[jimmers]

I should note something here......

Now let's assume that I start with an unreasonably abrupt impulse (let's call it 5 uS).
(And, yes, I can easily generate a 5 uS sound pulse using various methods.)
Even though most of the energy in that impulse will be at inaudible frequencies, enough will extend into the audible range that we will hear it as a click.
...

If it is truly unadulterated, I would expect the listener to hear nothing.

That's what I was questioning, maybe I was too subtle (?)

As for my other quoter, try reading what I wrote.

Edit:

Sorry I overlooked this was a "Discussion in 'Sound Science'" I arrived here via a link in another thread.

cue:
"Back to Earth Back to Reality".

 

[gregorio]

HOWEVER:
1) in order to do so we will have to make certain assumptions about the filter we used
(we'll assume that, if there is equal amplitude in two samples, then the pulse was equidistant in time between them - but this assumption relies on our filter spreading the energy symmetrically in time)
2) the new waveform will be very different than the original
3) more importantly, unlike the original, our new waveform will have a much more gradual envelope
3a) as a result, mechanisms that rely on sensing abrupt edges of waveforms will be less able to accurately "find" the beginning edge of the impulse
3b) current research seems to strongly suggest that our brains do in fact look for those "edges"
3c) this in turn suggests that turning a sharp impulse into a more gradual band limited waveform may compromise the accuracy with which our brains can determine its exact beginning
3d) and this, in turn, suggests that doing so may reduce the accuracy with which our brains are able to utilize this particular location cue
(if the starting time of the impulse cannot be determined distinctly, then we will have the equivalent of a blurry image when we attempt to compare them)

An audiophile myth which you keep repeating and which I've explained is nonsense:
1. Agreed, assuming a linear phase filter but a minimal phase/apodizing doesn't, you only get post-ringing, not pre-ringing.
2. What original?
3. What original?
3a. What beginning edge of the impulse?
3b. Not that I'm aware of. All the research I'm aware of suggests that ITD, measures/compares phase relationships of the signal reaching different ears. How can the brain measure/compare edges when there are no edges?
3c. A suggestion based on edges which don't exist.
3d. A further suggestion based on edges which don't exist!

A sine wave does not have an "edge"! Modulated sine waves do not have an edge! Anything other than sine waves cannot exist; they cannot travel through air, even if they could, your ear drum cannot respond to them, an analogue current can only be sine waves and our transducers (mics, speaker drivers) can only respond to or recreate sine waves. So, what "original" waveform are you talking about in 2 & 3? You CANNOT be not talking about an original waveform, you can ONLY be talking about digital data which cannot exist as a waveform and then you're complaining that this data which cannot be a waveform becomes distorted when we try and turn it into a waveform, huh? Let's put it another way, let's say we invented a theoretical system and filter which could perfectly reconstruct your impulse, what then? What are you going to convert it into? You can't convert it into an analogue electrical signal because you'll loose your "edges", you cannot use some other method because your speakers/headphones will distort your edges, as will the air and your ear drums.

... if the starting time of the impulse cannot be determined distinctly, then we will have the equivalent of a blurry image when we attempt to compare them

And how can we have anything other than a "blurry image"? ONLY "blurry images" can travel through air, ONLY "blurry images" can be recorded, reproduced and heard. Think about it for a moment! With a square wave you have an instantaneous rise time ("edge"), a speaker cone would have to be in two different places at the same instant in time to accurately reproduce it, the molecules in the air would have to be in two different places at the same instant in time to transfer that square wave, so would your ear drums and so would the electrons in the analogue electrical current.

G

 

[gregorio]

Why does it only work on continuous sine waves? What goes wrong with other signals? ... I tested this on Audacity. I created pink noise at 96 kHz.

I'm not sure how that's a test of "other signals", pink noise IS continuous sine waves.

G

 

[Darren G]

And how can we have anything other than a "blurry image"? ONLY "blurry images" can travel through air, ONLY "blurry images" can be recorded, reproduced and heard. Think about it for a moment! With a square wave you have an instantaneous rise time ("edge"), a speaker cone would have to be in two different places at the same instant in time to accurately reproduce it, the molecules in the air would have to be in two different places at the same instant in time to transfer that square wave, so would your ear drums and so would the electrons in the analogue electrical current.

