[sdiy] Digital is more analog than analog... and it has 319 dB headroom...

cheater cheater cheater00social at gmail.com
Sun Mar 3 12:59:06 CET 2024


On Sun, Mar 3, 2024 at 11:57 AM Tom Wiltshire <tom at electricdruid.net> wrote:
>
> This is splitting hairs. The point he's making is that there's bags more accuracy available for a digital system to model a situation than an analog one. In that sense, the digital is the better analog (in the other sense). And that's plainly true.

Well, the problem is... that's not *quite* so. You probably know the
following, but it bears bringing up:

1. merely changing the amplitude of a signal in floating point is
non-trivial if you don't want to compromise on your insane dynamic
range. Just a simple multiplication won't cut it if you want to be
able to go down to (the equivalent of) the least significant bits and
listen to just that.
2. every floating point algorithm loses some of the precision. there
is a whole science of optimizing floating point formulas - even simple
ones - for maximum precision, and no one form is good for everything -
you have to accept a compromise no matter what.
3. aliasing is uncorrelated and therefore noise, and any digital
signal chain can have a bunch of it. good ones won't. the rest will,
and that's 99%. therefore it's essentially intrinsic to digital domain
processing. just that alone dips the 12318 dB dynamic range to low
double digits.
4. non-linearities in digital models are done using polynomial
approximation, and, last I checked, those approximations were series
with infinite amounts of terms, whereas computers can only add a
finite amount of terms. It's usually just the first few terms for
practicality of finishing the sample processing on time without the
CPU combusting. All those missing terms are non-adherence to the thing
being modelled, and therefore an error signal. That can create massive
amounts of error signal - in pathological scenarios (fuzz, overdrive)
the error signal itself will have a gain easily reaching 100 dB over
the non-error portion of the signal.

So, it's true - if you don't change the amplitude, do any filtering,
do any non-linearities, do any pitch shifting, or do any generation
(like an oscillator or envelope or gate), then yes, digital is better
than analog. Other than that, analog is better than digital at "doing
analog" for virtue of sharper non-linearities, what noise is present
being musical (unlike aliasing), etc. Quantifiably so, with numbers
you can compare...

That's not to say I don't like digital synths, they're great, and
digital non-linearities with limited terms are cool too when you want
them, it's just that people try to shoehorn them into being something
they're not. It's like trying to turn a pig into a goat.

> It's a reasonable point, but I don't think it really goes that far: "Modern computers are really powerful"? Nice work, Sherlock!
>
> TBH, the whole analog vs digital thing is pretty stale after 40 years.

Agreed on both points. Which is why the video is so ridiculous. The
guy sold his moog and needs to go out there and dress it up in some
insane philosophy, like he's had a thought that no one had before. All
just so that he doesn't lose face in some completely imaginary rat
race.


