I have some software that I am working with now. It does exactly what you want. However we (the software writer) and I are not quite ready to market it.It will show both a waveform, which is not that useful, and a bargraph showing the relative level of each overtone.
As a saxophonist I was surprised to find that the saxophone's second overtone was nearly as strong, sometimes stronger than the fundamental, yet we still identify the fundamental by ear as "the pitch." We don't confuse it with the the second overtone an octave higher.
This software is to be marketed for the analysis of timber, or tone quality... to identify the actual differences in the tones of various instruments, mouthpieces, reeds and players.
Feel free to contact me at tenorman1952@yahoo.com