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I've already answered this in the original thread. But in a nutshell, for those who don't want to bother with the original thread (although if you're reading this one you've probably already seen the original) what FM has left out is that we use what's called the two's complement numbering system in digital audio, where the most significant bit tells us whether the sample of the waveform it's describing is a positive or a negative value. A zero or off state indicates a positive value, and a one or on state indicates a negative value.
So, to illustrate this simply, let's picture a three-bit representation of a sine wave. If it starts at the zero crossing, it'll be represented by 000. Then it goes up to 001. Then to 010. Then to 011. Then back to 010, 001, and back to 000. Then it goes down to 111 (seems counterintuitive, but although it's describing the negative portion of the waveform with the lowest amplitude, it's still "all bits on" because the first bit tells us it's on the negative side of the waveform and the remaining two tell us that it's the "highest" negative value). Then we go down to 110, then 101, then 100, then back up to 101, then 110, 111, and back to 000. If we assume that this was sampled with proper anti-aliasing filters, then we can redraw the waveform through those points and come up with a perfect sine wave (assuming we have proper reconstruction filters...in other words, we'd draw it as a sine wave rather than a triangle wave or something like that).
Now let's do that again, but with four bits. Here's how it would go:
0000->0001->0010->0011->0100->0101->0110->0111->0110-> 0101->0100->0011->0010->0001->0000 (back at the zero crossing)
Now if you make all the assumptions that we made with the first example and redraw that, it will also be a perfect sine wave. In addition, they will be the exact same amplitude as each other if the maximum value for each is digital zero (which is the way it is). We didn't take sampling rate into account, but if we figure that this was a 1 Hz sine wave and the first example was sampled at 12 Hz and the second at 16 Hz, then both sine waves will be identical.
So what did that extra bit in the second example do for us in this case? Nothing...it just gave us an extra value between the zero crossing and 0 dBFS on the positive side and an extra value on the negative side. So we've got two extra samples to describe the wave, but do they give us any more accuracy? No, they don't. Both waves are exactly identical. The only advantage to having the extra bits is if we wanted to describe a wave with a smaller amplitude. If we have our playback system set where a 0 dBFS signal is amplified and comes out at 100 dB SPL, with the 3-bit signal we could also reproduce a sine wave at (rounding off for simplicity's sake) 94 dB SPL (or -6 dBFS). Nothing quieter than that would be accurate, would it? No, because if we had a sine wave that fell between two values it would be assigned to whichever one was closest and wouldn't sound right.
However, with our 4-bit system, we could record and reproduce the 100 dB SPL/0 dBFS sine wave and the 94 dB SPL/-6 dBFS sine waves just as well as with the 3 bit system (but no more accurately, even though we'd be using an extra bit or an extra two values), but we could also record and reproduce a sine wave at 88 dB SPL, or -12 dBFS. Do you agree thus far?
It's the same thing with 24 vs 16 bits...sure, you've got many more values, but they're only being used to describe sound you can describe perfectly with the 16-bit system until you get below the least significant bit.
Originally posted by funkatron is it possible that we could be seeing the start of the first fist fight in history over bits of data?
I don't think so. I think its a totally harmless debate that I'm learning a lot from (gonna have to reread lots of it, too). Fascinating tech stuff. The particular bit/rate stuff MIX never goes into (I still love MIX), with such detail, that is. Keep going, FM and Duardo!
Glad to hear someone's getting something out of it! I've actually learned a bit as I've tried to formulate my responses. I have no intention of getting into a fistfight with anyone, but even so I think this battle (or at least some variation thereon) has been fought before on various and sundry forums. So let's get to it...
Now serious. Are you making fun of me?
Not intentionally...at least not in this thread. Sorry if my example showing the binary notation wasn't appreciated. Just thought it might make this stuff easier to visualize for some of us.
But what counts HERE is the SAMPLEVALUE the bits represent aka The Meaning, not how it is notated!
I agree. I think that all that counts is that which affects what we hear.
But that doesn't change any of the facts I mentioned. You still confuse dBFS with Bitwidth and SampleValues.
I don't think I'm confusing them. Maybe I can be more concise in this post.
Since you don't read and/or don't understood my words, I will let Sonic Foundry tell you, ok ? This are simply 3 topics from the glossary of Sound Forge.
