I know what is the end result regarding the sound coming from the surround speakers, but I'd like to know a little more about what kind of processing is taking place in these expansion schemes.

They all try to do the same thing. If it's stereo content like music, I'd rather just listen to stereo. The "music" modes of these all introduce ugly artifacts (maybe Neural THX doesn't, but that one is very front-heavy). What exactly do you need? Mathematical formulas?

With these schemes' "music" modes, you're pretty much limited to what you prefer. There's no objective way that I know to say which is "better". I like Neo:6 music if I had to choose one.

The "movie" modes, though are pretty different. Dolby Pro Logic II has actual content specifically encoded for it, so when you play it, the surround effect is very good. Most notably, PS2 and Gamecube games have this feature. It is pretty great, you do get discrete (enough) 5.0 channels. I'm not sure that DPLIIx has content specifically encoded for 7.1 channels, but IIx is mostly used as a replacement for Dolby Digital EX matrix. I haven't read anything official, but by the way my receiver behaves, I think the DDEX flag is read by most receivers as a DPLIIx flag to expand 5.1 into 7.1. You can still use DDEX manually, but I think it's pretty much the same, haven't found any differences.

For content not specifically designed to be expanded (i.e. non-DDEX content), I don't use DPLIIx, it gave me weird sound sometimes. If a sound was supposed to sound from both side-surrounds to give an impression of "surround-ness", they could come from the rear as if it was a rear center channel.

The other formats' movie modes don't have specifically-encoded content available. The Creative ones specially, I don't give a crap about. I am also a Dolby Headphone fan, which works very well with DPLII.

As far as the actual processing involved, in most cases these algorithms try to separate ambience from direct sounds, using the ambience for playback on your rear/surround speakers and direct sound for front and center. Complexity of these algorithms can range from simple left/right correlation stuff to more elaborate freq-domain processing schemes. I bet you could also use blind sound source separation techniques to obtain more information about sound source location.

Dolby Surround decoding was pretty simple:
Center = Left + Right
Rear = Left - Right, low-pass filter it at around 7 kHz, and delay it by 20 to 50 milliseconds or so. The filtering may have been mostly because the analogish "bucket-brigade" delay lines ran at rather low sample rates.

You can approach this with a passive surround decoder by hooking two rear speakers in series, then wiring 'em across the left and right hot terminals of a stereo receiver. To get the appropriate time delay, put the surround speakers 20 feet or more behind you, if possible. I've watched a few movies with that setup, and at times it was startlingly effective. Dynaco introduced a little box, the QD-1, that did this (with a couple of passive faders) back in 1971.

Dolby ProLogic added some fancier processing and "steering" that does things like reduce the volume of the front speakers when a large surround signal is detected.

Since Dolby has patented their methods, other companies will implement things just differently enough to avoid persecution.

An effect you sometimes got on boomboxes (and I think on certain Carver products) enhanced stereo width by subtracting a little of one channel from the other. Kind of the opposite of the crossfeed circuits that are sometimes used to improve headphone listening.

And then there's the 3D sound processes. This explains them a lot better than I could without plagiarizing Wikipedia: http://en.wikipedia.org/wiki/3D_audio_effect

This is indeed an example of the correlation tricks I was referring to. Subtracting stereo channels leaves you with the uncorrelated, so mostly ambient, signal. Delaying this signal is making smart use of the Haas effect. By keeping the delay below 40 msec. the human auditory system is not able to distinguish between the original and delayed signal. It will however increase the sense of space and improve localization, probably due to some masking effects going on in the ear. Bob Katz's K-Stereo system uses this phenomenon in a recursive way. With every recursion a delayed signal is mixed with the original signal and delayed again. In this way the total accumulated delay will be longer than the Haas delay but every signal signal is delayed by a interval below the Haas delay. This increases ambience, even on mono recordings, without introducing artifacts.



I wouldn't think the newer virtual Dolby and DTS NEO modes will resort to cheap tricks like adding artificial reverb to upmix their stereo signals. Frequency domain ambience extraction and sound source separation require quite heavy maths and processing power. I would assume that the Dolby and DTS R&D departments put quite some effort in making their upmixing algo's sound good.