Since any real sound is by nature a complex sine wave based on the harmonic series, every sound is made up of many simple sine waves. Since a sound is constructed via the combination of these waves, it would be nice to have an algorithm to deconstruct the waves as well.
Prove or disprove that it is possible to define an algorithm that takes as input the equation that represents a complex sine wave made with some number, n, harmonics, or constituent simple sine waves, and outputs each individual simple sine wave's parameters (frequency, amplitude, etc...). Also, if possible, construct the algorithm (though a non-constructive proof is acceptable for proof or disproof).
For example, given the equation for the following complex sine wave, determine the parameters for each individual harmonic that makes it up.
You may assume that the 'music' is static over time (unlike the above picture), such as an instrument holding (perfectly) a tone.
Note, this website has a pseudo-tangential heuristic solution, and this site might provide some background.