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

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Does this mean the LeCleach horns have that honk as well?

After looking at the confusion of data reach presented under different conditions and windows, it seems the application here still needs some perfection for it to become really usefull. What I mean is, it either can be used to objectively determine the fidelity of a system that corresponds with listening impressions, or it has to provide additional means to alllocate source of problem to assist in further improvements. Up to now, the way it's being used, certainly does not fullfill either objective.
 
Hello Jean-Michel,

I refer to this.
...

Elias simply has proven wavlets to deliver the best resolution in visualising quarter wave horn honk.
Jean-Michel's "quasi wavelet" code has shown comparable results too.

...


Michael
So I am curious, what "quarter wave honk" are we talking about, and at what frequency? Is it seen using wavelet transformation on any type of horn, waveguide? How does this so called "quarter wave honk" compare with the main signal? Personally, I really don't see how much better this wavelet transformation of impulses shows better information than a CSD, yet we have so many people that believe in such without a clear explanation comparing the two using the same impulse in a convincing way. Maybe I'm not used to viewing these in a sonogram type of display.
 
I'm not against wavelet transformation, but we need to understand what we are looking for and why. For example, in the CSD, each shift in windowing basically shows the total frequency content after the beginning of the window to the end of the window which basically is stationary. This means our focus is on what is taken out as we shift the window starting point.

So what can we say about wavelet transformation? It seems that multiple resolution is necessary, however, how we shift the window and what kind of processing is necessary with each shift of the window is closely related.
 
Ok.
You are prepared for prove ?

Michael


What I said was don't bet that a reflection can not be eq'ed. I did not say an arbitrary response can always be eq'ed. What will determine if the reflection can be eq'ed to perfect response is if at the measurement position the response is minimum phase or not. Since reflections typically have lower magnitude that the direct sound due to longer path length and lower than unity reflection coefficient, the net sum of the direct + reflected signal has a good chance of being MP. Below is a case where a single reflections is considered. The top shows the double impulse and FR for the system. The lower figure shows the ed'ed result with the eq amplitude in green.

An externally hosted image should be here but it was not working when we last tested it.
 
Where do you see lack of understanding ? Have you already seen this topic been covered elsewhere in greater detail ?
What *I* see is lack of tools that suffice in time resolution for the matter....

LOL
As for “pretty plots” - be aware - that's kinda patented by Earl ! - to sound *exactly* like him, you would have to add “a bunch” though :D - but you possibly would have to pay for a license...

Michael

;)

Michael:

When I said lack of understanding I was not referring to wavelet analysis. I was referring to the the basic problem being that of reflection. The plot Ellis presented only shows a series of reflections after you already know it is a series of reflections. By looking at it alone it isn't clear whether is was a series of resonances, a single reflection or a series of reflection. On the other hand, looking at the impulse response would surely show the differences. :)

Ellis,

The same thing can be said of a standard burst plot. But let me make one thing clear, (at least to me). The differences between the wavelet plots you are presenting and a standard burst plot is this: The standard bust plot has the signal length (or window length) defined in terms of periods of the test frequency. I.E. an N cycle burst. The wavelets you are using have a fixed window. Thus it is the the number of cycles of the test frequency contained in the wavelet window which varies. With a constant window the time axis in seconds makes sense. With a constant number of cycles (window length goes like 1/f) a time axis in periods makes sense. And if, as I stated previously the frequency scale is linear instead of log then a burst plot of an impulse chain, then your echo file would appear sort of like this:

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


If the time scale was in seconds it would look something like this:

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


As you go from a 3 cycle to 5 to 10...cycles/burst the area between the red lines would also "fill in", (with other colors) so I just don't see where the epiphany is. I am sorry and I don't mean to be rude, but I just don't get it. The burst plot is a wavelet plot.

[edit] in the lower plot the spikes narrow because the burst is constant number of cycles and thus shorted as f increases. The overlay at the bottom is because the burst is longer than the time between reflections.


.
 
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Hello Soongsc,

I think you really misintepreted what Mige0 was referring to.

When Michael wrote: "Jean-Michel's "quasi wavelet" code has shown comparable results too." it means that the Matlab routine (quasi wavelets ) I wrote and which Mige0 uses now, leads on every impulse response he studied to results which are strictly equivalent to Elias' wavelet code.

This has nothing to do with the Le Cléac'h horn behaviour.

I gave my quasi wavelets routine in an text file attached with message:
http://www.diyaudio.com/forums/mult...-audio-measurements-what-how.html#post2135274

(everybody can use it for free..., there is a more recent wersion I can send too, though I refine the code everyday at the moment )

Best regards from Paris, France

Jean-Michel Le Cléac'h

Hello Jean-Michel,

It refer to this.

