I have this little question: Imagine some set of let's say 10 sinusoids, defined on the same interval (all with different frequencies, amplitudes, phases).
Then a friend gives you a linear combination of those sinusoids, not the sinusoids themselves. How can you retrieve them?
My question is then how can you find the most "pure" functions. I am wondering if there is some quantity that a function minimizes if it is a pure sinusoid instead of a sum of different sinusoids, and maybe that allows to find the transformation matrix needed to get back to the original sinusoids.
Do you have any ideas? Thank you in advance ;)