Fourier Transform of a Gaussian Pulse

1. Feb 3, 2013

cytochrome

1. The problem statement, all variables and given/known data
Consider a Gaussian pulse exp[-(t/Δt)^2/2]exp(i*w*t), where Δt is its approximate pulse width in time. Use the Fourier transform to find its spectrum.

2. Relevant equations
The Fourier transform of a Gaussian is a Gaussian. If a Gaussian is given by

f(t) = exp(-t^2/2)

then its Fourier transform is

F(w) = sqrt(2 * pi)exp(-w^2/2)

3. The attempt at a solution

I'm confused by the relevant equations (given by professor) because the exponents are not dimensionless... Nonetheless I just plugged and chugged to get

sqrt(Δt)exp^(-(pi * Δt * w))^2

since this creates a dimensionless exponent. I'm not sure where to include the 2 from the original Gaussian though...

2. Feb 4, 2013

rude man

Convolve your Gaussian transform with the transform of exp(iwt).

3. Feb 4, 2013

vela

Staff Emeritus
Can you show your work? It looks like you made some algebra errors along the way.