Excellent, than you should be able to read this and understand how this works.
Digital audio is sampled like this:
Is susceptible to this:
Repaired like this:
Encoded into this:
and the whole process is reversed in the DAC to produce the desired output. The quality of the dac's power supply, power isolation, sampling frequency, master clock source, bit depth, etc are all VERY important for reconstructing the electrical impulses we call "analog signal". Approximation? Yea, I guess you can put it that way... It's a crude way to put it though since the entire scheme is powered by MATH. None of this would be even remotely possible without math. To say that math and engineering is not applicable in audio is ignorance at it's finest.
Let me put it in terms you mechie might understand.
Try designing a skyscraper without math and all the engineering principles you've learned. It would be impossible. You wouldn't make it past the 3rd floor without statics, materials, physics, etc.
Or maybe try to build a bridge without math.... lol.
When did i say math wasnt important? all im saying is that your dacs run on mathematical models and are estimates. what makes those estimates any closer than anything else?
yes so whats the difference between the maths? of digital and analog and how does it transfer to sound. It doesnt. it all so close and close precise it doesn't matter. the models have gotten so good on the low end it is no longer necessary to have the super expensive models bc the tolerance is not much of an improvement. If you say audio is getting better by one half everyday then you will hit a point where the steps dont even matter anymore. We have gotten there.
your logic is that the models are better well im here to tell you that yes they are but by how much? in the past when you needed a dac it was bc you didnt have the horsepower to run the really good models. well now we do and there is no need for such a small buff bc it has all gotten so good. Im not saying dacs dont do anything they do, but it is so small its worthless.
Actually....it does. You know what made lego successful? Tight tolerances and revolutionary plastic casting.
False. There is always a spectrum of quality and a range of tolerances. Much like how there are different quality and range of pretty much any consumable good on the market.
I didn't say that. The overall change is very slow. There will always be a wide range of quality among what's available.
You're here to tell ME? This is what I've been trying to tell YOU.
No. Now you're talking about amps. That's another topic and less applicable since the OP isn't buying a high impedance set.
There will always be a range of quality with the higher end showing diminishing returns. Different people are able to appreciate those small returns at different levels and some make it higher up the curve than others. I have experience at a wide range of levels allong this curve and in my first response suggesting a good DAC I recommended ones that are a good match for where $200 headphones generally fall along that curve.
You're position is that since YOU don't appreciate anything above a certain level on the curve, the rest of the curve is bunk and anybody that has a trained ear is lying and claims to appreciate even the small incremented returns is lying.
HOLY SHIT im not saying there inst a difference I am saying the difference is so small it really doesn't matter. Go have some one blind test you with and with out a dac. I bet you cant tell. they have done this test so many times and it doesnt matter. here have fun http://www.tomshardware.com/reviews/high-end-pc-audio,3733.html