I have wave which I'd like to find the equation for which is obviously the result of adding two waves together.
I have tried using Lagrange Interpolation to some success however I was wondering if there was a way to extract the equation for which waves were added to make the wave in the first place.
This is my first time posting on here so I'm sorry if this is in any way not appropriate.
If you have the sum of two wave in the form of $$ y=a\cos(x)+b\sin(x) $$ then, $y$ can be written as $$ y=A\cos(x-\delta). $$ In fact, expanding the last equation as $$ A\cos(x-\delta)=A\Big(\cos(x)\cos(\delta)+\sin(x)\sin(\delta)\Big) $$ the equivalence is guarantee if $A^2=a^2+b^2$ as well $a=A\cos(\delta)$ and $b=A\sin(\delta)$.