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Author Topic: A Challenge to Fourier Or Not?...You Decide.  (Read 26006 times)

Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #15 on: May 28, 2005, 07:31:44 PM »

Analogue is the heart and soul of all music, Digital is just a step in the middle (a way to get from here to there)

but with music...Analogue is THE alpha and THE omega.


Smile




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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

dayvel

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #16 on: May 30, 2005, 10:24:40 PM »

But if you were as big as a quark, you'd think an analog-style description of reality was pretty silly.
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Dave Latchaw
Not an engineer - just a musician.

trevord

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #17 on: June 01, 2005, 01:08:28 PM »

yeah..
i remember a lot of debate.
The main problem is asymptotic relationships. The really interesting things in math happens in the "tends to" region and digital math doesn't cut it.

well..
it does within "acceptable limits"

If you think those problems are solved, talk to the people at Intel about the little floating point snafu that sent quakes thru the audio industry.

I was always amazed at the ease of representing physical systems with circuitry and vice versa.

I am not sure how it would apply to audio tho.
Normally you think of a "computer" replacing an actual circuit, so an analog computer circuit would replace an actual analog circuit?
Maybe it doesn't quite apply.

trevor

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danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #18 on: June 01, 2005, 02:15:45 PM »

trevord wrote on Wed, 01 June 2005 18:08

yeah..
i remember a lot of debate.
The main problem is asymptotic relationships. The really interesting things in math happens in the "tends to" region and digital math doesn't cut it.

well..
it does within "acceptable limits"

If you think those problems are solved, talk to the people at Intel about the little floating point snafu that sent quakes thru the audio industry.

I was always amazed at the ease of representing physical systems with circuitry and vice versa.

I am not sure how it would apply to audio tho.
Normally you think of a "computer" replacing an actual circuit, so an analog computer circuit would replace an actual analog circuit?
Maybe it doesn't quite apply.

trevor





Trevor,

The digital math provides a PERFECT representation of the analog signal, as long as you obey Nyquist and sample faster then twice the signal bandwidth. It is not easy to swallow with simple common sense, but it is is a fact. Check my paper "Sampling Theory" on my web site, and you may get a better sense of it.

What ever objections you may have to digital, it is not about the math. The sources of objections may be about resolution, truncation, aliasing, long time delays... all are implementations of perfect math model, and many of the issues are being addressed. The technology is not perfect, but it is better than it was, and will continue to improve.

Regards
Dan Lavry
www.lavryengineering.com
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trevord

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #19 on: June 01, 2005, 05:11:12 PM »

i am not talking about digital representation of analog as in a to d.
I am talking about the quality of the math algorithms' handling of small values.

For example if a formula tends to 0 with a asymptote, most algorithms "give up" quickly and the value of the formula becomes 0. This describes the quality of the algorithm (not the digital representation of an analog signal).

Math algorithms are far from perfect because they are the result of compromises between accuracy and  processing time.
These are valid design choices and the "correctness" of the choice depends on the context.
Some of these choices maybe things like..
Smaller terms of the polynomials are usually ignored.
The numbers of "taps" of a filter may be reduced.
etc.

In fact, some more complex scenarios are sensitive to the "initial conditions" and will not produce a solution if the input is not in the expected range.


To sum up.
I was not referring to the representation of an analog signal in the digital domain. It can be a perfect representation - we agree.
I was not referring to the theory (or equation) of a particular formula. Theoretically - the formula is correct - we agree.

I was referring to the implementation (trade-offs) of the formula by design choices made in a digital system.

Two examples...
The classic case is now the infamous pentium "NAN" flaw.
To (very) briefly sum it up.
FP representation changes when a number get very close to 0
The theory behind this works.
BUT
The Intel Pentium 4 implementation did an exception to execute special code to handle this case (thus making the FPU simpler and faster) - again - it works
Of course this meant FP operations which hit this would run orders of magnitude slower, but they (Intel) assumed this happens in only a small percentage of cases.
BUT
This is the bread and butter of most audio math algorithms.
(think reverb tail)
This resulted in the "CPU spike" most of you saw with your DAW, and the subsequent re-coding of most the math algorithms for these apps.

Another example is aliasing noise in virtual analog synths. Again - this is not the aliasing in the digital/analog conversion, this aliasing is the result of poor choices made in the implementation of the synthesis formulas (ae) by DSP programmers.
Which is why you have price differences in virtual analog synths.
(to "ear people" - your ears are right, there is a difference)

So the quality of the implementation of the math makes a very big difference.