So I am curious, what "quarter wave honk" are we talking about, and at what frequency? Is it seen using wavelet transformation on any type of horn, waveguide? How does this so called "quarter wave honk" compare with the main signal? Personally, I really don't see how much better this wavelet transformation of impulses shows better information than a CSD, yet we have so many people that believe in such without a clear explanation comparing the two using the same impulse in a convincing way. Maybe I'm not used to viewing these in a sonogram type of display.
 
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What I said was don't bet that a reflection can not be eq'ed. I did not say an arbitrary response can always be eq'ed.

Ok
I was not saying that looped reflections cant be EQ'ed – I was saying that a speaker with looped reflections can only be EQ'ed *either* for the time until the first reflection - *or* for the time after (more precisely - until next reflection occurs) – but it can not properly (like "normal" resonance can !) be EQ'ed for T = 0 to T = infinity.



...
I did not say an arbitrary response can always be eq'ed. What will determine if the reflection can be eq'ed to perfect response is if at the measurement position the response is minimum phase or not. Since reflections typically have lower magnitude that the direct sound due to longer path length and lower than unity reflection coefficient, the net sum of the direct + reflected signal has a good chance of being MP.

Ok
I still struggle with that min phase term I have to admit.
My solution in case of looped reflections (quarter wave behaviour) is that I see such a speaker as min phase till the first reflection and also as min phase after first reflection (again - until next reflection occurs) – but *not* as min phase from T = 0 till T = infinity
Might well be I'm wrong - but you have to show me...


Below is a case where a single reflections is considered. The top shows the double impulse and FR for the system. The lower figure shows the ed'ed result with the eq amplitude in green.

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


I don't get it what you show here, I admit.
Also I don't have the feeling that the SPL ratio of original sound / reflected sound has influence on being "really" min phase or not – to my understanding we can only discuss if the reflection is happening early with respect to period time of a certain frequency or not - thus the original, reflected and summ and are no longer distinguishable (as said, at a certain point we face the problem if we can identify any meaningful *frequency content* at all).

Michael
 
;)

Michael:

When I said lack of understanding I was not referring to wavelet analysis. I was referring to the the basic problem being that of reflection. The plot Ellis presented only shows a series of reflections after you already know it is a series of reflections. By looking at it alone it isn't clear whether is was a series of resonances, a single reflection or a series of reflection. On the other hand, looking at the impulse response would surely show the differences. :)

.

Ok
Elias test stimulus was an artificial one anyway – intended to bring up differences in visualisation.


;)
...
The same thing can be said of a standard burst plot. But let me make one thing clear, (at least to me). The differences between the wavelet plots you are presenting and a standard burst plot is this: The standard bust plot has the signal length (or window length) defined in terms of periods of the test frequency. I.E. an N cycle burst.
.
Here are some measurements I mad with Arta:
..



May I repeat that this was shown in the horn honk thread extensively...
The point with ARTA burst decay is that the time resolution *where it is needed* isn't good enough
Look at the pix here too:

http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted-8.html#post2126865

As burst decay visualisation is based on wavelet analysis - like Ivo Maneljan has clearly confirmed when I asked him - the issue here is simply a graphically one (visualisation part only !).
Adding
- scaling in frequency
- plus adding time / frequency trade off choice
- plus adding multi resolution feature
- plus adding normalization feature

– and we have all we possibly ever can have

:)


Michael
 
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The plot Ellis presented only shows a series of reflections after you already know it is a series of reflections. By looking at it alone it isn't clear whether is was a series of resonances, a single reflection or a series of reflection.

One plot alone does not always tell everything. That's why I presented a series of plots scaled with different wavelets to see what's going on (see above in this thread).


The differences between the wavelet plots you are presenting and a standard burst plot is this: The standard bust plot has the signal length (or window length) defined in terms of periods of the test frequency. I.E. an N cycle burst. The wavelets you are using have a fixed window. Thus it is the the number of cycles of the test frequency contained in the wavelet window which varies. With a constant window the time axis in seconds makes sense. With a constant number of cycles (window length goes like 1/f) a time axis in periods makes sense.

There is no need to limit oneself to use only fixed number of periods vs freq or fixed (time)length vs freq. With wavelets it's easy to generate any length of signal at any frequency. You select the option that best suits your particular needs in every case.



The burst plot is a wavelet plot.

Well, maybe in a vernacular language such a comparison can be made, if one persistently insists, and one is allowed to say so within a constructive spirit :D


- Elias
 
Here are some measurements I mad with Arta:

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


If the figure seems undetailed click here. I presented the burst response as both a waterfall and sonogram.
Hi John,
Are these measurements just designed to demonstrate the visibility of reflections or is this an actual speaker that is used?
 
Hello,

I did some simple wavelet reassignment to improve the visualisation and to make reflections more emphasisedly visible.

On the left is the wavelet transform of my ideal reflection test impulse response, and on the right is the reassigned wavelet. Amplitude scale is 40dB, colors are as in all of my plots before. Now no problem to identify reflections :D
An externally hosted image should be here but it was not working when we last tested it.



- Elias
 
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