A time-frequency puzzle

Illustrations of Time-frequency analysis: wavelets and adaptive approximations

As a practical example of "what the time-frequency analysis is all about" we construct a puzzle:
let's make a signal constructed from known components - add them all together - and see if one could guess what components we used! That can serve as a metaphor for a big part of Signal Processing - explain a signal through known functions. So, we'll use some canonical shapes:
simulated signal constructed as a sum of components shown below

A - sine wave, C, D and E - sines modulated by Gauss (Gabor functions), B - one-point discontinuoity (approximation of Dirac's delta).
Now let's see how some tools can help us solve this puzzle:

You might like to compare also the signal's power spectrum and spectrograms computed with window lengths 256, 128, 64, 32 and 16 points.

Java applets written by Dobieslaw Ircha.

PLEASE NOTE, that the above examples by no means prove one method's superiority over the others, which is of course impossible on one signal's example. This example signal was generated from the waveforms present in dictionary used for MP decomposition.