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[John Roberts {JR}]

I'm no math puke...  but the way this was explained to me several decades ago is a tone burst consists of two terms. #1 the continuous tone, and term #2 a gain function that instantaneously steps from full off, to full on, then full off again. So we have the pure tone of amplitude X, multiplied by a rectangular gain step function of Y. Using a ramped or trapezoidal gain function sounds less percussive and smoother.

If we gate silence on and off, we get nothing audibly significant. So this is effectively a gain modulation of a sine wave carrier tone. (Not to confuse things, I used to run music and speech through my tone burst gate, but that's another story).

I'm sure there are any number of different ways to explain this, but it is what it is, and thanks to Langston for some samples... isn't the internet wonderful?   Listen to if for yourselves.

 JR

[Per Sovik]

I'm no math puke...  but the way this was explained to me several decades ago is a tone burst consists of two terms. #1 the continuous tone, and term #2 a gain function that instantaneously steps from full off, to full on, then full off again. So we have the pure tone of amplitude X, multiplied by a rectangular gain step function of Y. Using a ramped or trapezoidal gain function sounds less percussive and smoother.

If we gate silence on and off, we get nothing audibly significant. So this is effectively a gain modulation of a sine wave carrier tone. (Not to confuse things, I used to run music and speech through my tone burst gate, but that's another story).

I'm sure there are any number of different ways to explain this, but it is what it is, and thanks to Langston for some samples... isn't the internet wonderful?   Listen to if for yourselves.

 JR

Yup, the gradual gain gives the ear time to get into resonance without exciting the "wrong" nerves.

[Charlie Zureki]

Without the math in the "old days", specifically Fourier's derivation of the Fourier series and the assumption of a repeating waveform, there would be no "analyzers" and there would be no digital sound equipment. We sometimes take for granted the science foundations upon which our current technology is built.

The question of what the output of a computerized FFT analyzer means when the input is a single cycle or part of a cycle is not so much a question of what is relevant, but rather whether the concepts with which we understand and apply FFT results to our work are correct or even defined at all. Sure, our black box will give a representation, but what do we need to know and what do we need to assume to interpret that?

The assumption of a repeating waveform is not to make the math calculations easier, it is fundamentally necessary to even define concepts like "frequency" and "wavelength". Without clear definitions of frequency and wavelength, how do we understand what our analyzer is telling us after it "does the work"?

   This is exactly what I meant by "relevant". We can take data all day long, but, we must know what data is relevant and accurate in order to lead us to solving a problem, or answer a question.  Taking the data is the easier part, analyzing the data is the hard part. 

   I'm not certain of the throughput-realtime & capture, analysis capabilities of many of the current versions of Acoustic Analysis softwares, but, benchtop analyzers like B&K and Larson & Davis can easily capture down to DC, and have thousands of lines of resolution....more that enough information of any sinewave measured, at any audio Frequency, and at any amplitude.

   All this talk about sub-sine waves/analysis is interesting, and it's study/application may be an integral part of some R&D lab, but, in professional Audio, it's not that important.

   Hammer
 

 

[Nick Hickman]

Hi Per,

When tones start or stop, there are lots of frequencies involved

No, there are not! Same with a square waveform, a pulse, or whatever. How something might be mathematically represented doesn't mean that it is.

It's certainly possible to confuse reality with measurement artifact, and I've certainly been guilty!  I mentioned, for example, the confusion that can arise because of the assumption inherent in Fourier techniques that the sample is cyclical.  However, try taking some number of cycles of some frequency with abrupt start and end and passing it through a notch filter that removes the frequency in question.  If only that frequency were present, you'd expect to be left with nothing.  But what you get is two clicks: one at the start and one at the end.

Nick

[Ivan Beaver]

     All this talk about sub-sine waves/analysis is interesting, and it's study/application may be an integral part of some R&D lab, but, in professional Audio, it's not that important.

   Hammer
 

HOWEVER-it IS all the little details that allow somebody to "rock".

If it wasn't for the "geeks" working on all of the very little details-we simply would not have the tools we have available today.

it is theunderstanding of 'little things" that allow it all to work and to get better.

As the understanding of the "little things that don't matter" that make one product better than another.

It is the guys who are locked away in their labs looking at the "little things" and understanding what they mean- who make the difference.

