What I'd like to do is create headphones that record external audio with a wide frequency range, and remap that range into a range that's human audible.
The only way I can think to do this is to do a Fourier transform on the incoming audio, shift/compress the chart, and then do a reverse Fourier transform to create output audio.
Is there an analog method to do this? Searching "analog methods to compress audio frequency range" is turning up nothing, so perhaps I'm just using the wrong terminology?
If this is not possible. Is there a practical digital approach? My assumption is that it would be to use a sliding DFT, which as I understand it is basically an iterative FFT. Transform the result, and then do sliding DFT in reverse to create audio. However I'm not sure that the last part is actually possible. Is it?