G

This^^^ Yes, and mics, transducers, and our ears do not have infinitely fast rise/fall times either, hence frequency limited.

 

[71 dB]

I'm not sure how that's a test of "other signals", pink noise IS continuous sine waves.

G

The difference of an impulse and white noise is phase. Both have flat magnitude spectrums.

 

[71 dB]

I can make one with a single monostable multivibrator or a digital file ..0.0,0,0,1,0,0 ... read at 200 kHz, with either fed into an electro-acoustical transducer.

Hmm.. …what analog signal bandlimited to frequencies below 100 kHz as required by sampling theory is going to give you ...0.0,0,0,1,0,0… ? Such analog signal does not exist.

If you put it to DAC, you get sinc-like ringing analog sound depending on your reconstruction filter. If you sample it back, you get a sinc-like sample values.

 

[bigshot]

CDs are for bums because they can't reproduce cosmic waves!

 

[jimmers]

Hmm.. …what analog signal bandlimited to frequencies below 100 kHz as required by sampling theory is going to give you ...0.0,0,0,1,0,0… ? Such analog signal does not exist.

If you put it to DAC, you get sinc-like ringing analog sound depending on your reconstruction filter. If you sample it back, you get a sinc-like sample values.

As for my other quoter(s), try reading what I wrote.
.

 

[frodeni]

This has been done many times, I find it to be exaggerated and fake sounding. Go to AES or NAB, somebody is always demoing some great new 3D or VR audio. I think it was Dolby demoing VR for headphones. It is always exaggerated. You want it sound real, place your microphones to capture what you want 360 hemispherical, spherical. Map the physical locations on the microphone. Place loudspeakers at the inverse of the microphones a few feet out and sit in the center. It will be real enough you will be looking over your shoulder.

You missed the point, as to virtually reproduce the physics of sounds, by using a headset, compensating for the physics of the head of the listener, on the fly or pre recording. As for using mono recordings, that is how greater parts of the industry work, as it is, right now.

 

[KeithEmo]

You're making a very basic - and false - assumption.
The original analog signal is a series of measurements of the pressure of the air over time.
It has no constraints and no limitations.... and no band limitations... and no windows limitations.
It is NOT a SinC function... it is completely arbitrary.
Set off a string of fire crackers.
Each pop is a single pressure wave, which expands, and eventually hits your ears.
What follows is a whole bunch of odd little squiggles in pressure as that wave bounces around and interacts with other stuff.
If I had a "perfect oscilloscope" I could draw a "perfect" picture of it.
There is no sound whatsoever before the first pop.

Things like "windowing errors" and "Gibbs ringing" do not exist in the original.
They are ERRORS that result from the conversion into digital.

1)
I'm going to hit a bell......... now.
In order to make an "accurate digital representation" of that signal - sort of......
You can sample it.
When you then reconstruct those samples, in order to do so perfectly, and get back a "perfect" version of the original (in terms of energy distribution) your reconstructed signal would have to extend backward in time.
Forget the practicalities of that.......
The original bell hit had ZERO energy before I hit the bell; your reconstruction does; therefore your reconstruction has an error.
(The bell was NOT ringing before I hit it... but, in your reconstructed signal there is ringing before the bell hit; therefore they are NOT the same.)
Therefore, the ONLY question is whether the error that we know exists is audible or not.

2)
A DAC does NOT use a SinC function.
The output of a DAC is NOT "a sum of sample-weighted sinc-functions with various delays"
The DAC (chip) outputs a stream on analog voltages - one for each sample you feed to it.
The DAC (chip) does not put out signal before it receives the fist signal (even if a "real" SinC reconstruction would require it to do so).

I'm not a mathematician....... but I believe that the "problem" is that the SinC function of a non-continuous waveform must extend forward and backward in time to infinity.
(The SinC function of a continuous sine wave needn't do that..... which is why the theory works perfectly for continuous sine waves.)

I can give you a more ridiculous - but still valid - example.......

