Wavelet Levels

The following image shows the x points used in the ellipse with noise added and evenly spaced intervals in green with the wavelet fit shown in red that contains all the levels j = 0,...6. Following that image is the same display except this time the wavelet fit only contains level j = 0. As it can be seen the higher levels add greater detail at a smaller scale, while the lower levels give the overall shape of the curve.

The following is the same graph as above except that wavelets of the higher levels are filtered so that only the ones that effect the right part of the function are used and thus as can be seen only the right side has the finer detail.