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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

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.


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