[Per Sovik]

Hi Per,
No, there are not! Same with a square waveform, a pulse, or whatever. How something might be mathematically represented doesn't mean that it is.

It's certainly possible to confuse reality with measurement artifact, and I've certainly been guilty!  I mentioned, for example, the confusion that can arise because of the assumption inherent in Fourier techniques that the sample is cyclical.  However, try taking some number of cycles of some frequency with abrupt start and end and passing it through a notch filter that removes the frequency in question.  If only that frequency were present, you'd expect to be left with nothing.  But what you get is two clicks: one at the start and one at the end.

Nick

Yeah, I won't argue with that fact. I can however argue that this is caused by the filter, and not by the inherent presence of other frequencies. Yes, we hear that there is something there, some measurements tell us there is something there etc. but a picture of the waveform inarguably shows nothing but the waveform. The transition from silence to the waveform and vice versa undeniably contains a sharp kink that a low pass filter would remove, and there is probably no way such a waveform would ever exist. How much of what we hear is distortion in the recreation process, and how much is "real"? Even if I am willing to concede that the kinks removed by the lowpass filter is a higher frequency component, there is no way I'll ever admit that a single cycle sinewave contain lower frequency components as suggested by FFT.

What does a square wave really sound like? 

Here are 1-2-4-8-16-32 cycle tonebursts at three frequencies. Suggests to me that it is the time, not the number of cycles that determines if we can hear the pitch, allthough it seems that the 400 Hz sample is somewhat easier to make out, suggesting that the middle notes are easier to to pitch-determine than octaves above or below.

http://www.norsk-karting.com/uploads/toneburst_200_lp.wav

http://www.norsk-karting.com/uploads/toneburst_400_lp.wav

http://www.norsk-karting.com/uploads/toneburst_800_lp.wav

Yes, they are low-passed 

[Patrick Tracy]

There has to be enough cycles for the ear to be able to "hear it".

I'm pretty sure I can hear it in one cycle. I was editing some plosives the other day and I began to see the LF. It seemed to be one cycle of something quite low but I did not measure the wavelength.

[Per Sovik]

I'm pretty sure I can hear it in one cycle. I was editing some plosives the other day and I began to see the LF. It seemed to be one cycle of something quite low but I did not measure the wavelength.

Really?? Editing, not just highpassing or teaching the singers the right "anti-plosive" mic technique?

Maybe I should make some burst samples at 100, 50 and 25 Hz ?

http://www.norsk-karting.com/uploads/toneburst_100_lp.wav

http://www.norsk-karting.com/uploads/toneburst_50_lp.wav

http://www.norsk-karting.com/uploads/toneburst_25_lp.wav

sorry for the crappy intervals

[Charlie Zureki]

HOWEVER-it IS all the little details that allow somebody to "rock".

If it wasn't for the "geeks" working on all of the very little details-we simply would not have the tools we have available today.

it is theunderstanding of 'little things" that allow it all to work and to get better.

As the understanding of the "little things that don't matter" that make one product better than another.

It is the guys who are locked away in their labs looking at the "little things" and understanding what they mean- who make the difference.

  Hey Ivan,

   Exactly,   and that's what my post said..... in R&D Labs, and, not so much to the pro audio provider.

  Hammer

   I am not downplaying the interest in learning more of the science behind audio, or any other topic. My point was that while there is a want/need to understand the theory/ science, the example would never come up in the real world. (one possible minor exception)

 

[George Friedman-Jimenez]

Here are 1-2-4-8-16-32 cycle tonebursts at three frequencies. Suggests to me that it is the time, not the number of cycles that determines if we can hear the pitch, allthough it seems that the 400 Hz sample is somewhat easier to make out, suggesting that the middle notes are easier to to pitch-determine than octaves above or below.
http://www.norsk-karting.com/uploads/toneburst_200_lp.wav
http://www.norsk-karting.com/uploads/toneburst_400_lp.wav
http://www.norsk-karting.com/uploads/toneburst_800_lp.wav
Yes, they are low-passed 

Very interesting, especially with the 25, 50 and 100 added. thank you. Two questions:
1) Do they all start and end at the zero crossing in the sine wave cycle?
2) If yes, why did you low pass them?