Yes, and once you're done with all the lossy digital filtering and processing at the mastering level and you're ready to ship out the music for the listener, you do some straightforward interpolation, cut the 192khz sampling down to 44khz and in the 0-20khz range there will be no information loss. That's the theorem.
If your DAC really wants to see 4N sampling inside itself then it can internally upsample your N sampling rate, fitz around with it, then downsample it before sending it back out.
If your DAC stage does not do a good job of that then you get a better DAC stage. If someone is ready to suggest that the current DAC stages do not do a good job of that then I'm all ears but there needs to be some concrete evidence of that, instead of "I can just hear it". The folks that make ic chips work to spec and if they screw it up then, in principle, said screwup can be measured and improved upon.
The problem is that there seems to be some synergy between not understanding the theorem and hearing something that contradicts it. You can dance around the theorem all you want but it's a theorem, it's not going anywhere. All the information required to fully reproduce N hz is available by sampling up to 2N hz. If your device is not availing itself of all that information then the device can be improved until it does; upsampling will not add any useful information.
The other wild goose chase is about how we hear better if the stuff up around 40khz or so is available. Well that takes care of any significant listening distance from the soundstage, such as the several hundred feet that separate some very happy listeners from the conductor at the Disney here in L.A. whenever I go to hear the symphony. It also takes care of all those centuries of measuring human hearing that indicate that 20khz is pretty much what you're going to get.
Someday our pets will learn how to play the synthesizer and make up their own music and they will certainly demand that octave between 20khz and 40khz. When that day comes, we will have to accomodate them.
I'm not going to argue with anyone that they don't hear what they say they hear, that is a difficult path to put it mildly. But theorems are theorems for very good, airtight reasons.
There is another part to this that is being overlooked.
Set aside the arguments about the frequency extension and noise floor (as well as the caustic comments about pets playing music), and the issue that remains is the one of the reconstruction of the analog waveform from the digital bit stream.
From Wikipeda:
What is a 'bit' of data? “In computing parlance, bit is the abbreviation for a single binary digit, represented by a 0 or a 1. A word is a binary number with more than one digit. Binary numerics are base-2; thus, each digit can only be a 0 or a 1. In comparison, traditional decimal numerics are base-10, having digits that can only be 0 through 9. For example, the 16-bit binary number 0110111110111010 is equivalent to the 5-digit decimal number 28602. The number of bits per word is simply how many digits there are in the corresponding number. The words in commonly used PCM digital audio formats are 8, 16 or 24 bits long. Larger words have higher resolution. The resolution of a 16-bit system can be calculated by using 216 which gives a value of 65,536. A 24 bit system (224) has a resolution of 16,777,216.”
Calculating values An audio file's bit rate can be calculated given sufficient information. Given any three of the following four values, the fourth can be calculated.
Bit rate = (sampling rate) x (bit depth) x (number of channels)
E.g., for a recording with a 44.1 kHz sampling rate, a 16 bit depth, and 2 channels (stereo):
44100 x 16 x 2 = 1411200 bits per second, or 1411.2 kbit/s
The eventual file size of an audio recording can also be calculated using a similar formula:
File Size (Bytes) = (sampling rate) x (bit depth) x (number of channels) x (seconds) / 8
E.g., a 70 minutes long CD quality recording will take up 740880000 Bytes, or 740MB:
44100 x 16 x 2 x 4200 / 8 = 740880000 Bytes
The reconstruction of the analog waveform between the extremes of frequency response and dynamic range is why SACD and DVD audio should, can, and does sound better than CD. There is “more information” to reconstruct the waveform.
Check out the following:
http://www.indiana.edu/~emusic/etext/digital_audio/chapter5_rate2.shtmlAlso, the analog smoothing is at play here: From the indiana.edu website:
" Because the output of a DAC creates a staircase wave (as in the sampling rate diagram of the previous module) instead of a smoother analog one, a smoothing (lowpass) filter tuned to the sampling rate acts to reduce the sharpness of those steps and the unwanted frequencies they can produce. The reason some super high-end audio applications have gone to not only 24-bits, but also to a 96K or 192K sampling rate is to make sure the roll-off of those filters—and the ADC anti-aliasing filters—are not in the audio range at all."
