If we are talking about loudspeakers here and not single input single output system, like an amp, then no single impulse response is going to give you what you want no matter if its analyzed by wavelets, FFT, or anything else that you can contrive. You have to look at the 3-D field response where things like resonances, diffractions and reflections cxan all be clearly sorted out. This is all discussed in my paper on Directivity. Trying to sort out 3-D effects like diffraction and/or reflection in a 1-D measurement is going to be a dead end, no matter what technique you use.
"Energy storage" - it seems to be a typical audiophile term here - it means whatever the poster wants it to mean.
"Energy storage" - it seems to be a typical audiophile term here - it means whatever the poster wants it to mean.
LOL
For a person awaiting “certain death in such thread” you are very active and alive, Earl!
Be it...
As usual (LOL) I don't agree neither to your negative attitude nor to your statement.
Given the results achieved - and shown here and in the horn honk thread - there was already a loooot to gain form wavelet analysis.
Also - you definitely are posting in the wrong thread - this one is about *wavelet transform "what is it" and ""how to do"
If you like to comment about *application* - there's the horn honk thread or any other you like to start...
Michael
For a person awaiting “certain death in such thread” you are very active and alive, Earl!
Be it...
As usual (LOL) I don't agree neither to your negative attitude nor to your statement.
Given the results achieved - and shown here and in the horn honk thread - there was already a loooot to gain form wavelet analysis.
Also - you definitely are posting in the wrong thread - this one is about *wavelet transform "what is it" and ""how to do"
If you like to comment about *application* - there's the horn honk thread or any other you like to start...
Michael
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No, its not so clear.
But one thing at least *is* clear – a “simple” resonance can be *completely* EQ'd – where as those looped reflections can *certainly not* be EQ'd
In the end this is what's to find out – besides - to pin down this special sonic pattern occurring or not.
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Regarding the ARTA burst plot you show – If you have a look through the horn honk tread you will notice that all those forms of visualisation have been examined in the light of quarter wave honk.
Bottom line – non has shown the *time resolution* needed here – neither does your example.
Wavelet analysis on the other hand has shown excellent time resolution if adjusted accordingly.
Michael
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So far so clear
– most easily seen here and subsequent:http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted-12.html#post2150033
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But this I didn't get :
What are you emphasising on here ?
Michael
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First, don't be so sure that a reflection can not be eq'ed. It can, but like any eq for multiple sources, it would be correct for only one point in space.
Second, the burst plots I posted were for a series of resonances. I presume Ellis' plot was for a single reflection for which the CDS and burst would look like this:
An externally hosted image should be here but it was not working when we last tested it.
The CSD basically shows the same thing as the wavelet . The problem is that when you look at the impulse response and frequency response I think the result is clearer. The burst clearly show a delayed signal and if the frequency scale was linear the delayed burst would move to th rings as the frequency increased in a linear manner.
I have noting against the wavelet. If it helps you identify a problem that's great. But I think understanding the problem is key to identifying it and a pretty plot is just a pretty plot. As I said before, all these plots are just different ways to look at what is contained in the impulse.
So far so clear
http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted-12.html#post2150033
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But this I didn't get :
What are you emphasising on here ?
Michael
That the analysis is based on a time invariant system. The impulse is static, i.e. not changing.
OOOh don't call them "just pretty pictures" that will certainly ruffle some feathers.
I agree with you however, and I've said this before. There is nothing new here, it's all been looked at before and we keep coming back to the standard impulse response and its smoothed FFT. I do like the idea of using wavelets of different window lengths as a way to achieve smoothing on the frequency domain data, because that makes some sense. The frequency domain always needs some smoothing and using a technique that is closer to how we hear seems logical.
Im starting to revert back to just thinking this CSD is damn good.....what doesnt it do that the wavelet does?
example.
Don't get me wrong its fun to create different types of charts but in the end the goal is to read and conclude something about a driver.
example.
An externally hosted image should be here but it was not working when we last tested it.
Don't get me wrong its fun to create different types of charts but in the end the goal is to read and conclude something about a driver.
The only difference is that a wavelet is a more mathematically precise operation - its an orthogonal transform. But as you can see that does not appear to have any impact on the data presentation.
Ok.
You are prepared for prove ?
To make things obvious, lets start with the most extreme case
http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted-7.html#post2123744
So - how you gonna EQ the blue trace of complete destructive summation after a certain delay time ?
Michael
You can download the IR file of Elias example here :
http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted-5.html#post2120124
Its not exactly resonances but rather a set of “echos”
Michael
I agree on “basically”
- but certainly don't agree on any CSD being of the same clarity in time resolution.As said – time resolution is key when we want to examine this facet of horn honk !
Your second statement is not under discussion at around here.
Too bad, you are not at all interested in horns...
Michael
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
- but you possibly would have to pay for a license...Michael
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John, the system is a series of attenuated reflections at 1ms intervals. The IR file (WAV) is posted in the Horn Honk thread (And Michael has linked it here too). It's a test file to compare the methods, and to see what to expect from more real and messy impulse responses.
Of course the impulse response I expect to be time invariant.
