About wlog...
wlog is a tool to analyze signals using wavelets. The wavelet tranformation has the property that it "divides"(or "decomposes") a signal in "smooth" S and a "discontinuous" D part. The tool is experimental but can be used to measure the smoothness (and noise-levels) of a signal. How the tool works
The best thing to do in finding out how the tool works, is to select a Sinus from the Signal menu: This visualises the wavelet decomposition of a smooth sinus signal.
Select the 'S-component' item from the Watch menu: This shows the Smooth S part of the signal that is decomposed. Make sure that 'Octave 1' in this menu is selected and you will see a smooth black sinus passing by on the screen.
By adding different octaves on the screen you see the daub4-wavelet decomposition of the smooth part of the signal on different scales. From octave 7 on, this signal is totally decomposed, leaving nothing but a flat line.
NOTE: You may notice that the higher the octave, the more 'blockier' it becomes. This has to do with the synchronisation as higher octaves signal have less datapoints than the lower levels. Select the 'Octave 3' from the Synch menu to lock the update speed of the display to a reasonable value.
Now select the discontinuous D component of the signal in the Watch-menu. Run over the different octaves and you see the following important feature of wavelet decomposition: for small octaves, the D(iscontinous) signal is very small (bcs. a sinus is a smooth signal, there is little discontinuity). This signal grows for higher octaves there is more and more in the D-part bcs. as the scale is growing, there is more and more discontinuity. Up till octave 6: the full sinus signal. This scale is the point were the whole signal is decomposed as in the D part. There is no D signal left after octave 6, bcs the wavelet decomposition reuses only the Smooth part of the signal.