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danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #20 on: June 01, 2005, 05:53:51 PM »

trevord wrote on Wed, 01 June 2005 22:11

i am not talking about digital representation of analog as in a to d.
I am talking about the quality of the math algorithms' handling of small values....

To sum up.
I was not referring to the representation of an analog signal in the digital domain. It can be a perfect representation - we agree.
I was not referring to the theory (or equation) of a particular formula. Theoretically - the formula is correct - we agree.

I was referring to the implementation (trade-offs) of the formula by design choices made in a digital system....

...So the quality of the implementation of the math makes a very big difference...




Thanks for clarifying. Now that I understand what you mean, I agree with all that you said.

Regards
Dan Lavry
www.lavryengineering.com
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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #21 on: June 01, 2005, 07:15:35 PM »

danlavry wrote on Wed, 01 June 2005 19:15

[Digital "technology is not perfect, but it is better than it was, and will continue to improve."


I agree with this.
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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #22 on: June 01, 2005, 07:20:32 PM »

trevord wrote on Wed, 01 June 2005 22:11

 This "aliasing is the result of poor choices made in the implementation of the synthesis formulas (ae) by DSP programmers.
Which is why you have price differences in virtual analog synths.
(to "ear people" - your ears are right, there is a difference)

So the quality of the implementation of the math makes a very big difference."



I also agree with much of this, many bad trade-offs have been made, and this may partially explain why the "ear people" continue to complain about digital's bad sound quaility.



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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

trevord

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #23 on: June 01, 2005, 11:07:29 PM »

it is so true.
what is even more disturbing is the fact that some of these issues we solved many years ago.

For example, the orignal korg oasys is a dream to listen to, i know i did not know how good a virtual analog could sound until i got the original oasys pci card. But this was how long ago, 10-15 years ago. I still fight tooth and nail to keep it going despite lack of support.

And with the pentium FPU problem - many programmers are opting for the "easy" way out by adding moise to low level signals when the signal gets low enough to cause the problem. So much for "pristine" mixing "in the box".

I have a lot of respect for "ear people", i am more a "math" person, but i have trained myself to go past the explanations when talking to ear people and listen to what they are really saying.
9 times out of 10 a good ear person will detect a problem before the math people figure it out.

thats why we need more ear people designers
if you throw enough money at the problem a good design is a no-brainer
but when you have to meet cost considerations you need an ear to determine which is the "best" solution
i think right now we seeing the most cost effective designs - not the best designs
(present company excepted Smile )
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RedBus

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #24 on: June 02, 2005, 12:24:57 PM »

Quote:


And with the pentium FPU problem - many programmers are opting for the "easy" way out by adding moise to low level signals when the signal gets low enough to cause the problem. So much for "pristine" mixing "in the box".



Stop right there before this misconception gets out of hand.

It is true that adding low level noise is an acceptable way to avoid the Pentium processor from degenerating a floating point signal into "denormal" representation, which incurs a 10x to 100x processing time penalty. BUT, that noise signal can be at -150dB to -200dB and still have the correct effect. Don't let anyone believe that they can hear that signal on top of the audio passing through the DAW's mixing bus.  
If you were adding that noise in an algorithm where it will get fed back, then there may be problems, but then that is the wrong choice to make for that design.

RedBus.
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trevord

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #25 on: June 02, 2005, 01:25:57 PM »

RedBus wrote on Thu, 02 June 2005 17:24

Quote:


And with the pentium FPU problem - many programmers are opting for the "easy" way out by adding moise to low level signals when the signal gets low enough to cause the problem. So much for "pristine" mixing "in the box".



Stop right there before this misconception gets out of hand.

It is true that adding low level noise is an acceptable way to avoid the Pentium processor from degenerating a floating point signal into "denormal" representation, which incurs a 10x to 100x processing time penalty. BUT, that noise signal can be at -150dB to -200dB and still have the correct effect. Don't let anyone believe that they can hear that signal on top of the audio passing through the DAW's mixing bus.  
If you were adding that noise in an algorithm where it will get fed back, then there may be problems, but then that is the wrong choice to make for that design.

RedBus.


i agree..
the point i wanted to make was..
a lot of lower priced (or free) DAW and VSTi vendors say use the "math is math" argument
but they are making choices which can affect the quality of the result.
Usually is goes like
an ear person says "it sounds funny to me"
the free VSTi guy says "math is math, we do it just like the big boys"
but if you probe a little deeper you may find some of these bad choices.

I think you are trying to prevent the usual round of "see i told you so" from ear people, but "math is math" is just as bad a misconception.

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RedBus

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #26 on: June 02, 2005, 04:25:08 PM »

Quote:

the point i wanted to make was..
a lot of lower priced (or free) DAW and VSTi vendors say use the "math is math" argument
but they are making choices which can affect the quality of the result.
Usually is goes like
an ear person says "it sounds funny to me"
the free VSTi guy says "math is math, we do it just like the big boys"
but if you probe a little deeper you may find some of these bad choices.



Part of the misconception is that the mistakes made by the "free" DAW or plug-in creators are duplicated in the commercial DAWs.  For confidentiality reasons you'll never see those actual engineers speak up and talk about what choices and why they made them in implementing summing et al.
Lynn Fuston's Awesome DAWsum CD dispells much of the myth when it comes to the current generation of DAWs.
The plug-in creators further down the food chain are trying to gets sales wherever they can (if it's not free), so they'll spin their own limitations however many ways required to get other people to buy.

This is starting to veer a long way off the original topic, but we are talking about the same plug-in creators who put the following kind of text in their press release (from Harmony Central).


ParametrEQ  Common Features:
"Low CPU usage"
"Randomize features: choose to randomly set the bandwidth, frequencies or gain separately."

and no mention whether there has been attention paid to word length issues or denormals...

RedBus.
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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #27 on: June 02, 2005, 06:15:43 PM »


What DAW Sum "myth" does Lynn's CD "dispell?"

And, perhaps more importantly, can we honestly attribute all the bad sound quality charges to only this narrow cause?

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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

trevord

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #28 on: June 02, 2005, 06:49:57 PM »

I think he is referring to the test which showed most quality daw software produced the same result when summing many tracks. (in an identical fashion).


But we are referring to the use of math for effects purposes (i don't think you have to use Fourier for summing).

IMHO - the differences between DAWs would show if there was a way to set set EQ (or some other effect) parameters on a track.

I am not sure there is a way to qualify the "correctness" of an effect processing implementation.

take EQ for example
there could be a theoretical output for a given Q,f and cut,
but some DAWs may strive to emulate more "musical" (vintage) EQ boxes, which is not wrong by itself.

Plus its not just the results of the math algorithm, but the ability of the DSP implementation to handle increased processor loads.

For example a particular effect implementation may sound good with no processor load, but if the design choice is too cpu intensive, then running more tracks may result in inferior sound (or outright failure).

Is a more "accurate" cpu intensive effect implementation better
than a less "accurate" implementation which can handle more tracks?

And we haven't even talked about what happens when the lesser accuracy produces a more pleasing / desirable sound.
With virtual analog DSP programming, for example, a major part of the difficulty is reproducing things like random frequency drift and imperfections in oscillator sync'ing


The only way to judge a good or bad math algorithm choice is how it sounds.

Even that may be misleading, because some DAWs use a less accurate effect implementation for real-time and a more accurate cpu intensive version for "printing" the track or for mixdown.

it's a very grey world when things go from theory to implementation.

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RedBus

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #29 on: June 02, 2005, 07:44:39 PM »

The Myth is basically that DAWs sound different because of the way their summing is implemented. The CD proves that given the same input files and the same fader levels, you get the same data (bit-for-bit accurate) out of most DAWs.  If you still hear a difference, it is because of other parts of your system.

If we start to discuss the implementation in the digital world of the flaws of a particular analog circuit, then the sky is the limit and people will have a right to their opinion if they say the digital version doesn't sound correct, etc.

Implementation in digital of the non-linear processes that sometimes goes on in the analog world (e.g. opto-coupler in a compressor) does bring us back to the trade-offs, good and bad, that people make.
One cardinal matematical rule about such implementation is that you have to deal with the higher frequencies generated in the process. Usually this means upsampling the incoming data and performing the whole simulation at a higher rate, then filtering it back down to the original rate.  The quality of this conversion dictates the accuracy of the model, assuming that your model was mathematically close to the analog process to start with.
But, one shortcut you can take is to not do the upsampling. That guarantees you get aliased audio when you do your analog simulation, but it may end up being an entirely new effect that you want to keep. I'm sure that this wouldn't work for all audio sources you throw at such an algorithm (assuming you were going for a model of a smooth opto-compressor instead of a grungy distorted comp), but it opens up new paths.

RedBus.
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