WTF!? Wavelet TransForm for audio measurements - What-is? and How-to?

[mige0]

... but we found that distortion in a well designed loudspeaker ( typically under 1% harmonic distortion) is masked by the muisc .....

Depends on the loudspeakers *you* like to design - I'd say


Listen to a well EQ'd modern AMT with incredible low inherent distortion – you most certainly change your mind....

Also have a look at the spectacular low distortion spec of the ScanSpeak D3004 for example and tell us those guys are developing just nonsense....
Those distortion measurements sadly are not enclosed in their spec sheet – so not even developed primarily as a "sales argument" only.

Bottom line – such generalisations do not hold and solely add to confusion and thread noise as much as the generalisation about phase changes not being of any concern – simply – it all depends on the context...


The context here loosely being pattern recognition focused at the time- frequency scale and more specifically WTF....


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BTW I like Bill Waslo's intro !
http://www.libinst.com/what_makes_a_speaker_sound_good.htm


About "time invariance" of a system you start with in your page - I've been told that we have to clearly distinguish between a single driver being "time invariant" as a whole – but not necessarily having "time invariant" behaviour from t = zero to t = infinite.

That's a very specific sonic pattern of "looping reflections" as you have different FR at different times – making it impossible to find a "right" EQing at all !


Michael

 

[john k...]

For reference,

Time?frequency representation - Wikipedia, the free encyclopedia

An Introduction to Wavelets In particular go to the Musical Tones section.

Wigner distribution function - Wikipedia, the free encyclopedia

Looking at those phase plots I am thinking, "What would you expect?" I mean if a perfect system were to reproduce two tones, 100 Hz and 1k Hz simultaneously and you looked at the phase vs time for each tone would you not expect to see the phase of the 1k Hz tone rotate 10 times faster than that of the 100 Hz tone?

And I hear discussion of interest in "time varying frequency response". But the thing is that when you look at any of these time-frequency transformations and compare the difference of the input and output all you have is the differences, or error, and it is not possible to ascribe what the source/cause of that error is. In the majority of cases if it likely to be some form of stored energy and nothing else. If you want to call the rise in amplitude over time of a resonance to its peak "time dependent frequency response" fine. But it is a manifestation of stored energy.

 

[soongsc]

But this is possible with many techniques. Many people in the hearing aid business swear by Coherence using real world signals as being very close to the perceived performance. Wavelets could not do coherence and hence would be highly susceptable to output noise contaminating the results. (I heard someone say that wavelets were immune to noise which is incorrect.) Coherence is fairly imune to this problem

Output noise is part of system performance. So as long as we can minimize exterior noise, it should not effect the system performance evaluation results in terms of fidelity until the system performance becomes so good that such noise dominates the results.

The idea came while I was reading this over a year ago.
THE WAVELET TUTORIAL PART III by ROBI POLIKAR
The idea is to calculate the wavelet transform of both the input signal, and the output, and generate a difference of these two which would be shown in a similar format.

Note that this would not help too much to determine cause of high difference values, but would rather be an indication of how true the playback is compared to the souce for a particular music input. This could be an objective means of fidelity measurement of playback systems.

 

[Joachim Gerhard]

I did not say that it is not worthwhile to design speakers with low distortion.
What i did say is that it is posible to design a speaker where the distortion is so low that it is swapped by the music provided the speaker is driven in it´s linear range.
I worked a lot with the Distortion Isolation feature of Praxis and found that the distortion of well designed speakers was not audible. The distortion isolation process alows to separate the linear part of the transfer function from the distorted part. The linear part can then be presented to the left ear and the unlinear part to the right ear over headphones. Switching in and out distortion i was not able to hear a diffence with well designed spaekers driven in their linear range.
Ceveat : when i drive this speaker with much higher volume distortion is rising to a level that is audible
Ceveat 2: some speakers have rising distotion at low volume so have a resolution problem
The answer is to measure disdortion at low, medium and high volume.
That prompted me to develop a high sensitivity speaker that measures well at low, medium and high volume and voila it sounds better at life concert levels and very low level at night then higher damped speakers with typical sensitivity of 87dB.
See my MPL thread.
Sorry that i over simplfied this complex problem.

 

[mige0]

And I hear discussion of interest in "time varying frequency response". But the thing is that when you look at any of these time-frequency transformations and compare the difference of the input and output all you have is the differences, or error, and it is not possible to ascribe what the source/cause of that error is. In the majority of cases if it likely to be some form of stored energy and nothing else. If you want to call the rise in amplitude over time of a resonance to its peak "time dependent frequency response" fine. But it is a manifestation of stored energy.

I don't agree but have answered in the horn honk thread as I think its more a discussion about specific sonic patterns than related to WTF :

http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted-12.html#post2150033

Michael

 

[mige0]

I worked a lot with the Distortion Isolation feature of Praxis and found that the distortion of well designed speakers was not audible.

