🚀 go-pugleaf

singlis@waikato.ac.nz writes:

>Thanks to all who replied about FFT segmentation.

>A Fourier Transform in 1D is a breakdown into the waveform component
>sin/cos terms. This sin/cos waves when added approximate (v. closely) the
>original waveform.

>How is the 2D case explained? Is the 2D transform a sum of "planar" sin/cos
>"waves", or is it more of a breakdown of the horizontal groups of vertical
>transforms?

Due to the separability, you can do row and column transforms after each
other, but you can do it the other way round as well, so this would seem
to be missing the point some way.

Another possibility is to view the term (xu+yv) in the exponential as
a dot product (x,y).(u,v).
If you view (u,v) as a vector, you can interpret the
value at index (u,v) as a complex exponential wave crossing the picture
in direction (1/u,1/v) (or was that (v,u)?) with frequency |u,v|. A real-
valued interpretation (phase and amplitude) would have to take index
(-u,-v) into consideration as well.