Me and my friend, both many years from learning string theory, had a recent debate about it anyway. He said he already partially discounts it because after learning waves, he believes any function, and thus any kind of physical process can be created through a superposition of an infinite sum of waves. Since string theory to our understanding is made up of primarily oscillating strings, he argues that it is a mathematical necessity for string theory to create equations for the physical world, regardless of whether the theory actually is "true" or not.
My understanding is that Fourier analysis can only create arbitrary periodic functions, can it in principal create any real world field or particle, etc.? Besides this, I argued that this might be a pointless question anyway, as if we can create a perfect model of the universe with string theory, then the question of whether the universe is really made of oscillating strings is more of a philosophical question that may not mean anything at all.
Through reading Brian Green's books I know that M-theory at least incorporates more than just strings, but I have no clue as to how things such as branes work, can his argument even apply to these other fundamental objects in string theory?
So my question is, is Fourier Analysis essentially what String Theory is? And if so, does that make it any less of a true physical theory of the universe?