Ah, my bad. You meant physical degree, not signal degree.
I prefer not "change in placement" but rather, "differential location". Change in placement implies head in vice.
So given a reference source 10 feet in front on axis, what does 1 physical degree to the side represent in ITD and IID?
I went through that exercise 15 years or so ago, providing graphs of ITD and IID accuracies required of the system to guarantee accurate placement within a 2d soundstage. Not as it were, what humans could do, but what accuracies were required of the system.
To wit, what ITD and IID would be required to place a source 6 inches to the right and 6 inches behind a reference source located 10 degrees off center 12 feet distant.
I recall I put up some of the graphs in either A. asylum or that other forum I used to go to, but all I got was drooling on the floor from the others.
That's why I only post here, despite the tendencies of quite a few here who just argue.
Jn
The answer seems obvious and contained in the question. So I invite you to think about it.
Anyway, whatever the subject, I note that, on this forum, the same contributors are entitled to the same attacks from the same handful of others.
Attacks on the person instead of a friendly exchange of arguments.
The subject therefore becomes more sociological and behavioral than scientific.
Please do not take out of context a specific statement intended to answer a specific error.
Your first word, "true", should have ended that context.
As I pointed out, when sampling just slightly faster than 2x, there is an amplitude uncertainty that can only be resolved with a large window.
Jn
Not true in theory. You just need an ideal ADC with infinite amplitude resolution.
In practice you can't have that.
Agreed, specifically clock jitter.
However, cone position will indeed create jitter of the hf portion of the audio, and it is conceivable that it can heighten our localization capability, or just muddy it..
Basically, a single full range driver thing.
I am unaware of any research along those lines however.
Jn
As simple as higher frequency? I hope you don't consider my question argumentative, actually, I don't give a toss, your continual complaining is amusing though 🙂
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Get some graph paper, draw a sine, then sample it at 0, 180, and 360 degrees. Zero is zero no matter how many decimal places.
Now, start at zero, sample every 179 degrees. 0, 179, 358, 537, 716....
You will find the sampled amplitude continues to get larger, reaching peak at 45 cycles.
It has nothing to do the ADC accuracy.
Edit: to be fair, I just realized you interpreted amplitude accuracy as per sample accuracy, whereas I meant accuracy of the sine constructed using the sample values. Your statement was accurate on its own, but not with respect to my intended content.
Jn
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There are errors of digital/quantized measurement that are related to data conversion. Quantizing samples, say, of a signal in the form of an analog voltage.
The linearity of a transducer is a separate source of error to consider. In theory, the way Scott Wucer and syn08 are talking about, we assume a linear transducer (which transducers should be, in theory).
You want to talk about practical transducers which are nonlinear enough that they may not behave exactly as linear models predict. In part it depends on how complex of a model we/you might choose to use.
In other words, I am saying that the argument all along has been between people talking past each other. One group is talking about theory, the other group and practical implementations.
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Please let me try to explain: If you take two sample points of sine wave, it doesn't matter which two samples they are just so long as the measurement of the two points is ideal (perfectly accurate).
That is because you would get the unique solution of the original sine wave regardless of which two points you take. Any set of two adjacent sample points taken at any phase of the wave will give the same reconstruction of the original sine wave after being processed by an ideal reconstruction filter. A human can't tell what the reconstructed output will look like only by looking at a set of sample points. A human doesn't see from visual inspection on graph paper that there is only one possible sine wave that will come out if the reconstruction filter (if it is an ideal filter!).
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Acoustic jitter at a full range driver, to first order, is linear and due to cone displacement, not in the least non linear.
Granted, there are also nonlinearities in the drivers, but first order is the change in physical distance to the ears. At a foot per millisecond, the cone displacement needed to jitter hf content 5 uSec is not that large. Simply raising the volume or even just the bass changes the jitter level.
