More from the bit/sample can of worms. . .

[gh10606]

This has been bugging me for a while. I've read Park Seward's three-page thread, and I've commented on the subject in other threads over the last couple of years.

Bottom line: I was a "D" student in all of my high school and college math and science classes. I tend to be one of the "use your ears" jerks, when people get too bogged down in the technical details of resolution, bit depth vs. sample rate, etc. There's obviously some level of "sour grapes" to it, because I can't hold a candle to Park and some of these other guys in a scientific debate.

BUT, I still don't buy the point I've seen repeated here recently that bit depth only affects dynamic range and not the overall "quality" (or resolution) of the sound (and that sample rate has MORE impact on the quality than bit depth). In quite a few of my posts I've referenced Roger Nichols on this point -- but until now I've never taken the time to search and find his exact quote. I'm not trying to be argumentative (no more so than I ever am [img]images/icons/smile.gif[/img] ), but I'm genuinely curious to see Park and others more scientifically minded than I react to the following:

(From EQ Magazine, October 1997 - Roger Nichols)

Bit Off More Than You Could Eschew?

Last Little Bit

Another thing that comes up quite a bit are questions about the difference technically between 16 bits and 20/24 bit stuff. The general consensus is that the difference between 16 bit and 20 bit is just the dynamic range and noise floor. 16 bits has 96 dB, 20 bit has 120 dB, and 24 bit has 144 dB. If you are recording rock music or something else that is mostly loud, then you don’t need the extra bits. Not true. Here is the way it works.

Lets say you record some really loud music with big bass, big sounding drums, blasting horns and whatever else you dig up. Now record it into any digital audio editing program and zoom way in to the bit level. Now pretend that you can zoom in until the difference between one level and one bit louder is one inch up on the graph and one bit lower in level is one inch down.

This is your step size for 16 bit. If the guitar level for that sample was half way in between, the converter could only give you a value that was either one inch up or one inch down. If you were recording 20 bit there would be 16 level choices between each inch mark. The accuracy is within a 16th of an inch. If you were recording 24 bits, there would be 256 steps between each inch boundary.

So, the resolution vertically is improved which makes the sound reproduction quality better. In the other direction, left to right on the graph, if you increase the sample rate to 96kHz, you are only doubling the resolution, but 24 bits increasing the resolution by 256 times. Cool, huh!

[Park Seward]

Far be it for me to disagree with Roger. He is one of the gods of the recording industry. I agree it took me some time to understand all of this and Nika can explain it better than I can. See if this lengthly explaination helps.

From Nika:

Oh brother. Here we go. I'll do my best to explain.

First, as illogical as it seems, bits does NOT equal better resolution of anything but the noise in its signal path. More bits ONLY equals dynamic range. I have no idea what the understanding is of the various people that are following this thread, so I don't know in what amount of detail to give my answer. I'm fairly new to this particular forum, though I frequent a few others. If I offend anyone, please forgive.

First we have to talk about the difference between "quantization steps" and "bits". The number of "quantization steps" from top to bottom is defined by how many bits we have. A 1 bit signal has two quantization steps (0 and 1) a 2 bit signal has four, a sixteen bit converter has 65,536, and a 24 bit converter has ~16,000,000. Remember that half of these steps are below the zero axis and the other half are above, so to look a 24 bit signal, the audio goes from -8,000,000 to +8,000,000. Cool so far?

Let's also define "noise" really quickly. Noise=white noise. Any other form of noise is considered noise WITH SIGNAL, and you'll get different results if you treat the "apparent" noise floor as the "actual" noise floor. The actual noise floor is where the signal actually drops off into white noise only. If your signal drops off into pink noise, or other filtered noise then you have not actually hit the noise floor yet.

"Signal to noise" ratio deals specifically with white, pure, natural noise. When discussions over signal to noise ratios are brought up it is implied that the noise being spoken of is the fundamental level of white noise.

Let's talk about a sine wave with a signal to noise ratio of 42db. This will take 7 bits, or 128 quantization points to accurately capture and reproduce this sine wave, accepting that a each bit gives us 6dB of dynamic range capabilities (a whole other lecture, but a commonly accepted point. Run with me...). This means that the signal will take up all of -64 to +64 quantization steps. Now, to hopefully answer your next question, the signal, when turned up to maximum in an 8 bit converter, will indeed register from -128 to +127, thus implying more "resolution". When put into a 16 bit converter, will indeed register from ~-32,000 to ~+32,000. This is an example where more "quantization points" are used to capture this audio. Unfortunately, though, it is specifically NOT more resolution. Let me try to explain why:

Even though we have essentially 65,000 points now to describe that sinewave, it is really divided up into 128 chunks of about 512 quantization steps. This is because we know that it is a 42dB signal, and a 42 dB signal can only be divided into 128 quantization steps by definition. It'd be like trying to draw a line on graph paper with a can of spray paint. The width of the spray is only so resolved. Attempting to resolve it further has you defining more than the spray actually yielded. Making more refined graph paper isn't going to help describe that artwork you did any better. The width of the spray here represents noise, and the resolution of the graph paper represents the number of quantization steps. So back to our situation, a 42dB signal can ONLY be divided into 128 steps, period. Trying to do more than that has you defining more accuracy than the signal has.

