(Thinking outside the nest…)
>(...maybe that means opening up the LPF as the gain knob setting is reduced)
Yes
And good discussion elsewhere in there, thanks Robert.
On Jun 17, 2014, at 4:07 PM, robert bristow-johnson <r...@audioimagination.com>
wrote:
> On 6/17/14 3:30 PM, Nigel Redmon wrote:
>> This is getting…nesty...
>
> yah 'vell, vot 'r ya gonna do? :-)
>
>> On Jun 17, 2014, at 10:42 AM, robert
>> bristow-johnson<r...@audioimagination.com> wrote:
>>
>>> On 6/17/14 12:57 PM, Nigel Redmon wrote:
>>>> On Jun 17, 2014, at 9:09 AM, robert
>>>> bristow-johnson<r...@audioimagination.com> wrote:
>>>>
>>>>> On 6/17/14 5:30 AM, Nigel Redmon wrote:
>>>>>
>>> ...
>>>>>> Anyway, just keep in mind that the particular classic amps don’t sound
>>>>>> "better" simply because they are analog. They sound better because over
>>>>>> the decades they’ve been around, they survived—because they do sound
>>>>>> good. There are plenty of awful sounding analog guitar amps (and
>>>>>> compressors, and preamps, and…) that didn’t last because they didn’t
>>>>>> sound particularly good. Then, the modeling amp has the disadvantage
>>>>>> that they are usually employed to recreate a classic amp exactly. So the
>>>>>> best they can do is break even in sound, then win in versatility. And an
>>>>>> AC-30 or Matchless preset on a modeler that doesn’t sound exactly like
>>>>>> the amp it models loses automatically—even if it sounds better— because
>>>>>> it failed to hit the target. (And it doesn’t helped that amps of the
>>>>>> same model don’t necessarily sound the same. At Line 6, we would borrow
>>>>>> a coveted amp—one that belonged to a major artist and was highly
>>>>>> regarded, for instance, or one that was rented out for sessions because
>>>>>> it was known to sound awesome.)
>>>>> what did you guys do with the amps when you borrowed/rented them? was
>>>>> your analysis jig just input/output, or did you put a few high-impedance
>>>>> taps inside at strategic places and record those signals simultaneously?
>>>> Yes. For instance, sweeping the EQ with incremental settings changes.
>>>>
>>> yes, another issue (which i didn't really touch on) is mapping the settings
>>> of the knob to the internal (to the DSP) coefficients and threshold values
>>> and such. that is "coefficient cooking" and is the same issue as defining
>>> Q in EQs so that the knob behaves like the ol' Pultec or whatever. your
>>> digital implementation might work very well, but if the position of the
>>> knob in the emulation is not nearly the same as it was for the venerable
>>> old gear (to get the same sound), someone might complain.
>> Oh yes, they *will* complain ;-)
>>
>>>>>> On Tue, Jun 17, 2014 at 6:58 PM, Nigel Redmon<earle...@earlevel.com>
>>>>>> wrote:
>>>>>>> On Jun 16, 2014, at 7:51 PM, robert bristow-johnson<
>>>>>>> r...@audioimagination.com> wrote:
>>>>>>>>> one thing that is hard to replicate is a sample rate that is infinity
>>>>>>>>> (which is how i understand continuous-time signals to be). but i
>>>>>>>>> don't
>>>>>>>>> think you should need to have such a high sample rate. one thing we
>>>>>>>>> know
>>>>>>>>> is that for *polynomial curves* (which are mathematical abstractions
>>>>>>>>> and
>>>>>>>>> maybe have nothing to do with tube curves), that for a bandwidth of B
>>>>>>>>> in
>>>>>>>>> the input and a polynomial curve of order N, the highest generated
>>>>>>>>> frequency is N*B so the sample rate should be at least (N+1)*B to
>>>>>>>>> prevent
>>>>>>>>> any of these generated images from aliasing down to below the
>>>>>>>>> original B.
>>>>>>>>> if you can prevent that, you can filter out any of the aliased
>>>>>>>>> components
>>>>>>>>> and downsample to a sample rate sufficient for B (which is at least
>>>>>>>>> 2*B).
>>>>>>>>>
>>>>>>>> This really goes out the window when you’re modeling amps, though. The
>>>>>>>> order of the polynomial is too high to implement practically (that is,
>>>>>>>> you
>>>>>>>> won’t end up utilizing the oversampling rate necessary to follow it),
>>>>> this is a curious statement *outside* of the case of hard clipping.
