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Author Topic: the "high frequency transients" fallacy  (Read 54183 times)

Joe Bryan

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Re: the "high frequency transients" fallacy
« Reply #30 on: March 04, 2005, 07:00:12 PM »

danlavry wrote on Fri, 04 March 2005 13:00


Transients (made by musical instruments) containing high frequencies beyond human hearing ALSO contain energy at frequencies within human hearing. It is impossible to claim that sonic alterations are due to high frequency when introducing such energy also alters the lower frequencies.



I think there a bit of semantic dancing going on. I don't qualify "high-freq transients" by saying they can't have low frequencies; it's a way of saying "a steep rise-time signal", just as you pointed out in your first examples.

Enough dancing. Why not try this very simple experiment: Take a simple 44.1k band-limited source and upsample it (using a good upsampler!) to 96k. Add a short full-scale tone burst at 40k. Hear any difference? If not, try turning up the output. (Make sure there's no attenuation in the signal path until the mains amp.)

Next, down-sample the mixed sounds, and listen again. Does this sound any different from the original before you added the burst? It shouldn't (unless you have a bad resampler!). It's as if the data was never added and the difference goes away. We can both agree on that point.

But what a bummer if you really wanted it to sound like it did with that extra HF energy!

A really good source of high-frequency *transient* energy is a kick drum. A lot of people deliberately smash their pres with this signal to give it some "character" and bring out the tone. The mic takes it up as far as it can go, and the pre takes over from there, adding distortion harmonics which interact.

That's what makes analog sound analog, and why digital doesn't.

-Joe
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zmix

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Re: the "high frequency transients" fallacy
« Reply #31 on: March 04, 2005, 11:35:57 PM »

Joe Bryan wrote on Fri, 04 March 2005 19:00

That's what makes analog sound analog, and why digital doesn't.
-Joe



Joe,

I can appreciate that you may feel like you alone are championing analog, but certainly we are all intimately familiar with the sonic limitations of digital audio, (I use analog processing rather than plugins for this very reason) and this claim seems to be prematurely conclusive.

It's important to remember that Dan's argument is that a system's ability to reproduce "high frequency transient" (sic) information is linked to system bandwidth, and not about the synthesis of harmonics due to circuit non-linearity.

My argument is that ultrasonic and infrasonic artifact can and do cause anomalous behaviour in the audio passband but that this should not be taken to the conclusion that the out-of-band information must be recordable to effectively capture these interesting sonic textures.

If the artifact introduced by smashing a mic pre creates interactive harmonic information vital to the tone of the kick drum (and I know it does), and this very fact distinguishes analog from digital then how do you suppose the sound that you have described makes it to the listener intact?

Do the CDs mixed today have less transient impact? Have you ever measures the transient response of a really good stylus, or better yet: lathe/vinyl/stylus/RIAA EQ ?

Seriously, can you direct me towards any data which suggests that transient information can exist beyond the system bandwidth (besides clipping, obviously)?

-CZ

David Satz

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Re: the "high frequency transients" fallacy
« Reply #32 on: March 05, 2005, 07:04:42 AM »

Joe, what you just described ("The mic takes it up as far as it can go, and the pre takes over from there, adding distortion harmonics which interact. / That's what makes analog sound analog, and why digital doesn't")--if that really occurs, then it's your way of using an analog recording system as an effects box, to produce bursts of distortion. No one would ever hear that sound in an unmiked live performance; it's being manufactured by the equipment.

You find it exciting, so OK. Any type of effect that anyone wants to use in a recording should always be available to any engineer who wishes to use it. On the other hand, we should also be able to bypass any effect completely, no? My opera singers may not want to sound like your ideal of a kick drum.

Digital audio has long been accused (falsely) of dumping huge amounts of distortion on listeners all the time. Your criticism is from the better informed, opposite side: that digital audio lacks a kind of distortion that you want to have in your recordings.