Let's design the most ridiculous filter imaginable.
It will be a super-duper-hyper-narrow bandpass filer.
It will pass 400.0000000000 Hz, with a cutoff of a million dB per octave.
I'm too lazy to do the math, but you will find that, due to the tradeoff between time resolution and sharpness
....our fun filter will take SEVERAL SECONDS to ring up to approximately full output level once it receives a 400 Hz input signal
....and our fun filter will ring detectably for several seconds after the signal stops (it will actually ring forever, but I've made sure it will ring powerfully enough that it will be easy to see).

I now create a tone burst that is 40 cycles of a 400 Hz tone (it exists for 0.1 seconds).
If I play it from reasonably good speakers in an anechoic chamber it will seem to start and stop quite suddenly.
I can create my signal by taking the output of a signal generator set to 400 Hz and gating it at the zero crossing point to pass ten full cycles and then stop.
(I'm going to gate it using an FET for a switch.)

Now I'm going to send this signal to my fun filter.

The input of my filter will be a 0.1 second set of ten sine wave cycles of a 400 Hz tone.
The output will NOT.
It will increase in level gradually and decrease (continue to ring) for several seconds.
The INFORMATION it contains will be the same (which satisfies Nyquist and Shannon).
(Nyquist and Shannon don't actually specify how long I have to wait for all of my information to "accumulate" or "reconstruct".)
However, the FORM of that information will be very different...... which may or may not satisfy a human being.

Basically, at the risk of being intuitive, the information theory says that, as long as you follow certain constraints, the SAME INFORMATION will still be there.
HOWEVER, their definition of the term "information" isn't intuitively what you might think.
I could post this message in Braille, or in MIME encoding...... the same information would be there...... but it would LOOK quite different.
Likewise, Nyquist & Shannon make a statement about the information.... but not about how our signal SOUNDS, or whether it is AUDIBLY the same as the original.

(When we design DACs, we do our best to design the filters and such so that the output also SOUNDS audibly similar.
Besides following the constraints, we follow other constraints that are based on acoustics and human perception.
For example, we don't spread out a tick over ten seconds - because we know that, even if the information content is the same, it will SOUND different.

I feel sick and tired today, so it's hard to think. The analog signal is a sum of sample-weighted sinc-functions with various delays. I don't get why this works only for sine waves.
Time errors shouldn't be dependent on delay. Why would a filter cause different time error for delayed signal? Doesn't make sense. That would require time-variant filters. Maybe it's all because the sinc -functions are actually windowed versions. In that case we can increase window size and reduce the error, make it as small as we want (need).

 

[KeithEmo]

Bingo.
But sampling theory does NOT say that "all analog signals must be band limited".
I can mechanically or electrically generate a signal whose voltage values at consecutive sample points are 0,0,0,0,1,0,0.
Rather, that is a limitation of what the input of the DAC will accept, and of the PARTICULAR sample rate you have chosen.
Essentially, by choosing to convert your analog signal into a digital signal at a specific sample rate, you have "signed up" for a series of requirements and constraints.
YOU have chosen to accept the constraint of band limiting your input to 100 kHz by choosing a sample rate that cannot successfully handle frequencies above that.

Hmm.. …what analog signal bandlimited to frequencies below 100 kHz as required by sampling theory is going to give you ...0.0,0,0,1,0,0… ? Such analog signal does not exist.

If you put it to DAC, you get sinc-like ringing analog sound depending on your reconstruction filter. If you sample it back, you get a sinc-like sample values.

 

[KeithEmo]

You're falling into a trap that a lot of people fall into.........

"The analog signal is a sum of sample-weighted sinc-functions with various delays."
WRONG!
The analog signal is AN ANALOG SIGNAL.
It may be EXPRESSED, for certain purposes, as "a sum of sample-weighted sinc-functions with various delays".
You could restate this as "for any analog waveform, you can define a sum of sample-weighted sinc-functions which will recreate it with any given level of accuracy".

One of the "catches", in very simple intuitive terms, is this....
If you start with a very simple continuous sine wave, that starts in the infinite past, and extends into the infinite future, you can express it as a very simple SinC function (it's going to have a single component with a single coefficient - it's a simple sine wave).
However, as soon as you make it in the least bit more complex, then the set of SinC functions you're going to need to describe it also get more complex - very rapidly.
For example - you can describe one sine wave with a single function.
And you can describe two sine waves mixed together with two.
Yet, to define a square wave, you need an INFINITE number (because a square wave is made up of a base frequency plus ALL odd order harmonics - an infinite number of them).
(It's not at all that "in ONLY works on sine waves"; it's that, as soon as you move away from simple sine waves, the errors increase very quickly.... and, as you approach short transients, the errors become very significant.)