The signal is going to fall within that 512 quantization step window, but exactly where within that window is not important because the resolution within that window of 512 quantization steps only helps to describe the white noise. But since this is white noise, it is unnecessary to describe it with precision, as any random area within that window is really noise. What this means is that the behaviour of the signal within that window of 512 quantization steps is totally random. *

So the signal will pass through all of these 128 groups of 512 quantization steps, but the fact that it does just that, and at what times it passes through these ranges is all we need to know. Exactly where within that window it passes is totally irrelevant and does not give us any better resolution of the actual signal itself.

Now if we turn the signal down 6db so that we are only using 15 bits of our 16bit system so that,even though the system is CAPABLE of 64,000 incremets from top to bottom, we're now only using 32,000 of them to describe this sine wave. We still only have 128 quantization steps for the signal itself, each of which is now divided into 256 quantization steps for the noise.

Now you can say, "what if the signal passes through that window of 512 or 256 quantization points in a very organized fashion?" Well then that would not be noise! That would be some sort of filtered noise, or not noise at all, and changes the situation entirely. We are no longer dealing with 42dB SNR. We're now dealing with some other signal to noise ratio. In other words, if the signal passes through that window of 512 quantization points dead on center then you have changed the situation. This no longer is 42dB SNR. if it really passes through dead on center then you actually have a sine wave that has more SNR than this sampling paradigm provides for (16 bits is what we're talking about), so this sine wave has a signal to noise ratio of greater than 96db, so we need to increase our bit depth until there IS a determinable resolution.

But that 42db signal is only ITSELF ever quantized into 128 discreet increments, and thus its resolution does not change no matter how many quantization points we add. As I said before, all that does is give you better resolution of a totally random noise signal.

So again, we need to be clear about using the word "resolution". The audio signal itself never has any better resolution than the minimum amount necessary to describe it, which can be ascertained by it's dynamic range (or signal to noise ratio). Increasing the bit depth does, in no way, benefit the "resolution" of the signal, and thus we try to avoid using that word to describe the effect of adding bit depth. All that adding bit depth does is allow us to accurately record material with wider dynamic range.

Again, I don't care HOW we use the word "resolution". The SIGNAL itself does not have any additional "resolution", "quantization steps", "discreet measurement increments", or any other term to describe units of measurement when we increase the bit depth beyond what is necessary to accurately describe the signal.

This all explains that bits only tells you how much total dynamic range the system is capable of. Any use of the higher number of quantization points to try to increase the audio's "resolution" is futile as it only hopes to describe with accuracy the system's random noise. This all feeds back to my point that you only need to record as hot as the dynamic range of your music allows. Any more than that is unnecessary. Thus, as I often say, "turn it down, it'll be fine!"

I hope this helps. For those reading along, follow this sidebar*

Nika.


*Sidebar: This is exactly how dither is done. Every sample is put through a random number generator where it adds a random number of quantization steps to the sample. If we're dealing with 24 bits being dithered down to 16bits, a random number from -256 to +256 is added. Then the last eight bits are lumped off. Just like in the situation above, this has randomized the signal to within a window of 512 quantization steps before lowering the dynamic range by truncating off the last eight bits - which are now completely noise anyway. It is this dithering process at the end that negates the need to accurately sample the noise going IN to the system. This brings Paul Frindle's comments into light

"Oh Guys, you seem to be making very hard work of this subject using the term 'resolution' and applying 'bits' to it as though they were hard boundaries. They are not at all hard boundaries if we dither the signal correctly.

In other words, since we're going to be randomizing the signal anyway, it doesn't matter exactly HOW random it is coming in. So 16 bits or 24 bits - providing for better quality resolution and randomness of the noise is therefore unimportant.

[gh10606]

Park,

Thanks for the quick reply. I had already read Nika's explanation in your thread. The point of my post was that Roger Nichols appears to contradict that explanation. I guess I'm really hoping to hear from Nika (and anyone else who has a thought on it).

It seems to my unscientific mind that Nika's concept of "fully describing" a wave is impossible. Just as it's impossible for a computer to "fully describe" a curved line. At some point -- if you zoom in far enough -- there's got to be a jagged edge. So, the higher the resolution, the smaller the jagged edge becomes -- hence an increase in quality.