But please be careful what you ask for, especially when it's distortion built into recording equipment. There can't possibly be an effect that always improves audio under all circumstances. For every EQ setting, for every form of euphonic coloration that can be added, there will always be at least one track somewhere that's better off without it, no?

Actually, though, if I understand you correctly, your beef isn't really with digital audio--it's with any clean recording system. You might, for example, have disliked Nagra analog recorders such as the model IV-S which used anti-distortion circuitry to prevent as much tape squash as possible. If you're into comparing live versus recorded as I am, this gave Nagra recordings more life and realism. But it frustrated anyone's attempt to use gentle tape saturation as an effect, so some engineers used to shut that circuit off internally.

--best regards
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bobkatz

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Re: the "high frequency transients" fallacy
« Reply #33 on: March 05, 2005, 09:54:54 AM »

Well said, David. May I please take some of your statements and quote them (with attribution, of course) for the second edition of my book?

The one thing I can add is that although mixing analog "outside the box" sometimes seems to offer increased sonic separation compared to mixing digitally inside the box, that this MUST BE due to some kind of "euphonic distortion". The OBJECTIVELY measured stereo separation is always better inside the DAW when digitally mixing, so all that I can say is that some of the distortion added during the mix in the analog console appears to increase the separation. Furthermore, this improvement is not universally noticed with everyone's analog mixing setup. Only the very best DACs, clocking and certain analog consoles or summing matrices appear to give an increase in stereo separation and similar transparency (though the clarity is almost always reduced) compared to the digital mix inside the DAW.

Dave Hill has researched mechanisms by which the ear appears to hear increased stereo separation when small amounts of harmonic distortion are added. I believe it is a real effect as I hear it when I adjust the pentode control in the HEDD-192. I just think it is important, as Dave Satz points out, to realize that this is a form of distortion, and it may or may not be pleasant to the ear when applied to all recordings.
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Joe Bryan

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Re: the "high frequency transients" fallacy
« Reply #34 on: March 05, 2005, 12:27:29 PM »

Zmix-

The simple test for whether the media transfers the original sound intact or not is to ask yourself if you've ever heard a CD or vinyl record that sounded better than the original master or mixdown.

David-

One of the nice things about digital is that you can choose when to apply the types of non-linear processing I described (assuming you have the algos and processing power), and when to keep it pristine.

I've done many classical recordings with a Nagra (for WFCR in Amherst, Mass. and syndicated for NPR) where "clean and pristine" was essential. We always used at least one backup deck, which was sometimes digital, and the results were nearly as good (given the converter quality at the time). If I were to go out again today, I'd take a clean pre and go straight to digital. That's one situation where digital has surpassed analog.

On the other hand, I wouldn't track mic'd guitar amps or drums direct to digital through this same setup. It sounds terrible compared to tracking to tape through colored pres. Once the analog character is imparted, a digital transfer can be done. That's a situation where digital still cannot replace analog.

Having worked on and designed both analog and digital systems, I'm very familiar with each system's limitations and advantages, and while these differences were quite pronounced in earlier equipment, they're becoming less so as advances in circuit design and DSP modelling are being made. However, analog equipment still offers advantages where non-linear artifacts are important (specifically the increased detail and imaging caused by distortion as Bob mentions).

I truly believe the next frontier for digital processing is to recreate the non-linearities inherent in the best analog environments. This doesn't exclude continuing to make digital systems more linear and reducing distortion in the analog signal path. On the contrary, in order to accurately recreate these desirable analog non-linearities, the digital system must be even more accurate in order to eliminate the *undesireable* artifacts introduced by converters and analog I/O circuits.

-Joe
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David Satz

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Re: the "high frequency transients" fallacy
« Reply #35 on: March 05, 2005, 03:15:08 PM »

Joe, you wrote, "The simple test for whether the media transfers the original sound intact or not is to ask yourself if you've ever heard a CD or vinyl record that sounded better than the original master or mixdown."

To which I can only reply, "Huh?"

