Have you read the HDMI specs?
I can tell you that HDMI uses (up to) 3 channels of balanced serial data onto which things like video and multiple audio soundtracks, and other data is multiplexed at a very high data rate.
You must be a brave man to try and make a circuit to analyze the data stream, extract only the digital audio data then convert to analog, filter and playback.
My honest advice, buy a unit to do this.
It doesn't really seem to be that brave to me. This technology has already been pioneered, I just need to know how they do it. Buy pretty much any entertainment system with a good stereo receiver these days, and it does this. I don't know what magical chip they have inside that does it, but it can be done. And I've see units as cheap as 100 dollars that can do it, so it can't be an expensive component.
I figure if I built this device it would be great if I could just split the HDMI cable from my motherboard, send one to the LCD for video and one to this receiver unit for true 5.1 audio.
They do make HDMI splitters
. Does your receiver have HDMI, or is that what you're trying to build?
If your receiver doesn't have HDMI, I'd consider a 5.1 USB soundcard instead of HDMI.
I think that's the easiest, cheapest, best, way to do it. With a USB soundcard, the right drivers, and the right applications, you should be able to handle any format as well as set-up bass management, etc. If you get one that supports Dolby Pro Logic II, there are "soundfield" options for using the surround speakers with 2-channel stereo. (I have my home theater system set-up for reverb in the rear channels when playing stereo music.)
If your receiver/head unit doesn't have HDMI but you really want to use it, I have some ideas.
I don't have a receiver at all atm. I'm wanting to do this for my carputer so I can take the HDMI out from my motherboard and split it into the individual channels to have connections for the speakers. Instead of doing it the way I have it right now and taking a single stereo left / right output and just duplicating it to the rear speakers and amplifier for the subwoofer. I mean doing that works, I would just prefer a cleaner output that can have better balance adjustment and a proper low frequency line to the subwoofers. The motherboard I'm using does have SPDIF out too, but I think that is just as complex to split to individual channels as HDMI is.
I have seen small devices that can supposedly do what I want, but was hoping to build it myself so that I can make some customizations to it and add a 4x50w amplifier for my door speakers all in one unit. For example this device on ebay claims to be able to do it: http://www.ebay.com/itm/350247932081?ssPageName=STRK:MEWAX:IT&_trksid=p3984.m1423.l2649
Oh and the problem with a sound card is drivers. Right now my carputer is running on Android 4.1, it will not recognize most sound cards. But it does output 5.1 sound through the HDMI (I've tested that using my in home stereo receiver). And my carputer is a headless unit (or rather the carputer is the head unit I guess hehe) currently. The carputer does everything, I'm just using a secondary small amplifier for the door speakers.