In one case, I made a convert, by asking how many (sample) points it would take to exactly reproduce a specified straight line.
He started with "You need an infinite number of points!", but eventually realized that you really only need two points to exactly solve the equation y = A + B x, where A and B are the two unknown coefficients.
With that out of the way, I then asked him how many points one would need to solve the equation y = A sin(w t), where "A" and "w" were the two unknown coefficients, assuming both points were no more than a period apart...
This simplified way of looking at it doesn't require understanding complex discrete time mathematics, or even the Fourier series. But it still requires high-school level math (sets of linear equations, trig and inverse trig functions, etc.) So it won't work on someone who is completely clueless about math.
It helped a lot that this particular discussion was with a smart recent high-school graduate; he knew enough mathematics to come to the correct conclusions. He'd just been led to the wrong conclusions by the current cultural beliefs in the superiority of scratchy, hissy vinyl.
-Gnobuddy
Come one, Gnobuddy, then why do we still listen to music at all and not just read the composer's notes? Because we want the continouus line.
Jan.didden, because not everything written is true, and new experiences are made all the time. Our ears may have some hysteresis, which is best overcome by a broader spectrum. Just as we are not meant to hear the HF bias of analogue tape machines conscientously yet we need it, if we want to get the most from analogue tape machines. Music is not meant to be a fully conscientous thing, is it? What about freedom of imagination? The CD, MP3 and so on have suppressed this some and caused digital stress.
Jan.didden, because not everything written is true, and new experiences are made all the time. Our ears may have some hysteresis, which is best overcome by a broader spectrum. Just as we are not meant to hear the HF bias of analogue tape machines conscientously yet we need it, if we want to get the most from analogue tape machines. Music is not meant to be a fully conscientous thing, is it? What about freedom of imagination? The CD, MP3 and so on have suppressed this some and caused digital stress.
I have no https here.
You don't have to; they have.
But I guess if you are determined to stay ignorant, you'll always find a way.
Jan
The whole point is that you do get the "continuous line" from digital audio. And it's a better continuous line than you get from vinyl or tape, without ticks, pops, scratches, surface noise, tape hiss, audible wow and flutter, print-through, et cetera, et cetera.
Judging by the prevalence of the "digital equals staircase" explanations all over the Internet, most non-technical people don't understand the role that the anti-aliasing filter plays in reconstructing the "continuous line" from the digital samples; the filter doesn't just remove image frequencies, it also turns those discrete samples into a continuous, analog, line.
This is easily seen with an oscilloscope on the (analog) outputs of any CD player.
-Gnobuddy
That is the problem we often face. Person puts up daft idea. Lacks sufficient background knowledge to understand rebuttal; in bad cases lacks any awareness of the depth of his ignorance. Claims that as his daft idea has not been proved wrong (in his own eyes) then it must be right and we are all daft/deaf/poor/ignorant/deluded to believe otherwise.Gnobuddy said:
I must admit that it took me a while to grasp this - although I think you mean reconstruction filter, not anti-aliasing filter.
A wise person once said: “He who knows not and knows not he knows not: he is a fool - shun him."
Harsh, but when it comes to someone who glorifies in his own ignorance, perhaps true?
Indeed I do, thank you for the correction!
It took me a while to grasp, too. The mathematics and concepts that make digital audio work are not particularly intuitive or easy to grasp, or we wouldn't have needed an uber-genius like Claude Shannon to figure it all out for us!
-Gnobuddy
The maths are not so complicated to design digital audio,
they need skilled chip circuit drawers, like the tda1541, the achievement of this century.
bits are drawn into patterns meaning numbers left and right channels, clocks are made of capacitors discharging and charging and amplified crystal vibration impulses
none of this in a vinyl groove it is straight a natural sound , so more likely to relax the listener than electronic sounds.
they need skilled chip circuit drawers, like the tda1541, the achievement of this century.
bits are drawn into patterns meaning numbers left and right channels, clocks are made of capacitors discharging and charging and amplified crystal vibration impulses
none of this in a vinyl groove it is straight a natural sound , so more likely to relax the listener than electronic sounds.
I think you mean last century.
Pleasant and natural are two completely different things. Why do people confuse them so?
What on earth do you mean? African Black Mamba venom is entirely natural, and so very pleasant!
-Gnobuddy
Back in the late 1990s, I designed some IIR and FIR filters running on a Texas Instruments 56000 series DSP chips. Back then, I designed the filters in Matlab, and used it (Matlab) to generate the filter coefficients. It was complex, but within the reach of a smart science or engineering undergrad. So, yes, it was not very complicated to implement the filters.
It's even easier these days. Smart people have created tools that make it easy for ordinary people to create filters - just click and drag a few points on a computer screen! Most DAWs (digital audio workstation software, used for recording audio) have this sort of capability now.
But implementing filters was not the math I was talking about - I was talking about the math that describes how an FIR or IIR filter works in the first place, and how to calculate the filter coefficients for a given frequency response.
That is fairly complex stuff, and not very intuitive, as witnessed by all the nonsense we see written about it. What ordinary person could come up with the idea that delaying a signal multiple times, and adding up all the delayed signals with the right weights, would let you create almost any frequency response of your choosing? It took geniuses to see these possibilities, and then to prove them mathematically.
-Gnobuddy
Come on, man. What about all the other garbage that is in a vinyl groove? The stuff that was so not-relaxing that I found myself avoiding entire categories of recorded music on vinyl because it sounded like crap to me, that I was subsequently able to enjoy immensely, and yes, relax with, after it was released on CD?
But this actually brings me to another question regarding audio and the sometimes stressful ways we discuss it. For example:
I assume these are personal observations, since there are no citations or other attempts to substantiate the claims made. But to me, stating personal opinions as facts in this manner can come off as a little arrogant - sometimes more that a little, depending on the claims.
When I express a personal opinion or make a claim that can't be cited or otherwise substantiated, I always try to include qualifiers like "I think," or "to me," etc. from time to time. I know this can sometimes sound conceited ("Well, this is what *I* believe"), but I think it's necessary to err a bit on the side of caution, especially in written communication.
Am I just being pedantic here? Do you guys read something like the above as an opinion and move on, or does it stick in your craw a little?
Last but not least: I don't mean to single you out, gabdx; it's just that you provided such a good example.
-- Jim
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There is also the not-so-insignificant question of what the stylus does, which usually isn't what the groove does.
One major source of vinyl playback distortion is "tracing distortion", a geometric effect caused by the fact that the cutting stylus that made the master record has razor-sharp edges, but the playback stylus does not, instead it has a circular or, at best, elliptical or "hyper elliptical" contour.
This, literally, means that the playback stylus does not follow the same curve that the cutting stylus carved into the record. Massive mounts of harmonic distortion are created by this mismatch.
And that's in a best-of-all-worlds scenario. It can be much worse: I've seen electron microscope photos of the walls of a groove in a vinyl record, showing the stylus actually moving in anti-phase to the original groove. The cartridge wasn't even remotely close to reproducing the sound in the groove, instead it was literally carving its own noise into the vinyl!
This sort of permanent deformation of the original signal on the record can be caused by excessive tip mass of the stylus, or excessive tracking force.
And we haven't even talked about the ticks, pops, scratches, surface noise, wow, print-through from adjacent grooves, etc, etc.
Why on earth are so many people still so keen to believe that trying to shake a tiny rock on a tiny stick 20,000 times a second is a good way to accurately reproduce music?
-Gnobuddy
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