Here are the reasons for creating and using high-resolution formats:
1. More samples per second. For example, up to 192,000 samples/sec on DVD-Audio compared to 44,100 samples/sec on a CD. More samples means less artifacts or smearing introduced by interpolation between samples. It's like comparing a video at 15 frames per second with motion blur to one at 60 frames per second with motion blur. The one at 60 fps will seem more realistic and less smeared because there's less time for blurring between actual frames.
2. Higher sample rates mean that the cutoff frequency of a device's filter can be pushed into the higher frequencies, further away from the audible spectrum. According to the Nyquist theorem, a CD can represent tones up to 22,050 Hz, around the range of human hearing. However, the filter needs to return to zero before the end of that range. When the first CD players came out in the '80s, manufacturers decided to set the cutoff frequency near the top of the spectrum with a steep slope downward. This is known as a "brick wall" filter because of the slope's near-vertical drop. Unfortunately, the slope was so steep that it caused very audible artifacts and distortion at lower frequencies. Manufacturers then decided on a softer slope that began further back in the frequency spectrum. This solved the problems that the brick wall filter had caused, but also meant that there was a necessary dip in the high frequencies. Now, at 192,000 Hz, the cutoff frequency can be set closer to 96,000 Hz, which means that the audio in the audible spectrum (~20 Hz to 20 kHz) is unmolested by the filter.
3. Higher resolution or bit-depth means that a greater range of amplitudes can be represented. In pulse code modulation (PCM), each pulse can be represented by a 1 or 0. For a CD, which is 16-bit, there will be 2^16 values. 2^24 for 24-bit.
16-bit = 65,536 possible values.
24-bit = 16,777,216 possible values.
Therefore, a 24-bit stream's amplitude is roughly 256 times more accurate than 16-bit.
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Sorry for the long post, but I feel that high-res doesn't get enough respect. Hope you enjoyed it! Maybe it will clear up some concepts for people who are "on the fence" about pursuing new formats.
Edited for accuracy.