The simple test for whether a medium transfers the original sound intact or not is to listen to what goes in and listen to what comes out. If they sound the same, then the medium transferred the original sound intact, within the limit of your hearing ability.

If the output sounds "better" than the input (whatever "better" may mean to a given listener on a given day) then you've got a "feel-good box" of some kind--an effect that you definitely want to keep on hand for when you need it, but certainly not a medium that has transferred the original sound intact.

--By the way, when I was an engineer at RCA Studios I heard the master tapes for many "revered" Red Seal LPs. Without a doubt, LPs on a good playback system can sound far, far better than the master tapes from which they were made. Vinyl LP isn't even remotely a sonically transparent medium, and the old engineers had learned how to tailor the sound of the master tapes so that the LPs would sound great.

But most audiophiles--and apparently many audiophile journalists and other opinion makers--have never had the chance to hear such master tapes. They may well have imagined that their vinyl LPs were giving them a transparent window onto the sound quality of the original recordings; what's to prevent that assumption? But it simply ain't so.

Indirectly that's one reason many early CDs were so bright and harsh sounding. Most record companies simply transferred their mixed, compressed, equalized fourth-generation analog LP master tapes to digital. For the first time, the audio public was hearing what so many LP master tapes really sound like--i.e. awful, because it was never meant to be heard in that form.

Whereupon, in their reverence for the past, audiophiles attacked the messenger rather than realizing what they were really being told ... Fortunately, most of the record companies soon realized that these cheap transfers were losing them market acceptance, and that their experienced LP mastering engineers were desperately needed. Or the reissue engineers were allowed to go back to the original session materials and bypass all the unneeded generations of analog tape copying, meanwhile reconsidering (and in many cases moderating or bypassing altogether) the EQ and other sound processing that had been applied for the sake of LP trackability and higher average volume. That's when CD reissues of old analog recordings started to sound a lot better.

--best regards
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maxdimario

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Re: the "high frequency transients" fallacy
« Reply #36 on: March 05, 2005, 03:42:05 PM »

David Satz wrote on Sat, 05 March 2005 13:04


Digital audio has long been accused (falsely) of dumping huge amounts of distortion on listeners all the time. Your criticism is from the better informed, opposite side: that digital audio lacks a kind of distortion that you want to have in your recordings.

--best regards




my problem with digital, and I suspect the problem with a lot of other people is that when digital is used as a recording medium, especially in multitracking, the music that comes out is more dull and lifeless than when it goes in.
nothing to do with added harmonics etc.
I have discussed this with people who had tracked live to tape multitrack and then found that the feel and excitement of the music was lost when transferred to pro tools.

I love the way great mics and pres sound LIVE, and recording in digital takes away feel and human element in performance.

I have not tried the SLAM or weiss converters which I have been told on this forum  reputably don't manifest this problem, and I hope to hear for myself soon.

there are plenty of ways to distort a signal.

you don't need a 500 lb studer to achieve the analog warmth thing.
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Joe Bryan

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Re: the "high frequency transients" fallacy
« Reply #37 on: March 05, 2005, 04:09:03 PM »

David Satz wrote on Sat, 05 March 2005 12:15

Joe, you wrote, "The simple test for whether the media transfers the original sound intact or not is to ask yourself if you've ever heard a CD or vinyl record that sounded better than the original master or mixdown."

To which I can only reply, "Huh?"

The simple test for whether a medium transfers the original sound intact or not is to listen to what goes in and listen to what comes out. If they sound the same, then the medium transferred the original sound intact, within the limit of your hearing ability.

If the output sounds "better" than the input (whatever "better" may mean to a given listener on a given day) then you've got a "feel-good box" of some kind--an effect that you definitely want to keep on hand for when you need it, but certainly not a medium that has transferred the original sound intact.


You're right, my question wasn't worded very well. My point was that for me there's invariably some loss in the medium. Most people will disagree, since MP3s are more popular than ever.

