Creating odd harmonics without the fundamental I'm interested in creating a series of odd only harmonics, without the fundamental, for audio use.

As an example the input could be a sine wave at specific frequency $f$ and output is $3f$, $5f$, $7f$, etc. - but without the original $1f$.

Since the $1f$ (in a real audio system) is unknown and the input is multi-tone, just filtering the $1f$ out is not an option.

Any idea for replacing an input of $1f$ with an output of $3f$, $5f$, $7f$, etc. ?

Edit: Additional information from the deleted post

Example: Let's assume the fundamental to be anything possible between 100 and 4000 Hz. Whats more, what if the input is multitone (as most music is...). 50 and 425 Hz input simulatenously ??

Im looking for a mathematical function which can recreate any fundamentals odd harmonics, in a multitone input...
Im looking for a mathematical function which can recreate any fundamentals odd harmonics, in a multitone input...


(emphasis by me)

What you ask for is not possible. If you demand multiple tones and complex tones as they appear in music, then your problem leads to a conflict. A complex tone comes with overtones. Even if you have a process that adds odd harmonics to each sinusoidal component, then the even overtones of the fundamental frequency will contribute even harmonics. That is because an odd number multiplied with an even number is again even.

So circumvent that, you would have to identify the fundamental frequency of complex tones first, leading you directly to the problem of polyphonic pitch detection which remains mostly unsolved.

Maybe you should explain what you're really trying to accomplish, as in what the application is that you have in mind. With that information it's quite likely that we can come up with a relaxed set of requirements that can actually be implemented.