t^2/a^2)

i=sqrt(-1) w=omega=constant a=constant

This looks sort of like a gaussian integral:

integral of e^(-a*x^2)dx=sqrt(pi/a)

but I couldn't see how to do it...

The answer given by the book is sqrt(pi)ae^(-a^2*w^2/4)

Anyone know how to do this??