Btw, I think another reason a lot of the early CDs sounded terrible is because the converters weren't as good as they are today.

-Joe
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danlavry

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Re: the "high frequency transients" fallacy
« Reply #38 on: March 05, 2005, 04:32:13 PM »

Joe Bryan wrote on Sat, 05 March 2005 00:00

danlavry wrote on Fri, 04 March 2005 13:00


Transients (made by musical instruments) containing high frequencies beyond human hearing ALSO contain energy at frequencies within human hearing. It is impossible to claim that sonic alterations are due to high frequency when introducing such energy also alters the lower frequencies.



Enough dancing. Why not try this very simple experiment: Take a simple 44.1k band-limited source and upsample it (using a good upsampler!) to 96k. Add a short full-scale tone burst at 40k. Hear any difference? If not, try turning up the output. (Make sure there's no attenuation in the signal path until the mains amp.)

-Joe




Joe,

What you said shows that you do not know the ABC’s of signal theory!

A burst of 40KHz sine wave requires infinite bandwidth. That is an unreal test signal!
If you wish to modify the burst with an envelope “gentle enough” to be sure it is contained within the 96KHz sampling, you can not exceed the impulse response of a 48KHz bandwidth!
You "just ignored" the limits on the "burst envelope" by the bandwidth, but that is only half of what you "ignore":  

A burst of 40KHz is not just a 40KHz high frequency signal that lasts for a while! It has an envelope, making it a transient. In fact a radio guy would say the envelope is the signal and the 40KHz is the carrier, to later be demodulated leaving the Pulse envelope. That is how radio works.

A burst of 40KHz sine waves can contain noticable amount of energy in the audio band!!!  A single sine wave with 40KHz lasts 25usec. Say we are talking about a single burst of 10 cycles, that is 250usec long. Basically you can look at the burst as multiplying a 40KHz sine wave by an 250usec pulse. But it is also correct to look at it as a 250usec pulse multiplied by a 40KHz sine wave. A periodic square wave with 250uSec cycle is a 4KHz signal. One burst is not periodic for ever, but it does contain audible energy, including a 4KHz component and its harmonics interaction with the 40KHz sine wave. So what do you wish to do? Go for a 5 cycle burst(8KHz fundumental)? 1 cycle burst? Remember, you can not just arbitrarily do that. The signals can not have an infinite bandwidth!

So the point is: A 250usec burst contains energy in the audio band. Put a  few of those bursts within some msec of  each other, and /or raise the level (as you suggested) and you will have more audio band activity.  I have stated it a number of times. Your view of a signal burst shows that you do not really understand the difference between steady state and transient.

Regards
Dan Lavry
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zmix

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Re: the "high frequency transients" fallacy
« Reply #39 on: March 06, 2005, 11:09:26 AM »

This is one of the more fascinating topics I've seen in a long time, and I think it would be useful at this time to clarify a few points before this topic becomes too heated and spins out of control.

Dan has brought up a very interesting point about bandwidth and transient information.

"Transient signals cannot contain information outside the bandwidth of a system".

Joe claims that this theory requires a bandwidth limited system and it therefore applies only to signals in the digital domain.

"Transients are generated as artifact of a system and these do exist beyond the bandwidth of a system".

Can one of you provide some measurement data to back this up? Define a bandwidth... 20kHz perhaps? An FFT analysis of a 192kHz file should demonstrate these assertions.




In a different forum, I noted that an 1176 limiter has an attack time constant as fast as 20uS, this represents a single cycle at 50kHz. The waveform distortion imposed by this limiter can certainly generate harmonics in the ultrasonic range, yet in the February 2005 issue of Sound on Sound, Joe states that his DSP simulation of this limiter did not require upsampling...which seems counter to his assertions here.

Now, if this is the same Joe Bryan I knew from Ensoniq, he's a brilliant DSP programmer and knows a thing or three about analog design, too. So, if this is you Joe, which one is it?

