Finer and Coarser Resolutions :: Advanced Concepts (Wavelet Toolbox)

Wavelet Toolbox

Finer and Coarser Resolutions

The organizing parameter, the scale a, is related to level j by . If we define resolution as 1/a, then the resolution increases as the scale decreases. The greater the resolution, the smaller and finer are the details that can be accessed.

j
10
9
...
2
1
0
-1
-2

Scale
1024
512
...
4
2
1
1/2
1/4

Resolution
1/2¹⁰
1/2⁹
...
1/4
1/2
1
2
4

j	10	9	...	2	1	0	-1	-2
Scale	1024	512	...	4	2	1	1/2	1/4
Resolution	1/2¹⁰	1/2⁹	...	1/4	1/2	1	2	4

From a technical point of view, the size of the revealed details for any j is proportional to the size of the domain in which the wavelet or analyzing function of the variable x,

is not too close to 0.

Wavelet Decomposition: A Hierarchical Organization Wavelet Shapes