What is HD matrix surround™?
It's a discrete multichannel track, originally matrixed in a stereo sound, and then hardware decoded (hence the HD) using the best, and rarer, matrix hardware decoder.
It is matrixed, and therefore not discrete.
Matrix encoding does not allow one to encode several channels in fewer channels without losing information: one cannot fit 5 channels into 2 (or even 3 into 2) without losing information, as this loses dimensions: the decoded signals are not independent. The idea is rather to encode something that will both be an acceptable approximation of the surround sound when decoded, and acceptable (or even superior) stereo.
via https://en.wikipedia.org/wiki/Matrix_decoder
But will it sound better than, for example, Dolby Pro Logic II?
Albeit DPL II is a great matrix surround decoder, some older technology *may* sounds better, or in a different way... at the end:
Reading the info at https://en.wikipedia.org/wiki/Dolby_Pro_Logic , I can conclude it will ONLY sound better (or more discrete) than DPL2 if :
(It was thouroughly tested and checked on a DPL1 system to make sure that the artefacts and intent sound acceptable OR no discrete surround mix exists) AND (Only during section when the steering/gating system is active)
I am assuming that the decoder is single-band. A multiband decoder will go somewhat towards DPL2
When the gating system is not active (ie, cannot decide btw M/S and L/R dominance), a DPL2 decoder would do better as it can steer effectively 128 to 1024 (or more) bands depending on the FFT size.
there are some interesting plugins for popular software like Foobar2000, that decode somehow a matrixed track;..., but it *seems* hardware decoders produce decoded tracks of better quality.
Software decoders are typically free, you can make one fairly quickly (based on consumer DPL1), but would not sound goot/discrete. Some Proprietary software decoders will sound better than the free ones, because they put in more effort to make it sound goot (FFT/active matrix, etc). FFT takes much more effort to figure out what is right, and how to do it, etc.
I'll quote DTS Neural upmix (used FFT) as one of the best surround upscalers. It is proprietary (&paid), but easily available. It works as well upscaling normal stereo as on matrixed stuff. I also typically put on additional DSP to process the back to move transients back to the front, to give more discreteness (QQ Mashtactic).
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E3:
I beleive it is possible to make a DPL1 Pro decoder in software, but I have never come across documentation comprehensive enough to determine the gating thresholds/etc. OTOH, I can probably figure out the thresholds for DPL2 decoding because I know FFT & DTSnu well enough.