This would be a niche-use application, but it would be cool to be able to upsample and re-dither 16-bit 44,100 lossless audio to 24-bit 88.2 / 96Khz with the missing harmonics/overtones/resonant frequencies added back in, regardless of processing power the calculations would take. The result could 'sound' better/smoother due to lack of modular distortion that can occur when simply recording at a high sample-rate.
Of course, I realize this is a touchy subject for some people, but hey, if we can do the math I say, why not? There used to be a piece of software that would do this called 'Any Time' but it seems to be long-gone. Used to take about an hour to calculate one audio track. Of course with my 20-core workstation, shouldn't take nearly as long
I don't know of anyone else out there who has done it since.
The results on a frequency analyser, at least visually, were pretty impressive.
I included a result below, this took 15 hours
to complete as the program is only single-threaded
From the Help-file:
"Under [ High frequency range extrapolation ] you can enable a unique feature that adds over-tones to the upper frequency range (this is only applicable when decreasing the pitch and/or increasing the sample rate where an otherwise "empty" upper frequency region would otherwise be present). It does this by analyzing the input audio and determine the both highest component-tones, and the "frequency envelope" at every instance, then extrapolating the frequency envelope upwards and synthesizing a series of over-tones. The amount of audio energy in the synthesized overtones can be controlled by a Spectral slope parameter (this is expressed as a "dampening per octave factor"). You can also control if all harmonic over-tones or only a select few (only even over-tones, or only a geometric series of over-tones) shall be synthesized. Note that the program will only produce harmonic overtones - i.e. ones that sound good to the ear! There very few other programs that can extrapolate higher frequencies (e.g. one is used in the "mp3Pro" or "AAC+" formats, where they call it "synthetic bandwidth extension"), and in our experience far from all of those few existing seem to even obey that simple principle of producing harmonic over-tones..."