Krav
Head-Fier
- Joined
- Jun 18, 2010
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I personally never believed this "SACD equals CD" nonsense, because on my system the difference between the two is like night and day.
It got me thinking why some people believe CD can even theoretically be equal to SACD (or, say, 96/24 recordings), and I realized that those people are victims of some gross misconceptions:
(1) The Nyquist Theorem. For those who understand what the theorem actually proves, it is patently obvious that the sampling rate of 44.1KHz is not sufficient to accurately record and reproduce live sound. An excerpt from http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem: "In essence, the theorem shows that a bandlimited analog signal that has been sampled can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency in the original signal ... The theorem assumes an idealization of any real-world situation, as it only applies to signals that are sampled for infinite time; any time-limited x(t) cannot be perfectly bandlimited. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world signals and sampling techniques, albeit in practice often a very good one."
(2) The myth of 16 bits covering the whole human hearing dynamic range. 1 bit of encoded signal amplitude is roughly equivalent to 6 db. Since the bit of a sample code word and decibels are both logarithmic quantities, 16 bits are equivalent to 6 db * 16 = 96 db, wich is indeed the range of a typical 44/16 DAC. The dynamic range of hearing, however, is 130 db: http://hyperphysics.phy-astr.gsu.edu/HBASE/sound/earsens.html. So, even in the case of pure sine wave, 96 db is not sufficient to cover the whole dynamic range. 24 bits fare much better: 6 db * 24 = 144 db. But wait, it gets even more interesting...
(3) Forgetting about multiple frequencies. At any given time, human hearing system can distinguish among about 24 different main frequencies (overtones are perceived as parts of the main frequency). Add a one more in between, and it will fuse with the two adjoining frequencies, the tree being perceived as one. This is actually a good news for recording, as practical music recordings don't usually contain over 24 main frequencies at any given time, and typically much less.
Now, imagine visually adding those frequencies together to form the resulting signal that is to be digitized. Let's don't take overtones into account for now, as their amplitudes are usually (but not always!) significantly lower. Imagine that at certain point in time all of these 24 sine waves are at their maximum positive amplitude. The resulting signal would have to be at 24x the amplitude of maximum allowed amplitude of an individual wave, which is roughly 6 db * 4.5 = 27 db. Which brings as to the overal dynamic range that is sufficient for reproduction of any practical music of 130 db + 27 db = 157 db!
Now, all of the waves maxing out at precisely same moment is a rare occasion, and if the recording tract clips momentarily, it won't be noticeable to most people, so the 24 bits range of 144 db is almost always sufficient. Still, this phenomenon is one of the reasons professional digital sound processing equipment uses at least 32 bits resolution, 48 bits having been quite common for the last decade, and 64 bits becoming more common now.
(4) Not taking into account multiple channels. SACD is a 5.1 format, that is, it contains 6 channels. Doubling number of channels provides 6 db bost to the dynamic range, so 6 channels can provide roughly 9 db of boost. 144 db (coming from 24 bits) + 9 db (coming from 6 channels) = 153 db, which gets pretty close to the ideal range of 157 db. In practice, two of those channels typically contain ambient sound information, so the overall boost is not that large, yet even 6 db are very helpful. Needless to say, the imaging of a 5.1 system is dramatically better than that of 2-channel one. It adds to the "presence effect". Subjective suppression of unwanted room reflections by the louder back channels also plays its role in creating the "teleportation" feeling, as music sounds much closer to what the artist and recording engineers intended, without room echoes and colorations.
Now, SACD is not an ideal format. Its dynamic range is roughly equivalent to 120 db at 96 KHz sampling rate. And it is not surround enough, 7.1 being much closer to what is needed to provide a full illusion of "being there". So the current champion in home music reproduction is actually Blu-ray. Both DTS-HD master audio and Dolby True HD are capable of lossless recording of 7.1 24/96. I consider Blu- ray a successor to SACD, and, interestingly enough, it was also developed by Sony.
SACD is amazing, yet live music recorded in Blu-ray lossless formats can be jaw-dropping. I think this is the future - live concerts and elaborately mixed recordings rendered in Blu-ray.