Another catch is this...
In order to make things work "perfectly" all we have to do is to bandwidth limit the input signal.
Let's assume that, if we can"limit the bandwidth perfectly" no audible errors will be introduced.)
However, in reality, there is no such thing as a perfect filter; this means that whatever filter we use to do our band limiting will also introduce errors.
In fact, there is an inverse correlation between time errors and the sharpness of a filter.......
If we choose a filter with a gradual slope, the time errors will be minimal, but the band limiting will be imperfect - and so we introduce aliasing errors.
And, if we choose a filter with a sharp slope, we can minimize aliasing, but at the cost of various time errors like ringing.
(In other words, the same theory that says this would all work perfectly if we had a perfect filter also says that there's no such thing as a perfect filter.)

While there are certainly filters that introduce more than the bare minimum of errors - there is in fact a minimum for a given situation beyond which no filter can ever be "more perfect".
Beyond that we're trading things off.
For example, a typical "apodizing filter" "trades pre-ringing for post-ringing".... which is a nice way of saying that it reduces pre-ringing (which is believed to be audible)....
but at the cost of increasing post-ringing even more (but post-ringing is believed to be less audible - partly because post ringing occurs on most "natural" sounds, while pre-ringing does not).

In simplest terms.....
Start with a 100 Hz square wave.... which is a collection of every odd order harmonic of 100 hz.
If you were to try to reproduce it using a SinC you would need an infinite number of terms (impractical).
So band limit it.
It will now be incorrect because you have truncated the series......
You will also have introduced additional errors by whatever band limiting filter you used.
(Now you get to decide WHICH of those errors is audible......... note that the errors we have now are not simple "extra harmonic components" like normal distortion.)

I feel sick and tired today, so it's hard to think. The analog signal is a sum of sample-weighted sinc-functions with various delays. I don't get why this works only for sine waves.
Time errors shouldn't be dependent on delay. Why would a filter cause different time error for delayed signal? Doesn't make sense. That would require time-variant filters. Maybe it's all because the sinc -functions are actually windowed versions. In that case we can increase window size and reduce the error, make it as small as we want (need).

 

[RRod]

You're falling into a trap that a lot of people fall into.........

"The analog signal is a sum of sample-weighted sinc-functions with various delays."
WRONG!
The analog signal is AN ANALOG SIGNAL.
It may be EXPRESSED, for certain purposes, as "a sum of sample-weighted sinc-functions with various delays".
You could restate this as "for any analog waveform, you can define a sum of sample-weighted sinc-functions which will recreate it with any given level of accuracy".

One of the "catches", in very simple intuitive terms, is this....
If you start with a very simple continuous sine wave, that starts in the infinite past, and extends into the infinite future, you can express it as a very simple SinC function (it's going to have a single component with a single coefficient - it's a simple sine wave).
However, as soon as you make it in the least bit more complex, then the set of SinC functions you're going to need to describe it also get more complex - very rapidly.
For example - you can describe one sine wave with a single function.
And you can describe two sine waves mixed together with two.
Yet, to define a square wave, you need an INFINITE number (because a square wave is made up of a base frequency plus ALL odd order harmonics - an infinite number of them).
(It's not at all that "in ONLY works on sine waves"; it's that, as soon as you move away from simple sine waves, the errors increase very quickly.... and, as you approach short transients, the errors become very significant.)

Another catch is this...
In order to make things work "perfectly" all we have to do is to bandwidth limit the input signal.
Let's assume that, if we can"limit the bandwidth perfectly" no audible errors will be introduced.)
However, in reality, there is no such thing as a perfect filter; this means that whatever filter we use to do our band limiting will also introduce errors.
In fact, there is an inverse correlation between time errors and the sharpness of a filter.......
If we choose a filter with a gradual slope, the time errors will be minimal, but the band limiting will be imperfect - and so we introduce aliasing errors.
And, if we choose a filter with a sharp slope, we can minimize aliasing, but at the cost of various time errors like ringing.
(In other words, the same theory that says this would all work perfectly if we had a perfect filter also says that there's no such thing as a perfect filter.)

Every time error has a corresponding frequency error. In the case of audible ringing, you hear it because it's at a frequency where you can hear it. This is why you don't hear the pre-ringing of a steep lowpass filter at, say, 20kHz, because you can't hear at or near 20kHz, at least not at amplitude of the ringing.

 

[KeithEmo]

First off.....

"Nyquist" says: A continuous time signal can be represented in its samples and can be recovered back when sampling frequency fs is greater than or equal to the twice the highest frequency component of message signal.
Note that it's talking about "continuous time signals" and not impulses.

Here's a paper that outlines some of the ways in which Nyquist is commonly mis-interpreted.....
https://www.audiostream.com/content...-about-it-tim-wescott-wescott-design-services

Also note that Nyquist talks about information ...... which is not exactly the same as "sound" or "audio quality".

I could take this posting, and convert it into Olde English font, or even Braille, and it would contain all of the original INFORMATION.
However, it would LOOK very different.
Likewise, I can convert a square 1 millisecond pulse into a ten second XinC waveform, and it will contain all of the original energy.
In fact, if it's done very well, it will even contain all of the original time information (you will be able to figure out where the original energy was located).
However, the waveform itself will be very different, and the difference will be obvious if you do anything other than look at 'the basic information it contains".

I think they said that 44.1 sampling rate can perfectly reproduce any sine wave representing sound that the human ear can hear. That's good enough for me. I tend to listen to music with human ears.

It doesn't matter if I use fancy equipment or cheap equipment. I haven't ever seen any evidence that super audible frequencies are audible, so higher sampling rates don't have much purpose for my human ears. Feel free to believe that pigs can fly and you can hear things that other humans might not be able to, but there's plenty of evidence on Nyquist's side and on the side of audiologists who have established the thresholds of human hearing. The ball is in your court to either prove that Nyquist is wrong and the audible range isn't perfectly reconstructed; or that human ears are capable of things that no one tested them for before. I think both of those things are unlikely, but the best way to test that would be a simple line level matched, direct A/B switchable, double blind listening test between Redbook and high sampling/bit rate audio. Go to it tiger! Achieve that and you'll be the most famous audiophile in the world! Maybe they'll add a KeithEmo corollary to the Nyquist theory.

 

[KeithEmo]

Electrically I can generate that using a wide variety of devices.
The simplest would be a type of logic gate called "a one shot".
I could also simply "dial it up" on most signal generators.
Getting it into the air from there would be a bit trickier..... I suspect a piezoelectric transducer could do it.

Alternately, I could generate it directly as a sound in the air by using some sort of electric discharge... or a tiny explosive charge.
I'm betting I could also generate something similar by mechanical means..... (A tiny little hammer hitting a tiny little metal plate - well damped to suppress ringing.)

And, yes, it will be altered significantly by being passed through the air.
And, yes, speakers and microphones are indeed going to introduce a lot of ringing and other interesting alterations.
(I have heard of test microphones that are claimed to have a response that extends beyond 100 kHz.)

I would also note.... and this was my point..... that a single non-repeating impulse has components of ALL frequencies in it.
(Although it has the most energy at higher frequencies.)
Therefore, assuming we could deliver it to the air, that 5 uS pulse would have SOME energy in the audible range (although perhaps not very much).
(For example, if I were to repeat my 5uS impulse every 1/500 second, there would be a 500 Hz modulation component... if it never repeats, in theory the components would extend down to 0 Hz, at every decreasing amplitudes.)

Not really interested in the the arguments generally, I have 99+% of my music as CD or rips thereof so there ends my practical/investment interest in "high res".

I am interested as to what amplification and transducers you used to "easily generate a 5 uS sound pulse" and the measurement techniques and equipment you used to verify you had created a 5 uS sound pulse.
I assume by "pulse" you mean something like this:

If you can actually generate a 5 uS sound pulse wouldn't transmission through the air alter the profile?
And as for hearing it wouldn't you be hearing resonances in your hearing equipment triggered by it?

Just wondering...