Good for you - makes speaker design easier - but as for me - it does not hold...

Michael

 

[gedlee]

I worked a lot with the Distortion Isolation feature of Praxis and found that the distortion of well designed speakers was not audible.

Well I completely agree.

 

[Elias]

Hello John k...

Looking at those phase plots I am thinking, "What would you expect?" I mean if a perfect system were to reproduce two tones, 100 Hz and 1k Hz simultaneously and you looked at the phase vs time for each tone would you not expect to see the phase of the 1k Hz tone rotate 10 times faster than that of the 100 Hz tone?

You don't have to have expectations to learn more from the phase plot. Of course phase rotates faster for signals having higher frequency, but that is not the point. The point is how constant is the rotation. Always when there is a problem, a reflection for example, the phase rotation speed is not constant! That will be clearly visible.

But the thing is that when you look at any of these time-frequency transformations and compare the difference of the input and output all you have is the differences, or error, and it is not possible to ascribe what the source/cause of that error is.

This is not true. Wavelets will give you a high changes that you'll find the reasons behind observations. See examples in the Horn Honk thread.

I think what you should propably do is to try these methods yourself and see.

- Elias

 

[Elias]

Hello Joachim Gerhard,

Can you share any tips for wavelets from your experience?

- Elias

What Wavelet Analysy alows is looking at certain restricted aereas.
...
I found that way very revealing because it shows lokal problems in stark contrast graphically.

 

[Joachim Gerhard]

What is use is the Wavelet Burst Generator in Praxis. I usually use a burst of 4 cycles with a Blackman Window Envelope. I put the burst into the speaker, say a tweeter. So burst center frequency is say 10 bursts from 1kHz to 20kHz. I capture the burst with a microphone in the nearfield, say 2 cm from the membrane. Then i do an ETC postprocess.
A perfect tweeter has no energy storage so the ETC looks like a perfect parabola.
It´s the amplitude envelope of the analytic signal.
If there is energy storage it will appear as eccess energy on the right side of the parabola. I learned that method from Siegfried Linkwitz and on his website Linkwitz Lab - Loudspeaker Design is a lot of aditional information and pictures. I will try to find the part of his website where he discusses that method.

 

[Joachim Gerhard]

Here is one method :Midrange distortion test

As you see you can use bursts with a higher number of cyrcles.

 

[Joachim Gerhard]

Here is another method with ARTA :

Spatial distortion

 

[Joachim Gerhard]

Hello MigeO !
I try to reduce any type of distortion as much as i can even when my listening tests tell me that good enough is good enough.
You never know. Maybe one time the perfect source with perfect recordings comes to the marketplace and i have to reaccess my findings.
Let me say so much that unamplified life music generated by acoustic intruments has a lot of natural distortion and masking is not fully understood until today.
Electronically generated music is different in that regard but a reference is missing here.
We need more research in that aerea about what is audible and what is not.
Geddes is trying hard to shed some light on it and still our real world loudspeakers designs differ a lot.
The best loudspeaker that i heard in the context of 16Bit 44kHz sampling was a prototype we developped at Essex University in 1993. It was a speaker with digital equalisation that was from the point of few of impulse response a true coppy of a very expensive
B&K laboratory measurement microphone. No energy storage at all from 100Hz up.
We made everything ourselves, Prof.Hawksford and Dr.Greenfield did the DA converters and the DSP, Dr.Bews did the Power Amps and the cables and I and Rolf Olstadt did the drivers, the cabinets and the mechanics. The passive solutions i see here are childs play against that. Unfortunatly the prototypes where stolen from the lab so i can not play them any more. It whould be interesting to do something like that today with 24Bit 196KHz but unfortunately the old "Dream Team" is ocupied with more important things nowerdays for example feeding the family.

 

[john k...]

Hello John k...



You don't have to have expectations to learn more from the phase plot. Of course phase rotates faster for signals having higher frequency, but that is not the point. The point is how constant is the rotation. Always when there is a problem, a reflection for example, the phase rotation speed is not constant! That will be clearly visible.


- Elias

Yes, if you start with sin (wt) and add a delayed reflection sin(w(t-td)) = sin (wt+phi) where phi = -wtd, for t >td, then there will be a discontinuous change in phase (and also of amplitude) at td. The speed of rotation will remain the same, however. But, the reflection is in the system impulse. Like I said, it's just a different way of looking at the impulse. You could also see thins in the frequency response by looking at the impulse windowed reflection free and with reflections.

But I guess I can see some advantage to some type of TFR for a system like a horn where you you don't have the luxury of windowing out the reflection generated internally to the horn. But I don't think it necessarily follows that wavelets are the best solution (they are certainly not the only solutions).

 

[mige0]

But I guess I can see some advantage to some type of TFR for a system like a horn where you you don't have the luxury of windowing out the reflection generated internally to the horn. .

