6. What are the basis functions in two dimensions?

They look like this.

Do[Print[j, k] ; ListPlot3D[Outer[Times, dct[[j, All]], dct[[k, All]]]],  {j, 1, n}, {k, 1, n} ]

11

[Graphics:../HTMLFiles/index_34.gif]

12

[Graphics:../HTMLFiles/index_36.gif]

13

[Graphics:../HTMLFiles/index_38.gif]

14

[Graphics:../HTMLFiles/index_40.gif]

21

[Graphics:../HTMLFiles/index_42.gif]

22

[Graphics:../HTMLFiles/index_44.gif]

23

[Graphics:../HTMLFiles/index_46.gif]

24

[Graphics:../HTMLFiles/index_48.gif]

31

[Graphics:../HTMLFiles/index_50.gif]

32

[Graphics:../HTMLFiles/index_52.gif]

33

[Graphics:../HTMLFiles/index_54.gif]

34

[Graphics:../HTMLFiles/index_56.gif]

41

[Graphics:../HTMLFiles/index_58.gif]

42

[Graphics:../HTMLFiles/index_60.gif]

43

[Graphics:../HTMLFiles/index_62.gif]

44

[Graphics:../HTMLFiles/index_64.gif]

dct

RowBox[{{, RowBox[{RowBox[{{, RowBox[{1., ,, 1., ,, 1., ,, 1.}], }}], ,, RowBox[{{, RowBox[{0. ... [{{, RowBox[{0.382683, ,, RowBox[{-, 0.92388}], ,, 0.92388, ,, RowBox[{-, 0.382683}]}], }}]}], }}]

dct//N//MatrixForm

( 1.` 1.` 1.` 1.` ... 0.38268343236508984` -0.9238795325112868` 0.9238795325112865` -0.3826834323650899`

idct//MatrixForm

( 0.25` 0.46193976625564337` 0.35355339059327373` 0.1913417161 ... 0.25` -0.46193976625564337` 0.3535533905932738` -0.19134171618254492`

Created by Mathematica  (April 1, 2004)