Wavelet Transform of Signal with 'noise'.

Cuthbert Nyack

One of the potential uses of wavelets is the identification of low level signals buried among components with larger amplitude. This applet attempts to show what is meant by this. The signal has frequency w1 with amplitude 1 and a component at w2 with amplitude a. Both signals occuring at the same time.

The parameter values (2.0, 1.0, 4.0, 20.0, 1.0, 5.0, 90.0, 1.0, 80.0, 0.5) show the signal at 90rad/s with amplitude 0.5 barely visible on the scalogram. However this is because the scalogram is normalised to its largest value.
To see the smaller signal change the parameters to :-
(2.0, 0.3, 4.0, 5.0, 1.0, 5.0, 90.0, 1.0, 80.0, 0.5). This moves the larger amplitude out of the area of the scalogram. If now the amplitude a of w2 is reduced to 0.01, the signal still remains clearly visible on the scalogram although not on the signal. The same result can be be obtained by amplifying a portion of the scalogram.

When enabled, the following gif image show how the applet should appear:-

The following applet amplifies by mag an area between nx,ny and nx + ndx,ny + ndy shown by the white box.

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