Actually the topic of delayed sources and subsequent comb filtering is inherent to *all* loudspeaker concepts to a certain degree - be it a 0 deg honker (transmission line) a 0-180deg honker (a horn or waveguide) or a 180 deg honker (open baffle speaker).

Any closed box speaker faces the same issue by the diffraction at any edge of the enclosure and even the "edge" of the diaphragm moving...

You simply can't side step the “alignment of diffraction”....


The only exception would be a perfect omni radiating into 4 Pi or the equivalent for infinite baffle.


When getting interested in horns its been of no small surprise that this honk thing - that is the most obvious fault there - has not been investigated more “in depth”.

What we actually would need is a precise tool to pin down not only that those effects happen but that also allow to detect the source as accurate as possibly to ease design process of horn contours by providing precise quantification.

Michael

 

[Elias]

And I hear discussion of interest in "time varying frequency response".
...
If you want to call the rise in amplitude over time of a resonance to its peak "time dependent frequency response" fine. But it is a manifestation of stored energy.

Clearly in the picture below there is no stored energy, but there is different variation of amplitude at different frequencies versus time.

An externally hosted image should be here but it was not working when we last tested it.

You see, the freq response depends on the signal you feed in. I hope more people would realise this. Wavelets gives you an opportunity to examine the quality and the quantity of the freq response versus time for different input signals. Freq response variations can come from various reasons: reflections, diffractions, resonances,... When you know how and how much freq response changes under different input signals then it's up to you to decide if it's acceptable for you or should you modify the design.

- Elias

 

[David_Web]

"Clearly in the picture below there is no stored energy"

The IR had log decreasing peaks every ms. If that's not stored energy then I'm not sure what is.
It is clearly re-radiating energy from the original pulse at different points in time.

 

[Elias]

"Clearly in the picture below there is no stored energy"

The IR had log decreasing peaks every ms. If that's not stored energy then I'm not sure what is.
It is clearly re-radiating energy from the original pulse at different points in time.

I take "stored energy" meaning for energy trapped in a resonance.

Anyway "stored energy" is an ambiguous definition. Better to talk about reflection, diffraction and resonance!

- Elias

 

[soongsc]

Any delayed release of energy is due to stored energy. This could happen in any for a energy transition. Deformed spider has energy stored in it; deformation of a diaphragm has energy stored in it. Better design releases this stored energy into other forms than acoustics as fast as possible.

 

[john k...]

Clearly in the picture below there is no stored energy, but there is different variation of amplitude at different frequencies versus time.

An externally hosted image should be here but it was not working when we last tested it.

You see, the freq response depends on the signal you feed in. I hope more people would realise this. Wavelets gives you an opportunity to examine the quality and the quantity of the freq response versus time for different input signals. Freq response variations can come from various reasons: reflections, diffractions, resonances,... When you know how and how much freq response changes under different input signals then it's up to you to decide if it's acceptable for you or should you modify the design.

- Elias

Sorry, it is not so clear at all. I can not tell anything form that plot that would contradict that there are a series of resonance peaks in the response. That is, this could be nothing but stored energy. Different variation in amplitude at different frequencies with time is a result of stored energy. What I see is that at and around specific frequences the amplitude rises to dark red, compared to bright red between those frequencies, indicating a resonance peak. These peaks then decay over a longer period of time. Stored energy.

You can use any signal you want for input and the result will always be a reflection of the impulse response of the system. If the impulse is perfect the output is identical to the input except for a scale factor.

The system impulse can always be expressed as

h(t) = δ(t) + e(t)

where δ(t) is the perfect impulse and e(t) the error. Any deviation form input = output is in e(t).

The question you are addressing seems to be whether or not the system is time invariant. If the system in not time invariance, then the response should change over time even when driven by the same input. If the system response changes with regard to changes in input then it becomes a question of time variance as well as nonlinearity. As far as seeing how the FR changes with input, you can just as well see if that happens by measuring frequency response with an impulse, an MLS burst, a chirp, a swept sine, a stepped sine.... You don't need a TFR to see that. Of course you will still be faced with separating out time variance from nonlinearity.

Reflections and diffractions all act as multiple sources and in that case I would expect to see discontinuous changes in amplitude where a delayed reflection (or diffraction) combines with the direct signal. These changes would be strongly dependent on the relative strengths of the direct and reflected/diffracted signals. And these are, of course, embedded in the impulse response.

Regardless of what input signal you use and how you process it, if to obtain the result you convolve the input with a sampled system impulse to obtain the output you are not going to see any effects of time variance of the system since once you measure the impulse it is static.


FWIW, here is a burst plot form Arta

An externally hosted image should be here but it was not working when we last tested it.

Looks remarkable similar to you plot from t= 0 on. Care to venture what the system is?