I spent months and months working with DSP engineer Jon Dattorro to tweak the tube amp simulation algos for the DP/4+ and my investigations provided much insight into simulating artifact within a tightly defined and very limited bandwidth system. I use my findings on a daily basis when mixing, as I have built specific analog circuits to add important (well, important in the pop/rock/R&B world, anyway) artifact to various instruments. Each of these circuits is inserted using D/A and A/D converters operating at the session sample rate, which is typically 44.1kHz (it's fascinating how quicky 48k has been abandoned in favor of 44.1).

These devices include tube circuits optimized for 2nd harmonic generation, single ended class A discrete circuits optimized for asymmetrical clipping, you know, the usual type of musical analog distortion missing from the digital signal chain.
The euphonious effect of these various signal chains are quite obvious, even at 44.1.

I am attempting to find a point of agreement for the two of you on this topic. My empirical finding is that my own nasty little circuits, which certainly do generate out-of-band artifact, provide all of the desired effect in a very band limited system and do so while operating on a band limited source signal.


Do we need RF bandwidth capabilities in our storage medium to provide an accurate reproduction of audible phenomenon, or is this perceived need for additional bandwidth simply a reaction to the undesirable artifacts generated in the audio passband by current non-oversampled DSP implementation?

maxdimario

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Re: the "high frequency transients" fallacy
« Reply #40 on: March 07, 2005, 06:30:07 AM »

an ideal circuit will reproduce a wavefront regardless of the dynamic range fluctuations, steady-state vs. transient, low frequency/high frequency intermodulation etc.

the ability to reproduce realistic sounding audio is not a function of high frequency response as much as it is the ability to reproduce sound waves generated by a musical event.

jangling keys will not sound real on a system that has 100KHz bandwidth and .001 THD if the waveform is not reproduced in a way that leaves the time/phase/wavefront information intact.

a system with an extended high freq. response is more likely to be stable at lower frequencies, but limiting bandwidth to 20 Khz in a non destructive way (if this is possible) will not change our ear's perception of the sound.

take a mic, with the best preamp you have and listen direct with headphones, then introduce a passive lc filter at 16 Khz or 18 Khz and tell me if you lose imaging or anything else.

some mics don't go any higher than 20-22 Khz.

the problem with digital is not so much the lack of ultrasonic information, as it is the brickwall effect and the mathematically-related artifacts of conversion.

and the fact that most converters have inferior analog electronics.

it's one thing to bandwith-limit a system that performs impeccably to 100 Khz without aid of corrective circuitry, quite another to utilize a system that is bandwidth-limited by  it's inherent nature.
digital systems do not reproduce ANYTHING above the sample rate limit.

this is a characteristic that does not occur anywhere in nature, and probably one of the reasons why digital creates so much confusion and misunderstood artifacts.
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danlavry

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Re: the "high frequency transients" fallacy
« Reply #41 on: March 07, 2005, 02:09:07 PM »

zmix wrote on Sun, 06 March 2005 16:09

Dan has brought up a very interesting point about bandwidth and transient information.
"Transient signals cannot contain information outside the bandwidth of a system".

Joe claims that this theory requires a bandwidth limited system and it therefore applies only to signals in the digital domain.
"Transients are generated as artifact of a system and these do exist beyond the bandwidth of a system".

Can one of you provide some measurement data to back this up? Define a bandwidth... 20kHz perhaps? An FFT analysis of a 192kHz file should demonstrate these assertions.



Dan has brought up a very interesting point about bandwidth and transient information.
"Transient signals cannot contain information outside the bandwidth of a system".

That relates to the subject of this thread.

Joe claims that this theory requires a bandwidth limited system and it therefore applies only to signals in the digital domain.
"Transients are generated as artifact of a system and these do exist beyond the bandwidth of a system".


That is not the subject of this thread. It does not shed light on the subject at hand, nor does it contradict it.

