So let's talk about the Fourier transform in the two dimensional case because all

that MR images we talked will two dimensional or three dimensional.

So we have to talk about two dimensional Fourier transform.

So two dimensional Fourier transform is very similar to the one dimensional case

but it's just extended to another dimension.

So now we will have signal in the image domain as f(x, y).

And then this image domain sooner, can be transformed

to the frequency domain by applying for two dimensional Fourier transform.

And that is denoted as F(u, v) here.

And then F(u, v) can be represented as integration of x,

y original immediate domain signal.

That is multiplied by complex sinusoidal signal, so equal to -j,

2pi ux plus vy, that is integrated as a problem dxdy.

And that is the definition of two dimensional Fourier transform.

And this is definition inverse Fourier transform.

So f(x, y) equals integration of F(u,

v), e to the j 2pi ux plus vy dudv.

So the basic concept is very

similar to the one dimensional Fourier transform case.

So F(u,v) represents a complex

sinusoidal signal in the original image domain signal.

And then f(x,y) so inverse Fourier transform represent the original

image domain signal as a linear combination of complex sinusoidal signals.