However, one point I like to make. Although this is not a thread about "time varying frequency response", but since the topic fits to wavelets here we go:
For the test 1ms reflection IR file, we generate a series of wavelet transforms formed by varying lengths of wavelet.
Here if the input signal (=wavelet) is short, individual reflections can be seen clearly: How do you define frequency response here? It is flat!
An externally hosted image should be here but it was not working when we last tested it.
A bit longer input signal and the reflections start to overlap: Here also the freq response is flat!
An externally hosted image should be here but it was not working when we last tested it.
More longer input signal starts to cause smooth combing effects: Freq response starts to have ripples. Response looks like having multiple of decaying resonances!
An externally hosted image should be here but it was not working when we last tested it.
Increase the input signal length some more and the comb filtering gets sharper: Freq response has ripples.
An externally hosted image should be here but it was not working when we last tested it.
Still longer input signal and the response starts to look symmetrical with deeper notches in the freq response:
An externally hosted image should be here but it was not working when we last tested it.
Now one may question himself: Which is the 'right' frequency response of this impulse response? Is it flat, or is with ripples? And if it is with ripples what is the deepness of the ripples (as it depends on input signal length)?
Also one can ask: Which of there pictures is the best representation of this system?
They all are correct! It depends what effect you want to see, and you'll have it with wavelets.
Consider also that 1ms reflections can be scaled, say, 2ms or 10ms reflections and the relativity still holds.
Wavelets allows you to scale your plots and your conditions to see more.
Also, you cannot know what is your frequency response unless you define the input signal you are using!
- Elias
Wavelets: a different perspective
Let me offer a brief, somewhat alternative perspective on the usefulness of wavelets. Although the first (discontinuous) wavelet was proposed by Haar in 1909, wavelets emerged as a huge 90s fad in physics, mathematics and computer science. There was initial excitement in using them for lossy compression of images, but in the end there was no clear advantage of wavelet-based compression (JPEG 2000) in comparison to JPEG (digital cosine transform) compression. Actually, this is an oversimplification. I think the small improvement in JPEG 2000 compression was counterbalanced by the increased complexity of creation and decoding.
In physics, wavelet expansion techniques were applied to the numerical solution of ordinary and partial differential equations. I followed the progress of wavelet methods in the latter context, eventually concluding that they were inconvenient and inferior, overall, to standard spectral techniques.
The power of any expansion scheme is related not only to the mathematical properties of the set of functions which are used, but also to the type of data one is trying to approximate by said functions. It was hoped that many datasets of interest (often physical ones like images) would require expansion in fewer wavelets than Fourier modes to obtain a good approximation, but in reality I don't believe wavelets lived up to the hype.
In the end, I would be surprised if one could really find a general application domain where wavelets significantly outshine traditional Fourier-Chebyshev spectral methods (of course, there are always "special" problems for which a given method will shine).
Let me offer a brief, somewhat alternative perspective on the usefulness of wavelets. Although the first (discontinuous) wavelet was proposed by Haar in 1909, wavelets emerged as a huge 90s fad in physics, mathematics and computer science. There was initial excitement in using them for lossy compression of images, but in the end there was no clear advantage of wavelet-based compression (JPEG 2000) in comparison to JPEG (digital cosine transform) compression. Actually, this is an oversimplification. I think the small improvement in JPEG 2000 compression was counterbalanced by the increased complexity of creation and decoding.
In physics, wavelet expansion techniques were applied to the numerical solution of ordinary and partial differential equations. I followed the progress of wavelet methods in the latter context, eventually concluding that they were inconvenient and inferior, overall, to standard spectral techniques.
The power of any expansion scheme is related not only to the mathematical properties of the set of functions which are used, but also to the type of data one is trying to approximate by said functions. It was hoped that many datasets of interest (often physical ones like images) would require expansion in fewer wavelets than Fourier modes to obtain a good approximation, but in reality I don't believe wavelets lived up to the hype.
In the end, I would be surprised if one could really find a general application domain where wavelets significantly outshine traditional Fourier-Chebyshev spectral methods (of course, there are always "special" problems for which a given method will shine).
Oops - way too much techincal info for this group (just kiding). Basically this is what I have found as well, but people here don't seem to want to hear that. Thanks for the input.
We all seem to agree that the impulse response is the common denominator, the ideal starting point. Given that I really do think that Prony method has the most chance of anything at being an effective expansion since its basis functional are all impulses. It basically expanding a complex impulse in a set of simple impulses. What could be more natural?
We all seem to agree that the impulse response is the common denominator, the ideal starting point. Given that I really do think that Prony method has the most chance of anything at being an effective expansion since its basis functional are all impulses. It basically expanding a complex impulse in a set of simple impulses. What could be more natural?
Here's a brief history related to wavelets:
An Introduction to Wavelets: Historical Perspective
The second - more detailed - one I've come across, I can't find at the moment..
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No hype here at all.
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.
You are certainly invited to show any better – as was Earl invited to start a thread about *his* (hypothetically) favourite analysis!
Michael
An Introduction to Wavelets: Historical Perspective
The second - more detailed - one I've come across, I can't find at the moment..
#########
No hype here at all.
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.
You are certainly invited to show any better – as was Earl invited to start a thread about *his* (hypothetically) favourite analysis!
Michael
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