Can one of you provide some measurement data to back this up? Define a bandwidth... 20kHz perhaps? An FFT analysis of a 192kHz file should demonstrate these assertions.

It is very easy to show that circuit non linearity produce high frequencies, but it has NOTHING to do with the topic. Perhaps it belongs in a topic such as: “Designers, make sure you circuit is linear, or else you will have unwanted harmonic generation…”

If you pay careful attention to what I previously said, an FFT of a 10 cycle burst of 40KHz for a 96KHz (or 192KHz) will show more art effects then you could shake a stick at. Some of it will be due to aliasing of the infinite high frequency content included in such the burst. Please read what I said previously. You will see energy buildup at the alias frequencies on an FFT!!! The way to avoid the aliasing is to go for a legal signal.
An FFT is not an analog process, it requires sampling, thus it is susceptible to aliasing, just like an AD. One way to shape the signal to be “legal” is to filter it to avoid aliasing.  In fact an FFT is not even the proper tool for analyzing transients. That by itself is a whole subject.

Regards
Dan Lavry
www.lavryengineering.com
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danlavry

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Re: the "high frequency transients" fallacy
« Reply #42 on: March 07, 2005, 04:03:31 PM »

maxdimario wrote on Mon, 07 March 2005 11:30



a system with an extended high freq. response is more likely to be stable at lower frequencies, but limiting bandwidth to 20 Khz in a non destructive way (if this is possible) will not change our ear's perception of the sound...

some mics don't go any higher than 20-22 Khz.



a system with an extended high freq. response is more likely to be stable at lower frequencies, but limiting bandwidth to 20 Khz in a non destructive way (if this is possible) will not change our ear's perception of the sound.

Stay on topic please. Some people in audio advocate higher bandwidth on the grounds that we hear- “extra high” frequency transients. I say it is wrong to have separate criteria for transient bandwidth and steady state. The same bandwidth that defines the music, defines all of it, transient or not.

The advocates of the high frequency transients story theorize that one can hear a difference when introducing high frequency energy at frequencies above steady state listening tests. I have been explaining that transient high frequency energy (not steady state) comes with (is coupled with) an audible energy, unless special conditions are met (narrow transients occurring very far apart). Therefore, listening to a difference does not prove that one hears high frequency energy.

This thread is about dispelling the BS about our ability to hear transients at higher frequencies than the rest of the music (such steady state tone hearing tests). It is NOT about what bandwidth to use when designing for good audio performance.

some mics don't go any higher than 20-22 Khz.

Most mics, and speakers do not go above 20KHz, yet we had a suggestion to do a listening test with a 40KHz burst. When Joe suggested  to take a 44.1KHz signal, up sample to 96KHz and  add a 40KHz burst, he should have also said VERY STRONGLY to be sure that everyone (including himself) use speakers or headphone capable of at least 40KHz. The irony here is that anyone following the suggested test and is hearing  sonic difference on standard speakers, would be actually proving my point which is that the energy is within the speaker bandwidth, in most cases not over 20KHz.

This is an example of the kind of half-baked BS we are dealing with. To begin with, the proposed 40KHz burst test is missing the issue about high frequency transients also having low frequency content (due to the transient “envelope”). And again, given that whatever one hears, cannot be attributed to the energy above the speaker bandwidth, it is not “extra” high frequency energy. In other words, those that followed the instructions (how to do a 40KHz burst) carefully, and heard a difference with normal speakers or headphone, have in fact proved my point experimentally. And the few (anyone?) that happened to be equipped with a 40KHz speaker are in no position to say that it is high frequency they hear.

Feel free to start a thread about bandwidth and circuits or whatever. I know I am being extra stubborn here about not changing the subject. Here is why:
I am trying to dispel a myth, and there are many people that do not want to hear what I say. One of the common methods to put a damper on my comment is to CHANGE THE SUBJECT. Once it is changed, other people get off track and the message gets lost.

