rule42
New Head-Fier
Yes, of course. I'm just trying to fit how the time and frequency domains work together in harmony. That should be obvious.
MATLAB is extremely powerful, with a matching price tag. It is updated with new features every 6 months. It includes Simulink, which is peerless for general purpose modeling/simulation. There are some fairly recent, very nice GUI features, but it is primarily command-line. I currently use MATLAB/Simulink and LabVIEW.@SoundAndMotion and @gregorio . Thank you both for the replies. All nice and clear. No, about the right level of complexity for now before I delve into it a bit deeper. I like trying to follow examples through as a way of learning, so do you think that Octave would be the best free tool for that? I've not used Matlab but have some familiarity with Python from over 20 years ago (including Numpy and a little Scipy) and they don't seem too dissimilar. Or stick with Python of course.
(1 and 1a). Gregorio, you deserve a calm, thorough, civil (no insults) response to this part and some previous posts. The back and forth sniping of "yes it is" - "no it isn't" helps no one and reflects badly on both of us, IMHO. Rather than relying on "my take" or "your take" (see below), I'll try to mostly quote directly from published sources. I've read most of [Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the IRE, 37(1), 10-21.] and I've skimmed [Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE mobile computing and communications review, 5(1), 3-55.] and [Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 47(2), 617-644.][1] Who "two"? Me and Claude Shannon, Nyquist and Shannon? Don't forget Stephen Hawking and the there's Wittaker, Kotelnikov and others who contributed or discovered the theorem independently. As for getting our "story straight": You are confusing YOUR inability to understand the story with the story not being straight. The "story" is (again!): The signal IS "completely determined" plus there is ALWAYS some amount of noise; in theory zero noise would require an infinite number of bits and in practise even with an infinite number of bits there is still some amount of noise, due to the laws of physics (Thermal noise for example)! The real issue then is one of how much fidelity: How much of that "completely determined" signal do we want to recover or conversely, how little noise do we want obscuring that "complete determination"? You want to recover a significant amount of the "complete determination" AND use a bit depth which introduces a great deal of quantisation noise. Digital Audio/Sampling Theory allows for this scenario, because quantisation noise is effectively separate from the "complete determination" (perfect signal). The (band limited) "complete determination" can therefore be recovered/exposed (to any arbitrary level above thermal noise limits), by moving/redistributing the quantisation noise away from the frequency band occupied by the "complete determination" (as defined by the Gerzon-Craven Noise-Shaping Theorem). It should be obvious therefore, that you need to provide enough audio bandwidth to accommodate both the band of frequencies occupied by the "completely determined" signal + the band of frequencies occupied by the (redistributed) quantisation noise. The large amount of noise introduced by 4bit quantisation would need to be redistributed over a large band of frequencies, the vast majority of which would need to be in the ultrasonic range and therefore a far higher sample rate would be required to accommodate that audio frequency band.
Why don't you read the EVIDENCE ALREADY PRESENTED? Specifically, page 13 of the Lipsh*tz-Vanderkooy extract linked previously where two examples are given, an example with just 1 bit and another with 8 bits. The latter for instance demonstrates the perfect ("completely artefact free") recovery of the "complete determination" of any signal within an audio band of 0-20kHz with a SNR of 120.4dB using just 8bits, plus a sample rate of 176.4kS/s to redistribute the quantisation/dither noise (to above 20kHz).
1a. Saying it is insufficient does NOT contradict my previous quote of Shannon, it ENTIRELY agrees with it!
2. The game us two are playing is called Science, if you're "tired" and want to play a different game you're in the wrong forum!
3. By "we all" do you mean everyone except you?
3a. But you don't have to?
3b. No, YOU quit saying it's "your take", it is NOT my "take", it's Shannon's "take", I'm quoting him exactly and directly, with nothing added or taken away.
3c. I did not say (Shannon's "take") was incontrovertible, I said it was "logically incontrovertible". The reason our exchange is going nowhere is because you are effectively illogically controverting it! You've presented no evidence al all, only an example which you don't believe is possible but which the evidence I've presented (Lipsh*tz-Vanderkooy extract and the Gerzon-Craven Theorem) indicates it's entirely possible, plus of course, SACD actually demonstrates it!
