24bit vs 16bit, the myth exploded!
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SoundAndMotion

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@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.
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.

Octave is a free MATLAB clone. It is a few years behind the latest version of MATLAB and has nothing like Simulink. There are minor differences from MATLAB, but with very little effort, you can use m-file scripts (for MATLAB). But it is extremely powerful and free. I used Octave a few years back; it is a great, powerful substitute for MATLAB!!

I've never used Python, other than tiny projects with my son. A few years back, a colleague tried to convince me to switch. With the scientific packages (NumPy, SciPy, Matplotlib, IPython and pandas), he said it was at least as powerful as MATLAB, and free. There has been a recent push to use free software for publicly-funded research. So R for stats and (scientific-)Python for experiment control and general purpose analysis. You can get it for nearly anything: obviously WinPC, Mac, Linux, but even iPad and RaspberryPi.

I strongly support and encourage learning this stuff by taking different types of signals and seeing what happens when you ... "play". As an in-depth guide you can use this nice book, but the example code is in BASIC. There are also books, where the examples are MATLAB (works for Octave too) or Python, or PM me if you want some quick tips or direction on particularly enlightening exercises. ...lots of help online...
 
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rule42

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Great info that @SoundAndMotion . I'll download and have a play with Octave to see what I can do with it over the next few days. Looks great free software and will no doubt do way more than I want, which is 'play' as you describe, plus there seem to be loads of tutorial/examples online for it or Matlab ones that seem basically the same. Might PM you for pointers to nice examples in a few days time. That book you link is great too (well the first few chapters are nice and gentle so far). Many thanks.
 
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SoundAndMotion

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[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
(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" [Lipshitz, 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 Lipshitz & 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 :peace:
 
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post-14359188
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71 dB

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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.
This automatic deletion of the 4 letter words starting with f and s is so stupid.
People are attacked online all the time. If you are triggered seeing 4-letter words then better stay offline, becuase the internet is full of s**t.
 
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post-14359230
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SoundAndMotion

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@gregorio , is this you?

I never realized how hard your work is :wink: Good job! :thumbsup:
(Have fun!)

LATE EDIT: My wife said this can be seen as a jibe. That is NOT the intent. It is an attempt to reduce tension, and a lighthearted way to say I respect your competence in your field... with perhaps a hope for reciprocation.
 
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TheSonicTruth

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(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 :peace:
Lipschitz.

There, should duck the censor algorithms.
 
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pinnahertz

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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
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.

Obviously, capturing "more" than you think you'll ever need is not necessarily a bad thing, but insisting on a verifiable and repeatable audible improvement because of it is without much substance. Yet, Waldrep's company is also perhaps the only one that faithfully supplies real HD audio throughout the entire production chain, from capture to release, including the use of microphones with actual response above 20kHz. So he does have some of the best test material. What I find is a far bigger factor in the quality of his recordings is they are just well done (mostly), and are still well done regardless of actual resolution.
 
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[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.
1. I am NOT telling you what he meant, I am quoting him directly.
3c. There is no "take" on bit depth, Shannon's statement is proven true, as it stands!

2. Shannon, Nyquist et al., did NOT create sampling theory stuff, they created the Sampling Theorem upon which Sampling Theory is based.
2a. Yes it does, because it is the foundation of Sampling Theory. However, their work was not the end of the development of Sampling Theory.

3. Yes it will, otherwise you are saying Shannon was wrong. Let's put the issue the other way around, let's say Shannon was somehow wrong, that his statement/proof is incorrect and in fact a signal is not "completely determined" with a more than x2 sampling rate, it also requires a certain bit depth (an infinite bit depth in theory but we'll ignore that for now) and therefore with 4 bits Shannon's Sampling Theorem fails; the signal is not "completely determined" and "won't survive 4-bit bit-depth". How then does Noise-Shaped Dither work and why does it even exist? How can noise-shaped dither reveal the signal down to some arbitrary level if the signal has not "survived" (is not "completely determined")?

Mark Aldrep has (unconvincingly) critiqued your OP of this thread in his reply to one of his reader's comments.
I agree with @pinnahertz but I'd go a step further, systems such as he (Waldrep) are NOT "very rare", they're non-existent! He also makes some other beginner mistakes or more likely some other omissions, for example he consistently ignores noise-shaped dither, which give 16bit in practise a dynamic range of 120dB. This makes a nonsense of his statement "A larger dynamic range — matching the capabilities of human hearing without compromise — DOES MEAN HIGHER QUALITY!" - because a dynamic range of 120dB significantly EXCEEDS "the capabilities of human hearing"! Also, what in the "real world" of music requires 120dB dynamic range?

Mark Waldrep does make some excellent recordings, he's also generally a good source of accurate information and has eloquently debunked all manner of audiophile myths regarding audio formats, with the exception of the audio format he sells! As pinnahertz also stated, even though the benefits of Hi-Rez are inaudible, at least he actually makes/sells what he is purporting to sell!

G
 
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Almost 10 years of arguments guys, come on we're almost there! :):deadhorse:

Like a big happy family. :o2smile:
 
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