In a previous post you said “the ears know best”. Indeed the ears can tell you IF something was heard, The brain can tell you IF what you heard is liked, if it sounds like the original (assuming you heard the original). The HOW and WHY questions must be answered by a scope or test gear.

The ear can differentiate a 1KHz square from sine wave, but does not know that there are exactly 20 possible harmonics in the square wave (to 20KHz), that only the odd harmonics exist and so on. The ear cannot tell you much technical information. The ear may not be the tool to tell you if a subtle sonic  difference is due to some low level base band activity or some 40KHz.

It is true that the brain can be well trained to recognize differences in  pitch, timbre and much more. We can all tell a piano note at 200Hz from a 1KH flute Smile
However, the statement “the ear knows best” does not belong in a technical discussion.
For example, it takes more than an ear to know about hearing frequencies beyond human hearing, which is the subject of this thread Smile

Regards
Dan Lavry
www.lavryengineering.com

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danlavry

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Re: the "high frequency transients" fallacy
« Reply #43 on: March 08, 2005, 12:33:05 PM »

I stated that a 40KHz burst (a few cycles of 40KHz) contains energy at frequencies other than 40KHz. Let me amplify:

One can view a 40KHz few cycles burst as a multiplication of a continues sin wave (40KHz) by a gate - a single pulse, with amplitude 1 over a limited time (the pulse duration) and zero elsewhere. It is common to start and stop a burst at a beginning and at an end of sine wave cycle.

Those that studied signal and circuit theory, would be familiar with the fact that multiplication of two time domain functions (waves), in this case a sine wave and a square pulse, is a process of convolution in the frequency domain. In this case, the frequency domain of a 40KHz sine wave is represented by a single line (unity at 40KHz and 0 elsewhere). The frequency domain representation of a single pulse has a shape of sin(x)/(x). The convolution yields the outcome.  

The energy content of 8 cycle burst of a 40KHz cos wave (amplitude vs frequency plot):


index.php/fa/772/0/


The plot is known as the "spectral density function". It is the straight forward Fourier transform of a gated cos wave F{cos(w*t)*U(t)}, where U(t) is a gate lasting 8 cycles of 40KHz. (A more common plot is the magnitude of the spectral density function, but I I presented the spectral density to show the connection to the time domain.)
The horizontal is the frequency axis, showing peak amplitude at 40KHz. Note that there is activity all the way down to DC. Also note that I am showing the energy on a linear scale. The low frequency activity is much more pronounced when doing it on a log scale - the amplitude within the audio band is only 20dB below the peak at 40KHz.

Regards
Dan Lavry
www.lavryengineering.com
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danlavry

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Re: the "high frequency transients" fallacy
« Reply #44 on: March 08, 2005, 06:01:47 PM »

This is and expansion of the previous post, showing that a short burst of high frequency tone contains energy at the hearing region.

I can include only one plot per post. Here is the next plot, showing the frequency content of two bursts. This plot was done simulating a 40KHz at 192KHz rate. (The previous one was a simulation in a 96KHz system).

index.php/fa/799/0/

The red curve is a 50 cycle burst. It does not have too much energy below 20KHz. It is "on it's way" to becoming a steady state 40KHz signal with energy only at 40KHz. As we increase the number of cycles, we approach a single vertical line at 40KHz and zero elsewhere.

The 3 cycle burst plotted in blue carries a lot less energy (only 3 cycles), so I multiplied it by 17 (to show it side by side against the red plot). That multiplication is near the ratio of 50 cycles to 3 cycles (50/3=16.666 thus nearly 17). Note that with only 3 cycles in the burst, the wave is a lot less like a steady state, therefore the energy is spread "all over the place", a lot of it is below 20KHz.

Narrow bursts do not carry much energy, making them less audible to start with. But whatever energy is there (due to the short burst), is spread all the way to DC.

This is general electronics engineering, and essential to the development of quality products.

Best Regards
Dan Lavry
www.lavryengineering.com
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