# 2D Fourier transform

• Dec 1st 2007, 06:38 AM
lavian
2D Fourier transform
how can I find the 2D FT for this problem

μ
(x, y) =1/a exp(− pi x^2a^2 )1/b exp(− pi y^2b^2 )

• Dec 1st 2007, 08:05 AM
CaptainBlack
Quote:

Originally Posted by lavian
how can I find the 2D FT for this problem

μ
(x, y) =1/a exp(− pi x^2a^2 )1/b exp(− pi y^2b^2 )

$\displaystyle \mu(x,y)$ is seperable so you can write $\displaystyle \mu(x,y)=\eta(x) \nu(y)$.

Then:

$\displaystyle (\mathcal{F}_2 \mu)(u,v) = (\mathcal{F}\eta)(u) (\mathcal{F}\nu)(v)$

RonL
• Dec 1st 2007, 09:55 AM
lavian
thanks CaptainBlack
but I am stil confused
Do you mean I should find the FT of μ(x) and FT of μ(y) and then multiply them together
I do not know from where you get the variable "u".
• Dec 1st 2007, 02:25 PM
CaptainBlack
Quote:

Originally Posted by lavian
thanks CaptainBlack
but I am stil confused
Do you mean I should find the FT of μ(x) and FT of μ(y) and then multiply them together
I do not know from where you get the variable "u".

$\displaystyle u$ and $\displaystyle v$ are the two special frequency variables coresponding to the $\displaystyle x$ and $\displaystyle y$ variables.

I don't know what you thing $\displaystyle \mu(x)$ and $\displaystyle \mu(y)$ mean $\displaystyle \mu$ is a function of
two variables.

RonL