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...