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Sooo .. I've been thinking about this stuff. We all know that we sound different from what we hear of our own voice. It is easy to find out how others hear us by recording oneself and listen to it.

But what about the other way around?

Is there a way to transform our voice in a way that others can hear us as we perceive our own voice? I find it to be a quite interesting question. Sadly I couldn't find anything on the web after a couple google searches. Has nobody thought about this or is it impossible because of some reason that I'm not seeing?

Any leads on this would be appreciated :).

It is not impossible but it is not going to be a walk in the park too.

What you would be trying to do is to add to the voice signal, those vibrations that are delivered to the ear via the bones and are not accessible to anyone else.

But this is easier said than done in an accurate way.

Sound propagation through a medium depends very much on its density. Sound travels at ~1500m/s in water and with less dissipation than it travels in air (~340m/s). Bone is denser than air, therefore sound should travel faster through bone. This means that "your" sound begins to excite your ears first, followed by the sound that you perceive via the "normal" air channel. In reality, bone has an internal structure that might be affecting the way different frequencies pass through it but at the range of frequencies we are talking about, perhaps we can consider it as an equivalent solid. This can only be approximated because any attempt at measurement would have to be invasive but also because hearing is subjective.

Hearing, or the perception of sound is a HUGE contributor of difficulty here. The ear itself, the outer ear (the visible bit), the canal and the inner mechanism work together in very complicated ways. This is the subject of psychoacoustics. One example of this complex processing is phantom tones where the brain is filling in things that are supposed to be there. The brain itself may have already developed ways of isolating the self-generated signal that are inaccessible to us yet.

But, a simplistic (simplistic!) way to witness the differences between being the listener of your own sound and not is this:

Record a short and simple word (e.g. "Fishbone", a word that has both low frequencies (b,o,n) and high frequencies (F,sh,i,e)) with a bit of silence and loop it through an equaliser through your headphones. Start playback and synchronise your self uttering the word with the recording (so, something like "Fishbone...Fishbone...Fishbone..."). Now try to fiddle with the equaliser until what you hear and what you utter are reasonably similar.

At that point, the settings on the equaliser would represent the differences between the sound and what it is perceived through you and theoretically, any other speech passed through that equaliser would simulate how it arrives at your ears, as if you would have generated it with a source inside your body.

Hope this helps.

The most practical attempt that I am aware of is by Won and Berger (2005). They simultaneously recorded vocalizations at the mouth with a microphone and on the skull with a homemade vibrometer. They then estimated the relevant transfer functions with linear predictive coding and cepstral smoothing.

Before you get disappointed, let me suggest you to try another approach.

As I see it, you have two very different parts: knowing the equalization to do (personalized to each person), and applying it to a particular signal (your voice).

1st part: model of the internal human hearing system

There are professionals who are working to collect data on that, standardize that process, and so on. Afaik, there are efforts to develop measures and graphs beyond the classic audiogram (which measures air and bone signals). Some of them are "listening tests" (more subjective, but interesting as well).

Align to these professionals. If you follow their work, you just need their results. Let them do the heavy lifting. They know their part, which took them dozens of years of investigation. They are advancing in the knowledge you need.
Which is: a sort of audiogram to measure how someone hears 'within'. I bet they are graphing that. And you just need that graph.

2nd part: simulation

I've done something similar to what you try to do. From the audiogram of any person, you can hear on your own like him/her. This is done with ffmpeg. You can check it out here: comomeoyes.com

Basically, you record your voice, and an algorithm equalizes it with your personalized audiogram. This way, you can enter the audiogram of a person with hearing loss, and listen for yourself how he/she hears you.

I understand you would like to do the same, but with a different audiogram, one that models how the internal hearing system equalizes the sound.

I bet such kind of audiogram could already exist, and audiologists, medics, doctors in otorhinolaryngology, researchers and such may be discussing on the kind of accoustic tests to do to get the data they need to model a useful graph from the measurements.

Good luck. Your attempt could help others.