>>>>> oversample by 4x and you can do a 7th-order polynomial curve and later
>>>>> eliminate all of the aliasing. oversample by 8x and it's 15th-order. do
>>>>> *no* oversampling and you can still make use of the fact that there's not
>>>>> a lot above 5 kHz in a guitar and amp (so 48 kHz is sorta oversampled to
>>>>> begin with). you can fit a quite curvy curve with a 7th-order polynomial.
>>>>>
>>>>>>>> so
>>>>>>>> you still be dealing with aliasing. Modern high gain amps have huge
>>>>>>>> gain
>>>>>>>> *after* saturation. In practical terms, you round into it (with a
>>>>>>>> polynomial, for instance), then just hard clip from there on out, and
>>>>>>>> there
>>>>>>>> goes your polynomial (it can be replaced by an approximation that's
>>>>>>>> very
>>>>>>>> high order, but what’s the point).
>>>>> yes, we splice a constant function against a curve. if at the splice as
>>>>> many possible derivatives are zero as possible, that splice appears
>>>>> pretty seamless. this is why i had earlier (on this list) been plugging
>>>>> these curves:
>>>>>
>>>>> x
>>>>> f(x) = C * integral{ (1 - u^2)^M du }
>>>>> 0
>>>>>
>>>>> (C gets adjusted so that f(1) = 1 and f(-1) = -1.)
>>>>>
>>>>> you can splice that to flat values at +/- 1 and the nature of the
>>>>> function will not change appreciably from the polynomial in the region of
>>>>> the splice.
>>>>>
>>>>> anyway, the whole point is to give the guys with golden ears no cause to
>>>>> complain about hearing aliases. same with emulating sawtooths and
>>>>> hard-sync synthesis.
>>>>>
>>>>>>>> Anyway, you pay your money, you make your choices. Obviously some
>>>>>>>> really
>>>>>>>> good musicians making really interesting music use modeling amps. They
>>>>>>>> don’t have to be better than tubes, in order to be a win, just good
>>>>>>>> enough
>>>>>>>> to be worth all the benefits. If you’re a session music, you can bring
>>>>>>>> in
>>>>>>>> the truck with all of the kinds of amps that might be called on, or
>>>>>>>> you can
>>>>>>>> bring a modeling amp, for instance. And going direct into the PA or
>>>>>>>> your
>>>>>>>> recoding equipment…etc. I’m not going to make judgments on what people
>>>>>>>> should like, so I’ll leave it at that.
>>>>>>>>
>>>>>>>> One happy thing about the aliasing is that, given a decent level of
>>>>>>>> oversampling, it won’t be bad at lower overdrive levels. At the higher
>>>>>>>> the
>>>>>>>> overdrive levels, the harder it is to hear aliasing through all that
>>>>>>>> harmonic distortion you’re generating. So it could be worse...
>>>>> i really agree with this, Nigel. with *some* oversampling (but
>>>>> theoretically not sufficient oversampling), you can get away with a lot
>>>>> (like hard limits or whatever stuff goes on inside a transformer with
>>>>> core loss). i would not say that you have to oversample to a
>>>>> ridiculously high degree just because there is a hard-limit saturation in
>>>>> there or that your tube model is not a polynomial approximation (but i
>>>>> wonder why you wouldn't try to fit the grid-to-plate tube curve to a
>>>>> finite-order polynomial).
>>>> What I mean is... for a modern high-gain amp, the gain is on the order of
>>>> 2^16 (and the curve starts it’s significant bend up near 1). So most of
>>>> the signal, when you’re playing maxed out, is simply clipping hard. If
>>>> your goal is to not alias in the audio band at all, by figuring the max
>>>> harmonic component based on the order of the equivalent polynomial and the
>>>> highest freq of the guitar input coming in…well, your oversampling factor
>>>> is going to be a lot higher that you’re willing to implement.
>>> i understand. hard-hard-limit and you got harmonics going up to infinity
>>> anyway.
>>>
>>>> There’s really no point in calculating a continuous polynomial over that
>>>> range that I can see.
>>> well, if it splices *well* to the clip region, it might *still* have a
>>> point.
>>>
>>>> It’s no big deal—I just brought it up because I often see people, here and
>>>> elsewhere, go down the thought path of... "OK, I want to make a guitar
>>>> distortion unit…if I keep my polynomial to order N, I only need to
>>>> oversample by (N+1)/2...", completely forgetting that when, in their code,
>>>> they branch to limit the output to +/- 1, their polynomial order just went
>>>> out the window.
>>> yes, that's true (sorta). at least *if* the splice to the limited constant
>>> value is not smooth.
>>>
>>> but you can make a polynomial match as many derivatives (equal to zero) of
>>> the hard limit as possible (but that might be at cross-purposes to getting
>>> the polynomial to follow a tube curve) and for levels that hit that limit
>>> (so the code branches to the limit), if the overflow or spike isn't so bad,
>>> the behavior isn't so far away from the "ideal" polynomial and the total
>>> behavioral issue remains inside the window, i would think.