Quote:
It got me thinking why some people believe CD can even theoretically be equal to SACD (or, say, 96/24 recordings), and I realized that those people are victims of some gross misconceptions:
(1) The Nyquist Theorem. For those who understand what the theorem actually proves, it is patently obvious that the sampling rate of 44.1KHz is not sufficient to accurately record and reproduce live sound. An excerpt from http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem: "In essence, the theorem shows that a bandlimited analog signal that has been sampled can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency in the original signal ... The theorem assumes an idealization of any real-world situation, as it only applies to signals that are sampled for infinite time; any time-limited x(t) cannot be perfectly bandlimited. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world signals and sampling techniques, albeit in practice often a very good one."
(2) The myth of 16 bits covering the whole human hearing dynamic range. 1 bit of encoded signal amplitude is roughly equivalent to 6 db. Since the bit of a sample code word and decibels are both logarithmic quantities, 16 bits are equivalent to 6 db * 16 = 96 db, wich is indeed the range of a typical 44/16 DAC. The dynamic range of hearing, however, is 130 db: http://hyperphysics.phy-astr.gsu.edu/HBASE/sound/earsens.html. So, even in the case of pure sine wave, 96 db is not sufficient to cover the whole dynamic range. 24 bits fare much better: 6 db * 24 = 144 db. But wait, it gets even more interesting...
(3) Forgetting about multiple frequencies. At any given time, human hearing system can distinguish among about 24 different main frequencies (overtones are perceived as parts of the main frequency). Add a one more in between, and it will fuse with the two adjoining frequencies, the tree being perceived as one. This is actually a good news for recording, as practical music recordings don't usually contain over 24 main frequencies at any given time, and typically much less.
Now, imagine visually adding those frequencies together to form the resulting signal that is to be digitized. Let's don't take overtones into account for now, as their amplitudes are usually (but not always!) significantly lower. Imagine that at certain point in time all of these 24 sine waves are at their maximum positive amplitude. The resulting signal would have to be at 24x the amplitude of maximum allowed amplitude of an individual wave, which is roughly 6 db * 4.5 = 27 db. Which brings as to the overal dynamic range that is sufficient for reproduction of any practical music of 130 db + 27 db = 157 db!
Now, all of the waves maxing out at precisely same moment is a rare occasion, and if the recording tract clips momentarily, it won't be noticeable to most people, so the 24 bits range of 144 db is almost always sufficient. Still, this phenomenon is one of the reasons professional digital sound processing equipment uses at least 32 bits resolution, 48 bits having been quite common for the last decade, and 64 bits becoming more common now.
(4) Not taking into account multiple channels. SACD is a 5.1 format, that is, it contains 6 channels. Doubling number of channels provides 6 db bost to the dynamic range, so 6 channels can provide roughly 9 db of boost. 144 db (coming from 24 bits) + 9 db (coming from 6 channels) = 153 db, which gets pretty close to the ideal range of 157 db. In practice, two of those channels typically contain ambient sound information, so the overall boost is not that large, yet even 6 db are very helpful. Needless to say, the imaging of a 5.1 system is dramatically better than that of 2-channel one. It adds to the "presence effect". Subjective suppression of unwanted room reflections by the louder back channels also plays its role in creating the "teleportation" feeling, as music sounds much closer to what the artist and recording engineers intended, without room echoes and colorations.
Now, SACD is not an ideal format. Its dynamic range is roughly equivalent to 120 db at 96 KHz sampling rate. And it is not surround enough, 7.1 being much closer to what is needed to provide a full illusion of "being there". So the current champion in home music reproduction is actually Blu-ray. Both DTS-HD master audio and Dolby True HD are capable of lossless recording of 7.1 24/96. I consider Blu- ray a successor to SACD, and, interestingly enough, it was also developed by Sony.
SACD is amazing, yet live music recorded in Blu-ray lossless formats can be jaw-dropping. I think this is the future - live concerts and elaborately mixed recordings rendered in Blu-ray.
Quote:
