How to reconstruct/approximate the lost high frequencies in an audio file after it has been lowpassed?

I know the old Nero wave editor could do this, but are there any specialised/sophisticated applications for this?

Thanks

I imagine what you're looking for is high shelf filter -- any DAW worth its salt should have one. A high shelf filter is basically the same as an amplifier's treble tone control.

-bandpass

That's not what I'm looking for, I meant there is none of the original high frequency content left, like in a lowpassed mp3.
I need a software which can approximate the lost high freqencies based on the existing ones, a bit like spectral band replication but without any extra info about the high frequencies.

Edit: Maybe a bit offtopic, is any software out there which tries to eliminate encoding artifacts (ringing, dropouts...) from an mp3 file?

Creative claims X-FI does it.

One approach would be to take the original signal, pass it through a squaring operation (as in output = input squared), high pass filter the output of the squaring circuit at the roll-off point of the origional signal, and add the desired amount of the high-pass filter back to the source in the desired amounts.

That's cool, but the problem is that I can't implement it That's why I was asking if someone hasn't already made such application. I believe it would be really useful in making a lowpassed audio/audio sampled at a low frequency sound better...

I would try this task on a track just for curiosity.
Not going into theory I would filter a same length "white noise" file with a proper high pass filter to form the missing spectrum the way I think it should look like and then add with the existing file.

But what do you gain by adding noise? That's just filling the frequency "space" for the sake of filling it and seems very counter-productive to me.

What Arnolds suggests is attempting to fill the high frequency "space" with harmonics (that is, integer frequency multiples) of the existing audio spectrum. In this case then at least what you're adding is harmonically related to what's already there, but the idea of just adding noise is pretty pointless IMHO.

What you need is a harmonic exciter. There are many VST plug-ins out there for harmonic excitation (some free), but if you want something "standalone", you can check out Izotope's Ozone.

You could try the free VST plugin "Overtone GEQ" from Voxengo. It should work with pretty much any audio editor

Right! Your search keyword is usually "exciter". The goofy name comes from The Aphex Aural Exciter.

Diamond Cut Millennium ($60 USD) also has an exciter effect. (It might not be as good as Ozone's effect.)

It requires a few steps and some trial & error, but you can also "roll your own" with any audio editor that can do pitch shifting (without changing the playback speed):

1. Back-up your original file!

2. High-pass filter your file. (Use a sharp-cutoff filter. You'll have to experiment, but I'd say 5kHz might be a good starting-point.)

3. Increase the pitch of the high-passed file. (I'd start by doubling the frequency/pitch.)

4. Mix the pitch-shifted high-frequency file with the original full-bandwidth file.

You can experiment with different cut-off frequencies and different amounts (levels) of harmonic mix. And, you can try mixing-in more than one harmonic pitch shift into your file. It's probably a good idea to keep it "musical", buy using pitch shifts that are musically harmonic. You can do some research if you don't know how that... Full multiples are always OK (2x, 3x, 4x, etc)... But, it might not matter... I don't think harmonic dissonance is a big problem at high frequencies.

Ozone is a plug in.

There is a VST plug-in facility for Audacity, so thus far your investment is $0.00. There are a ton of freeware VTS plugins on the web.

The Ozone VST plugin (freeware) appears to have as its basic EFX, a clipper. IOW, it adds odd-order nonlinear distortion.

Voxengo VST plug-in (freeware) apears to have as its basic EFX, a second order distorter.

I said "I would try this task on a track just for curiosity."
Why I haven't done it by now. For two reasons:
I don't need it and I don't relay on my hearing to evaluate the results.
Maybe, it is interesting to mention that being capable of hearing tonal frequencies up to 11 kHz I can recognize a sound having 18.5 kHz bandwidth (mp3 @192 kbps) from its full bandwidth (22 kHz) original - it sounds "metallic". But I think it is not enough.

So, I am offering to do this experiment for someone who is interested in having the results and who is capable of performing suitable hearing tests to evaluate them.

As to the experiment, without a theory, if you high pass some sound you'll get a signal with some spectrum.
If you have another signal with the same spectrum do you thing both signals are different? No, they are not.

The idea of filtering a "white noise" is not mine and I think it works. After all the samples from a "noise" after their filtering are samples from another signal.

It is easy to synthesize a filter to get the high frequency components of sound from "withe noise" samples.
The only problem I see is the transition range of both spectra, low pass mp3 and added high frequency signal.

Thought they had a standalone app for that now? Maybe I'm thinking of RX...

And, yeah, the free exciter I use is called X-Cita. Difficult to use (poor interface), but sounds reasonable, and it's of course Audacity-compatible. I occasionally use it to add a little extra something when attempting to restore low sample rate audio.

This one puts out a mix of even and odd harmonics, generated via asymmetrical clipping.