Read them carefully, since they proof your words absolutely wrong.
Actually, I don't think they prove me wrong at all; they support what I've said. Maybe they say it better than I do, but I don't disagree.
First, they tell us how many sample values there are in various audio bit depths. I don't disagree with any of that. They also say that the maximum value is 100% or 0 dB, with which I agree. I think it should be clarified as 0 dBFS.
The "Waveform Display" says nothing I don't agree with either, and neither does the "Decibel (dB)" section. It talks about things I've mentioned, such as the fact that we perceive sound in a logarithmic scale, and indirectly it says that a maximum-value 16-bit sound is 6 dB louder than a maximum-value 15-bit sound, which has half the sample value as you've maintained. And I don't agree. What it doesn't say is what all those extra values mean on a practical level.
What you think now ? Sonic Foundry is wrong and all users of SoundForge are wrong too ??? Please think again!
No, that's not what I think, and that's not what I said.
And then you said : "Again, that makes sense intuitively...but when you consider that ALL of that extra resolution is below -96dBFS, it's ONLY an issue if the dynamic range of your material exceeds 96 dB (theoretically...in actual practice a bit less, but not much)."
Are you drunken maybe ? hehe
I stand by that statement, and I don't think that the Sound Forge glossary disagrees with me. Please point out specifically where it does. And no, I'm not drunken, I don't drink...although I tend to post pretty late at night, which probably doesn't help me when I'm trying to be clear.
That is BULL****************! Please let me proof it!
Please, be my guest.
The resolution below! ~90 dBFS in a 24bit System is rendered in ONLY 256 Steps! And NOT MORE!
Right, that corresponds to 8 bits. I don't disagree. And I don't disagree with your "proof" either, but I'm not sure what you're trying to prove. That a full-scale 4-bit sighal uses 16 steps, and that an 8-bit signal uses 256...I don't disagree with either of those statements.
That shows very easy that the "louder" signals are rendered better than the "quieter" signals.
That is where you are wrong! Sure, there are more values used to represent the "louder" signals, but that doesn't mean they're "better". They don't sound any better. There's no more resolution as far as our ears can hear. Sure, they're a little more accurate because you're pushing the quantizing noise further and further down. But that's all you are doing. You're not gaining any more audible accuracy.
Again, here's why, in a nutshell...it's not quite midnight yet, so maybe I can explain myself clearly.
Quantization noise is a result of sample values falling between "steps". This noise will always be less than half of the value of the smallest step since it will be rounded to the nearest one. As you know, halving the amplitude of a waveform results in a drop of 6 dB, so our quantization noise will always be 6 dB below the first step. We can call it "noise" instead of "distortion" since it's random. Each time we double the number of quantization steps (or, in other words, add a bit), that noise is cut in half and we gain another 6 dB of dynamic range.
So all that those extra values you're so excited about in the "louder" signals aren't important...they're not describing our signal any more accurately in any way that we can hear. They're just pushing the quantization noise further and further down into the noise floor. Unless we were recording a signal so quiet that we could actually hear the quantization noise, we're not gaining anything useful with that extra "resolution". If we are recording a signal that's that quiet (or, should we say, has parts that are that quiet) that's exactly when we do need to record at a higher bit depth, which is what I've been saying all along. Nothing you pulled out of the glossary or showed with your example even suggets otherwise, aside from you drawing the incorrect (but common) conclusion that more values actually translates to anything that makes an audible difference.
P.S. Looking forward to the "sampling rate" thread...sort of...
yeah i was most definitely kidding about the fist fight i've just never seen people so passionate (for lack of a better word) about bit rates. thats cool though its good thread even though its all way over my head.
Let us know if there's anything over your head and we can try to explain it more simply...simplest would be to say something like "24 bits is better no matter what" or "16 bit is fine if your source is within a certain dynamic range", but as you've seen it's not quite that simple...
There's certainly no harm in doing that, but in many cases it's just not necessary. It is convenient, though, in that you generally don't have to be quite as concerned with getting your levels to peak at 2 or 3 dB below FS or things like that. But if you are recording material with a wide dynamic range, I'd recommend both recording and mixing at 24 bits and dithering down to 16 in the mastering stage.
Fanatic Music, where are you? It's been a while...