I agree. My online library subscription has lapsed and its expensive to renew.
About the paper, I think the sphere is a very useful semi-analytic model. But, in practical situations, the large diffraction gain we see at f=c/(2L), where L is the effective baffle length, is missing entirely. Modeling multiple drivers is also somewhat problematic with a sphere. Finally, although I am not a big fan of offsetting drivers on the baffle to reduce the (on-axis) diffraction, the effect of offset is also missing from a sphere.
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An odd paper since all of that can be found in Morse from back in the 20's. I have been spherical models for at least three decades.
Aarts and Janssen have written a few papers for which the velocity profile on the radiating surface is not constant but has a surface distribution, whereas Morse for example is limited to rigid oscillation.
Some of these AES Journal papers are also published elsewhere and often are then free for download. Try to copy the name of article and Google it.
More about baffle diffraction AES E-Library A Diffractive Study on the Relation between Finite Baffle and Loudspeaker Measurement
AES has also open Access papers, mostly those with public funding
AES Open Access Publications
More about baffle diffraction AES E-Library A Diffractive Study on the Relation between Finite Baffle and Loudspeaker Measurement
AES has also open Access papers, mostly those with public funding
AES Open Access Publications
At lower frequencies then the nearfield shape applies. At higher frequencies an accurate anechoic or gated measurement is available. The problem is in the middle hundreds where the transition from 4pi to 2 pi occurs. Using data or predictions from a driver on a sphere is worthless if it doesn't accurately reflect your case.
That's exactly the point of the paper: that an accurate diffraction model improves the blending of nearfield and farfield curves. The tool for defining the particular diffraction curve for a given box shape is included (otherwise "the edge", LEAP, and a few others that preceeded could be used). No one is talking about using a single diffraction curve for all speakers.
David
Hilbert/Bode?
The mention of "Hilbert-Bode" transform reminds me that Bode derived the minimum phase transform in his book but never mentioned Hilbert AFAIK.
Does anyone know the first reference that Bode's transform was already known to mathematicians under the name of Hilbert transform?
It would be polite to include it in some work I plan.
I want to extract the minimum phase in LTspice to check for excess phase.
I see Charlie Laub and/or Jeff B have done this in Excel, any comments on the technique to do this?
Appreciate LTspice specific information from anyone too.
Best wishes
David
The mention of "Hilbert-Bode" transform reminds me that Bode derived the minimum phase transform in his book but never mentioned Hilbert AFAIK.
Does anyone know the first reference that Bode's transform was already known to mathematicians under the name of Hilbert transform?
It would be polite to include it in some work I plan.
I want to extract the minimum phase in LTspice to check for excess phase.
I see Charlie Laub and/or Jeff B have done this in Excel, any comments on the technique to do this?
Appreciate LTspice specific information from anyone too.
Best wishes
David
Hi Earl,
You mentioned in your post #80 the following;
“One should not use near field data any higher in frequency than absolutely necessary because strange things happen in the near field that do not propagate to the far field.”
Are you referring to the accuracy limitations in the near field response at frequencies above what D B Keele described as ka=1.6 ?
Regards
Peter
You mentioned in your post #80 the following;
“One should not use near field data any higher in frequency than absolutely necessary because strange things happen in the near field that do not propagate to the far field.”
Are you referring to the accuracy limitations in the near field response at frequencies above what D B Keele described as ka=1.6 ?
Regards
Peter
The minimum phase can also be "extracted" by using the cepstral separation method: Conversion to Minimum Phase
An "intuitive" tutorial for how this method converts the spectrum to the minimum phase form is at this URL: low-latency FIR filters
The approach that I used in the Blender can be found in the following reference, specifically eq. 9:
John Bechhoefer, "Kramers–Kronig, Bode, and the meaning of zero", Am. J. Phys. 79, 1053 (2011).
AIP Scitation entry: Scitation: Kramers-Kronig, Bode, and the meaning of zero
I found this paper to be a very nice walk through the topic, and it includes some very interesting applications.