But what do I know! [img]images/icons/smile.gif[/img]

Thanks again,

Glenn

[Doc]

Another perspective on the 'resolution' issue.
Please bear with me on the tech terms. I've tried to keep it simple.
I am a musician / artist foremost who considers electronics to be a scientific artform. [img]images/icons/tongue.gif[/img] Look at the Mandelbrot set. It is both scientific and very beautiful (IMHO). Oh dear, I may have spilled the beans. [img]images/icons/shocked.gif[/img]

Lets assume the maximum input and output level of a certain A/D/A box is 2 volts peak to peak into a given load and this box is capable of operating at 16 or 24 bits.
Lets also assume that the gain is adjusted so that a digital zero (16 or 24 bit mode) represents zero volts and digital full scale (again, 16 or 24 bit mode) produces 2 volts at the output.
Any given input signal within this range will produce exactly the same output level whether recorded with 16 or 24 bits.
It also makes sense to me that the 'resolution' of the analog signal reproduced at the output will be greater at 24 bits than it is at 16 bits given that they are both the same 'loudness'. This applies across the whole dynamic range. Not just the 'loud' or 'quiet' end.

It would be a different story if the output was not gain adjusted and the full scale 24 bit word produced an output greater than 2 volts OR the 16 bit fs word was less than 2 volts. Then the 'resolution' could be said to be the same and the dynamic range would be different.

As somebody famous more or less said, 'It is all relative' [img]images/icons/wink.gif[/img]

[espron]

Hi

I followed Park's other thread and it seems to me that there are some general misconseptions about digital audio lurking around.

First of all, I'm not going to say that there isn't any difference between 16 and 24 bit "resolution", 24 bits offer wider dynamic range and just sound better (using good converters, that is)

But, on the subject of sampling rate there seems to a bit of confusion. It seems to me that some people emphasize too much on how a waveform LOOKS graphically if you zoom all the way down to sample level. However, it's graphical representation and what you actually hear is not necessarilly the exact same thing.

Ok, so if you zoom so you can view each sample, you will see jagged "edges" or a step-like representation. Common sense would tell us that this is a problem that can be solved by increasing tha sample rate - this way, it would be a greater number of steps per time unit, just like you can make a curve look smoother on a computer screen by upping the resolution. Fortunatly though, this isn't so.

Fourieranalysis is a form of analysis that breaks down complex waveform, i.e music, to it's separate components. According to Fourier, all waveforms consist of a given number of simple sinewaves. A squarewave, for example, consists of a sum of sinewaves, the fundamental, and a indefinite number of harmonics. These harmonics will be high frequensy material, and can be filtered out to leave just the fundamental sinewave audible.

My whole point of all this is that whenever you see a sharp edge, or stair-like steps in a graphical representatin of a waveform, this tells us that the signal would have to consist of a high degree of very high-frequensy harmonics to make the waveform look like it does. Now, if we go back to the example of a filtered squarewave turning into o sinewave, the exact same thing happens when we run the sampled audio through the anti-aliasing filter, this filter will not allow any frequensies over half the sample rate frequensy, and thus eliminating all those harmonics that make up all the "jagged" edges.

This is why, if you look at a squarewave that has been sampled on an osiliscope, it no longer looks like a squarewave, the harmonics needed to make it look so has been filtered out - but it doesn't matter, we wouldn't be able to hear them anyhow. Actually what you would see on the osiliscope is a fair representation of what we actually can hear of a squarewave, given that a big enough number of the harmonics lie outside the audible range.

However, many people claim that they can hear a difference when you increase the sample rate, and rightfully so, what they probably hear is fewer artifacts of the anti-aliasing filter as this is allowed to work in an area further away from the audible program material. For example, direct stream digital, like used in SACD, eliminates the need for any such filters, and it sounds really good to my ears, many people describe the sound as beeing "more analog".

This post turned out to be quite long, and I hope no one is offended, it just seems to be a lot of uncorrect information around on the topic of digital audio. Also, apologies for my english spelling, but hey, I'm from Norway - you guys try posting here in Norwegian!

All the best

Espen

[Doc]

Espron,
Nicely summed up. Indeed, what is visible on screen is PRE filtering.

One thing you have said, however has me curious. <BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:<HR> For example, direct stream digital, like used in SACD, eliminates the need for any such filters, and it sounds really good to my ears, many people describe the sound as beeing "more analog".
<HR></BLOCKQUOTE>
Are you saying that Sony has done away with filtering all together? Can you please tell us more. I assumed (perhaps incorrectly) that SACD was in the 'high sample rate / gentle filter' category. <BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:<HR> you guys try posting here in Norwegian! <HR></BLOCKQUOTE>
Not a snowball's chance in hell for this little girl. Well done [img]images/icons/wink.gif[/img]

[where02190]

All the math aside, what do your ears tell you, as they are my final judge and jury....

[Ben Jenssen]

Thanks Espron!
For making your country proud.

Shall we all now go back to making music?