G
LOL, I thought you were shy about L*i*p*s*h*1*t*z's name, but I see the "bad part" is automatically deleted.
You're welcome.@SoundAndMotion
Many thanks.
(1 and 1a). Gregorio, you deserve a calm, thorough, civil (no insults) response to this part and some previous posts. The back and forth sniping of "yes it is" - "no it isn't" helps no one and reflects badly on both of us, IMHO. Rather than relying on "my take" or "your take" (see below), I'll try to mostly quote directly from published sources. I've read most of [Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the IRE, 37(1), 10-21.] and I've skimmed [Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE mobile computing and communications review, 5(1), 3-55.] and [Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 47(2), 617-644.]
Interestingly, I was originally planning to skip your "reading assignment" [Lip****z, S. P., & Vanderkooy, J. (2004). Pulse-Code Modulation--An Overview. Journal of the Audio Engineering Society, 52(3), 200-215.], but I was curious how Gerzon-Craven differed from the algorithm I posted. I read it and it turns out this is a really nice review. Thanks! Most of my response to you will come from this. It answers pretty much everything. I'll write the calm, thorough, civil response when I finish reading and have a bit more time.
2. If I tell you I have GarageBand on my Mac, and my son and I have played with some of the noises he made with his e-guitar, and therefore I can lecture you on best practices and normal procedure in recording studios (your field), would you get angry, laugh, shake your head... ? I laughed.
3. FYI, "we all" means me, you and the other 7+ billion.
3a. Of course I do. But I'm human and imperfect, and although I admit I'm wrong more than anyone I know (not because it's frequent, but because I find it important), I don't always do so. I should though.
3b. Shannon died in 2001. The only source for "his take" is his own well-written words. When you tell me "what he meant", either directly related to his words, or worse "what he meant" from what he left out, that is "your take".
3c Again, I don't take issue with the Shannon quote w.r.t our discussion; I don't agree with your take regarding bit-depth.
BTW, after carefully reading Lip****z & Vanderkooy, I realize I should not offer to dither or noise-shape, since those were not known and not included at the time Shannon, Nyquist, Whittaker et al. created the sampling theory stuff. Their work survives without dither/noise-shaping. But I'll dither (TPDF) and noise shape with my algorithm or any you provide anyway, if you want. (algorithm, not JAES theoretical paper; my membership in AES lapsed about 2 years ago). My signal will easily survive 44.1kHz sampling rate, as per Shannon et al., but won't survive 4-bit bit-depth.
LOL, I thought you were shy about L*i*p*s*h*1*t*z's name, but I see the "bad part" is automatically deleted.
Peace
Waldrep's entire justification for his work in HD audio is contained in this sentence from that thread, "I prefer to match the real world and let listeners strive to play it back — without compromise." He states this without reference to exactly what the "real world' actually is, but also freely admits elsewhere that he's not sure what matters, or even what about HD is audible, so he just strives to capture as much as possible. If you read more of his writings you find he freely acknowledges that both 24 bits and high sampling rates above 96kHz do not have much justification, but since verification and validation are so darn difficult, he opts for the "safe" route. Yet, it's all tempered by his statement, "However, it is true that recordings and systems with high-resolution, 24-bit capability are very rare. The run of the mill 24-bit downloads you get online don’t need 24-bits." And that's true even of his recordings.Hey @gregorio
Mark Aldrep has (unconvincingly) critiqued your OP of this thread in his reply to one of his reader's comments.
http://www.realhd-audio.com/?p=6234
[1] The only source for "his take" is his own well-written words. When you tell me "what he meant", either directly related to his words, or worse "what he meant" from what he left out, that is "your take".
3c Again, I don't take issue with the Shannon quote w.r.t our discussion; I don't agree with your take regarding bit-depth.
[2] I realize I should not offer to dither or noise-shape, since those were not known and not included at the time Shannon, Nyquist, Whittaker et al. created the sampling theory stuff. [2a] Their work survives without dither/noise-shaping.
[3] My signal will easily survive 44.1kHz sampling rate, as per Shannon et al., but won't survive 4-bit bit-depth.
Mark Aldrep has (unconvincingly) critiqued your OP of this thread in his reply to one of his reader's comments.
Almost 10 years of arguments guys, come on we're almost there!
Like a big happy family.