-Charlie
Hi David,
The term “Hilbert-Bode Transform” (HBT) was coined by myself about 15 years ago, when I implemented minimum-phase extraction algorithm in very early version of SoundEasy program.
To be honest with you, I think, that the term “Transform” is actually incorrect, but at the time, I could not think of anything better.
Initially, the only person who realized the potential of HBT in DIY circles was John Kreskovsky. The rest of the public was apprehensive. Today it’s a completely different story.
I use HBT extensively in SoundEasy and particularly in Ultimate Equalizer programs.
Please have a look at http://www.bodziosoftware.com.au/ for more information.
You are quite correct, that an author should acknowledge prior contributions in the field.
Hendrik W. Bode’s (PhD) book is called “Network Analysis and Feedback Amplifier Design”.
Best Regards,
Bohdan
Thank you. Looks to be excellent, will take in more when it's not so late here.
Not in my mainstream for electronics or acoustics, how did you find it?
Best wishes
David
Thank you. I have read some of the papers from your website so it's nice to be able to express my appreciation directly.
Do you have any prior references to the equivalence of the Hilbert transform to Bode's work?
I have a PDF of the 10th edition of Bode's book. I believe that some later editions have addenda. Perhaps Bode mentions it there.
Have you, or anyone else here, an edition with the additions?
Best wishes
David
There is another paper I can recommend that talks more about HOW to calculate the integral. I only found this recently after I came up with something similar on my own based on the Bechhoefer paper, but it describes how to split up the integral into parts, each of which are calculated separately and then summed to yield the phase.
T. Andersson et al, "Numerical Solution of the Hilbert Transform for Phase Calculation from an Amplitude Spectrum", Mathematics and Computers in Simulation XXIII, 262-266 (1981).
Info and Abstract are located here. Not sure where you can get the full paper online. I got it though my local University campus library.
This may be appropriate for the time domain results of an LTSpice .Tran simulation. Took a while to mull over, I had not considered that far ahead, only for the frequency domain of the .AC simulation. Thank you for the reference.
The local library has a copy so I will certainly check it out, your previous recommendation was spot on.
Only had a chance to fully read that Bechhoefer paper today and it's really excellent, so thanks once more.
I studied mathematical physics but that paper was after I left the field, made a pleasant reminder.
It is wonderful to find a whole new strand of information like that.
Are you in that area, or how did you come across it?
Best wishes
David
That seems like an odd history of the topic. First of all, the transform we are talking about is not the "Hilbert-Bode Transform", its just the Hilbert transform. There is no such thing in applied mathematics as the Hilbert-Bode Transform. In the audio field, Heyser clearly describes the driver response as a minimum phase network in his 1969 article:
AES E-Library Loudspeaker Phase Characteristics and Time Delay Distortion: Part 1
And, the Hilbert transform really is a transform. Specifically, its a linear, integral transform. The pair [A,P], where A is the amplitude and P is the phase, are called the Hilbert transform pair. It takes only a few lines to establish the fact that the loudspeaker amplitude response, A(w), is the Hilbert transform of the phase response, P(w). Heyser is not really careful to talk about the issue of negative frequency, which one will encounter when attempting to evaluate the transforms, but that turns out to be very simple to clarify.
I might also add that among physicists, the Hilbert transform pair [A,P] is often said to satisfy the Kramers-Kronig relations. Kramers, and Kronig independently, discovered the formulae in the context of optical response functions some 20 years after Hilbert first used the technique in the context of the Riemann-Hilbert problem.
Hi Jcandy,
Thank you for your comments, I agree with you.
As I said before, the name HBT is incorrect, but it has been used ever since in DIY circles. Perhaps this page explains it better:
The law of Bode and the Hilbert transformation
Best Regards,
Bohdan
Heyser explicitly notes the Hilbert transform for the amplitude/phase relation and it seems clear from the context that this was not news.
So who was the first person to point out the connection to Bode's work and when?
Best wishes
David
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