> > On 3 Mar 2024, at 09:11, cheater cheater via Synth-diy <synth-diy at synth-diy.org> wrote:
> >
> > Also, btw, I thought someone would catch that without it being
> > mentioned, but 300 dB isn't even the right number, even if we follow
> > the bizarro logic that the bozo in the video is following.
> >
> > This is from the second link:
> >
> >> Let’s forget about the decimal point for now, because that only
> >> scales a number up or down and has nothing to do with its
> >> accuracy. It’s the 53-bits that is important, so let’s get a feel for that.
> >> 53-bits represents a difference of 9,000,000,000,000,000:1. Yeah,
> >> that’s 9 quadrillion to one, from the smallest to the largest quantity,
> >> or a whopping, no, staggering, 319db
> >
> > you heard that right. according to this clown, scaling a number up and
> > down doesn't have anything to do with how precise of a quantity you
> > can describe. You can describe a cup of sugar? and you can also
> > describe 1000 cups of sugar? Doesn't matter - 1000 cups of sugar are
> > just 1 scaled up by a thousand, so being able to describe 1 cup of
> > sugar isn't any more precise than being able to describe a sack of
> > sugar. according to Mark Barton, at least. enjoy your pancakes with a
> > full burlap sack of sugar dumped into the skillet.
> >
> > in reality, that's not how floating point numbers work. they have the
> > ability to scale the significant by an exponent *exactly because* that
> > improves accuracy by orders of magnitude. specifically by 308 orders
> > of magnitude up, and 308 orders of magnitude down, so in total 616
> > orders of magnitude. without using the exponent field, the smallest
> > positive number you can describe with a float is
> > 1.00000011920928955078125. with using the exponent field, the smallest
> > positive number you can describe is a 0, then a decimal point, then
> > 307 zeros, then a two, and then some other digits. that's incredibly
> > more precise. the bozo in this video didn't do his basic research on
> > floating point numbers and now he's giving talking head interviews
> > about the topic. this guy can't even get his bullshit straight.
> >
> > If you wanted to really calculate the "dynamic range" of floating
> > point numbers you would calculate it this way:
> >
> > 1. what is the smallest number representable as a 64-bit float?
> > answer: 2.2250738585072014*10^-308 (call that V1)
> >
> > 2. what is the largest number representable as a 64-bit float? answer:
> > 1.7976931348623158*10^308 (call that V2)
> >
> > 3. calculate the ratio: V2 / V1 = 0.80792515178... * 10^616
> >
> > 4. convert to decibels: dB = 20 * log10 (V2 / V1) = 20 * log10
> > (0.80792515178 * 10^616) = 20 * (log10(0.80792515178) + log10 (10^616))
> > = 12318 dB.
> >
> > Twelve thousand decibels of dynamic range. Another ridiculous number.
> > And that's BEFORE dithering. This shows you how insipid it is to even
> > think in this manner.
> >
> > This hopefully brings the point that you shouldn't be talking about
> > what floating point numbers will or won't do unless you really *do*
> > know, have checked the technical references, have experience and
> > check your estimations at every step.
> >
> >
> >
> >
> >
> > On Sun, Mar 3, 2024 at 8:53 AM cheater cheater
> > <cheater00social at gmail.com> wrote:
> >>
> >>> It DOES keep the noise and distortion from building up and becoming audible after dozens, hundreds, or even billions of MAC-type operations
> >>
> >> you're wrong. i can take a full scale 64 bit floating point signal and
> >> get you that noise and distortion in 1 multiplication, or even one
> >> addition.
> >>
> >> i thought we were making fun of the disinformation, not stuffing it in
> >> a pipe and smoking it.
> >>
> >>
> >> On Sun, Mar 3, 2024 at 4:38 AM Ben Bradley via Synth-diy
> >> <synth-diy at synth-diy.org> wrote:
> >>>
> >>> The "300dB" dynamic range of "digital" totally misses the point. It
> >>> has nothing directly to do with DR. It DOES keep the noise and
> >>> distortion from building up and becoming audible after dozens,
> >>> hundreds, or even billions of MAC-type operations on each 64-bit
> >>> floating-point number. Surely he knows that, but it may be harder to
> >>> describe and is "less impressive" than the dynamic range of lots of
> >>> bits.
> >>>
> >>> On Sat, 2 Mar 2024 at 14:40, Gordonjcp <gordonjcp at gjcp.net> wrote:
> >>>>
> >>>> On Sat, Mar 02, 2024 at 08:19:29PM +0100, cheater cheater via Synth-diy wrote:
> >>>>> I'll leave this here:
> >>>>>
> >>>>> https://www.youtube.com/watch?v=kk-3vXOAtVo
> >>>>>
> >>>>> and supplementary material:
> >>>>>
> >>>>> https://cherryaudio.com/news/flashback-friday-mark-barton-on-analog-and-modern-digital-synthesis
> >>>>>
> >>>>> make sure to hit the bong extra hard before you look at any of that...
> >>>>
> >>>> As an exercise for the student, try to work out what sort of signal levels would be involved in "300dB signal to noise ratio".
> >>>>
> >>>> --
> >>>> Gordonjcp
> >>>>
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