?Sow

1D and 2D Discrete Fourier Transform

The question is what do the transform basis look like

DFTBasis[k_,n_,1]:= Table[ (E^(((2π I)/n)k j )),{j,0, n-1}]
DFTBasis[{k1_,k2_},{n1_,n2_},2]:= Table[ (E^(((2π I)/n1)k1 j1 ))(E^(((2π I)/n2)k2 j2 )),
{j1,0, n1-1},
{j2,0, n2-1}
]

ListPlot[ {Im[DFTBasis[4, 24,1]],Re[DFTBasis[4,24,1]]},
PlotStyle->PointSize[0.02],
Joined->True,
Mesh->All]

ListDensityPlot[ Im[DFTBasis[{1,0},{24,24},2]]]
ListPlot3D[Im[DFTBasis[{1,0},{24,24},2]]]