And yes, so many here talk past one another and display their frustrations in text. It is not limited to forums... I deal with this everyday, trying to explain bode plots/phase margin to motion control engineers, involute gear meshing issues on torque ripple to physicists, non orthogonal system coupling to mechanical engineers.
The best aspect of running a task force is the luxury of having everyone in the same room discussing, clarifying, engaging everybody, and listening to all opinions without dissing. On forum, it is hindered by using just the written word.
Jn
Granted, there are also nonlinearities in the drivers, but first order is the change in physical distance to the ears. At a foot per millisecond, the cone displacement needed to jitter hf content 5 uSec is not that large. Simply raising the volume or even just the bass changes the jitter level.
And yes, so many here talk past one another and display their frustrations in text. It is not limited to forums... I deal with this everyday, trying to explain bode plots/phase margin to motion control engineers, involute gear meshing issues on torque ripple to physicists, non orthogonal system coupling to mechanical engineers.
The best aspect of running a task force is the luxury of having everyone in the same room discussing, clarifying, engaging everybody, and listening to all opinions without dissing. On forum, it is hindered by using just the written word.
Jn
Mark, two points are insufficient to reconstruct both amplitude and phase, especially at 2x.
As I said, try drawing it out.
Jn
As I said, try drawing it out.
Jn
Is there any other aspect of jitter really? Clock jitter of course in the end effect data... Never heard any aspect of cone movement being referred to as "jitter" - that was new to me.
//
Would you please stop repeating this after having mentioned it so many times over and again.
Your opinion is clear to everybody, don’t try to Christen us.
Hans
Jn, you pencil would have to have a point sharper than a tunneling microscope needle to plot the points accurately enough. And you would have to keep your drawing errors equally small.
EDIT: A thought or drawing experiment: With only three sample points, you can't draw another other frequency and phase than the wave you started with. There is no other sine wave that will perfectly fit. You can try drawing a sine wave as best as you can then putting a dot at each point on the wave at three equally spaced intervals along the horizontal axis (compliant with Nyquist in horizontal spacing, of course). Then try to draw another wave or another phase through those dots. If it looks like you can do it, its only because your pencil point isn't sharp enough for you to do it accurately. The exercise may make it easier to grok why sample points are unique to identify a sine wav in terms of frequency, amplitude, and phase.
Look, people run into the same issue you have here with not understanding reconstruction of samples when they create intersample overs on CDs. If one looks at the sample points in a program such as Audacity, one never sees a sample point above 0dBFS.
However, peaks reproduced during reconstruction can be located between to sample points and those peaks can be higher than 0dBFS. Humans can't see that will happen from looking at the sample points, but the sample points do indeed require a peak there after reconstruction.
Similar type of thing happening with you and your graph paper plots. You don't think like an ideal reconstructor. You would be fired if that were your job 🙂
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Mark,
Pull up excel.
Column a, integer index numbers 1 to 100. ("Row index")
Cell 1g, starting angle in degrees, "S"
Cell 2g, sampling interval in degrees, "I"
Column b, an equation, value ="S" + "row index" times "I".
Column c, the sine of column b (make sure you convert to degrees, I always invariably mess that up.
Graph column A as the horizontal axis, column C as vertical.
Now you can play with sampling rate and sampling offset to see what I speak of.
My apologies, it takes longer to type this up than actually making the spreadsheet.
Jn
Pull up excel.
Column a, integer index numbers 1 to 100. ("Row index")
Cell 1g, starting angle in degrees, "S"
Cell 2g, sampling interval in degrees, "I"
Column b, an equation, value ="S" + "row index" times "I".
Column c, the sine of column b (make sure you convert to degrees, I always invariably mess that up.
Graph column A as the horizontal axis, column C as vertical.
Now you can play with sampling rate and sampling offset to see what I speak of.
My apologies, it takes longer to type this up than actually making the spreadsheet.
Jn
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You do realize it was a response to another's statement, right?
Are you saying I must shut up if what I say doesn't jibe with your thinking?
Happily, that is not how this discussion forum works.
Jn
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