>> Yes, Robert…but, with the kind of gain necessary…OK, so you have the y-xis
>> as you output level, x-axis as input. To view the entire curve for a Soldano
>> Super Lead Overdrive, for instance, you draw the curve of your choice to
>> rise from y=0 and give you a soft bend into y=1 (full output). The bend will
>> be somewhere around x=1, ballpark (maybe it’s x=2 or 3, to allow for lower
>> input levels, but the point is that it’s a small number compared to what’s
>> coming next)…then you allow for x=30000 or so (a flatline from the x=1..3
>> area). Is that not a pretty high order polynomial?
>
> well, yeah, and it might better be described as a function that is
> discontinuous with most of its derivatives, even the 1st.
>
> so
>
>> The point being, yes the polynomial would be handy at low gain settings, but
>> you still need to build this thing to work at extreme gain settings at the
>> same time.
>
> okay, you mean with it cranked up so that it virtually hard limits. that's
> not exactly what comes to mind about "warm" tube distortion. like those
> DevilDrive guys (or was it the Kemper guys) built a 12AX7 preamp to model
> (and i wonder how much that tells us about how a Fender Twin Reverb cranked
> up to arcweld behaves like).
>
> but this is hard clipping distortion, not zero-crossing distortion, right?
> in between the nasty hard limits, you might be able to decently model the
> tube curves with finite-order polynomials. specifically the mapping curve
> from biased grid voltage to biased plate voltage given a specific load line
> (which may be affected by power sag). maybe you can cover that quite well
> with a finite-order polynomial and emulate that with a finite sampling rate.
> but if it clips, might be nasty, regarding aliases.
>
> the only thing i know how to tame down a hard limit (and it may very well not
> be compatible with the characteristic tube curve) is to set as many
> derivatives as possible to zero and splice the hard limit to that thing.
> continuity to the 2M-th derivative including the hard limit.
>
>> So anything at the low gain settings is pretty insignificant for something
>> designed to handle the high gain settings.
>
> well, we gotta think sorta like the string theorists. we gotta imagine how
> to seamlessly glue together two ostensibly incompatible systems. like how do
> we crossfade from the low-gain behavior (the "warm tube sound") to the
> behavior we like when it's cranked up to arc-weld?
>
>
>> Hence my feeling that there not much point to calculating how much headroom
>> you have—you can pretty much count on infinity. There may be some reasons to
>> do it—I’m not demanding that I have the right idea, just simply explaining
>> what I meant by my comments. In reality, it’s not so clear cut, because as I
>> mention before, the more you get into a situation where aliasing will be
>> big, at the same time you are in a situation where you’ll have more
>> generated harmonics to mask the aliasing. In the end, aliasing is *mainly* a
>> problem if you bend a guitar note and you heard harmonics going in the wrong
>> direction. For some reason guitarists just can’t get around that (lol).
>>
>>>> BTW, the more the overdrive, the less the weaker upper harmonics of your
>>>> guitar matter, so you can cheat by rolling them off as you increase drive.
>>> a useful idea. more pre-LPF as the grunge gets cranked up.
>>>
>>>> But you can’t rely on that too much, because guitar players like to hang
>>>> analog distortion stomp boxes in front of your modeling amp, giving you
>>>> powerful higher harmonics. :-)
>>> yeah, but can't you *still* pre-LPF that signal (the output of the
>>> distortion stomp box) as the amp drive is cranked up? i dunno.
>> Yes, it’s definitely one place where you can win, and help yourself make the
>> best of a practical amount of frequency headroom. Probably the biggest
>> difference (between assuming direct, clean guitar strings as input, and one
>> that’s be pre-crunchified with a stompbox) is that for the former you might
>> get by with a lower-order filter, because guitar string harmonics drops of
>> pretty quickly by themselves. (So, you might design an amp sim that seems
>> relatively alias-free, then get a customer or beta tester complaining about
>> the aliasing, and that's were you find out that guitarists will still want
>> to run their stuff into your sim, even if you give them those functions in
>> DSP.)
>
> well, i know there can be different specs. but for a 32-tap FIR LPF, you can
> put the same brick-wall LPF on both guitar (that might not need it as bad)
> and the grunge box. it's just that for clean amp setting, you might hear the
> difference between your straight-grunge pedal and the LPF'd one (and it's
> less necessary, maybe that means opening up the LPF as the gain knob setting
> is reduced).
>
> --
>
> r b-j r...@audioimagination.com
>
> "Imagination is more important than knowledge."
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