Hornresp

[mige0]

Originally Posted by Jmmlc

(Eventually, if David is OK for that I can reveal a few tricks of my own about how to perform high speed quasi gaussian windowing and the fast sliding Fourier transform-not FFT.)

Jean-Michel Le Cléac'h

Yes sure, I would be very much interested in this !

As for the rest - I must have been "slightly off" to not see it correctly - thanks for putting it right.

Michael

[David McBean]

Originally Posted by Jmmlc

Eventually, if David is OK for that I can reveal a few tricks of my own about how to perform high speed quasi gaussian windowing and the fast sliding Fourier transform-not FFT.

Hi Jean-Michel,

Not a problem :-).

Welcome back.

Kind regards,

David

[David McBean]

Originally Posted by pumpkin1

I thought I read somewhere that there was a way to get a JMLC round horn. Am I right? How?

Hi pumpkin1,

Axisymmetric Le Cléac’h horns can be simulated in Hornresp by selecting the Lec flare option. Horn dimensions can be exported from the Schematic Diagram Window. See the Help file for details.

Kind regards,

David

[AndrewT]

I continue to be in awe at what you are able to get your coding to do.
Well done and thanks yet again.

[pumpkin1]

Thank you David. I too am in awe, w/o your software, I doubt much of this would be happening. I'm using a Radian 850pb in a 300hz round horn.

How important is knowing the exit angle of 10% as well as the length of the base of the horn?

[David McBean]

Originally Posted by pumpkin1

I'm using a Radian 850pb in a 300hz round horn. How important is knowing the exit angle of 10% as well as the length of the base of the horn?

Hi pumpkin1,

I am not sure that I understand exactly what you mean by "exit angle of 10%" and "length of the base of the horn".

If however (for example) you wish to design a full-mouth 300Hz T = 0.80 Le Cléac’h horn having a throat entry half-angle of 5 degrees (10 degrees included angle) to match a given compression driver exit angle, then this can be readily done using the Horn Segment Wizard. The horn axial length in this case will be 40.16 cm. See attached screenprint.

Kind regards.

David

[David McBean]

Hi Pumpkin1,

Further to my previous message, the Horn Segment Wizard can also be used to design a Le Cléac’h horn given parameters S1, F12, AT and Fta, rather than F12, T, AT and Fta, if so desired.

This allows the compression driver to be connected directly to the horn throat, without the need for a conical transition piece to match the compression driver exit diameter to that of the horn throat.

Kind regards,

David

[pumpkin1]

David-that's what I was trying to ask- thank you!!

[Jmmlc]

Originally Posted by mige0

Yes sure, I would be very much interested in this !

Hello Michael,

First we have to remember that when it comes to operations on arrays or when it comes to symbolic calculation (e.g. as with complex numbers expressed as exp[ait] ) Visual Basic is not that efficient. Even calculations using thousands of cos, sin, exp, etc. are very slow. Better to limit their number.

The spectrogram used in Hornresp on the Impulse Response is of the quasi wavelets type we have yet discussed on DiyAudio. That means that is operates with a sliding Fourier transform. But there is 4 original things:
1) the width of the Fourier window varies as the inverse of the frequency;
2) FFT is not used;
3) the Fourier window has a bell shape
4) convolution product is replaced by a simpler calculation.

The problem with FFT is that it uses discrete frequencies linearly set between 0Hz and Fs. This means that there is the same number of calculated values between the important interval 0 and 1000Hz and the interval 19000 and 20000Hz. As our audition is sensible to the log of the frequency in fact we don’t need the same increment between 2 frequencies at HF than at LF.

If you have ever used Adobe Audition (previously CoolEdit) you’ll see that as its spectrogram is based on FFT and it uses a linear frequency scale. This is a real pity and such spectrogram is nearly useless.

The spectrogram in Hornresp uses a log frequency scale and this allows that fewer values are calculated. From this results a first reduction of the run time.

A classic type of quasiwavelets spectrogram use at each frequency a convolution between the Impulse Response and a convolving pulse, the envelop of which (Fourier window) is a raised cosine or more rarely a Gauss curve. Those as 2 bell shape curves. The calculation of such convolving pulse and then the convolution leads to very long run times, incompatible with the use of Hornresp.

The problem is very much easier when the shape of the Fourier window is rectangular. It allows the use of Sliding Fourier Transform (SFT) much easier to compute as the convolution is very much similar to a sliding mean calculation (on both the imaginary and the real part). Apodizing is a refinement of this but increases the run time. But the main problem with a rectangular Fourier window is the artifacts it creates. We yet spoke on DiyAudio on the Constant Spectral Decay graph (CSD) that ARTA can calculate. When a very short or no apodizing is used the obtained spectrogram shows a lot of artifacts both in frequency (“wings”) and in time (loss of resolution).

How to have both the speed of a rectangular window based SFT and the lack of artifacts and fine resolution due to the use of a bell shaped window is a challenge. This is reached with the spectrogram routine used in Hornresp.

We said that if a rectangular Fourier window is used the calculation looks like a sliding mean and is easy to compute. Then how to obtain the benefit of a bell shape window using sliding mean?

The answer is simplistic. Consider a simple distribution made of a single Dirac (y = 1 at t=0 and y = 0 with t different than 0). If you perform a sliding mean (within an interval having a width of 15 as in the example shown in attached file) the new distribution is rectangular. Then, if you perform a second sliding mean with the same width of the rectangular window, the new distribution appears as an isocel triangle. The interesting thing is now: if you perform a third sliding mean with the same width of the rectangular window, the new distribution appears as having a bell shape. Smoothers but wider bell-shaped distribution can be obtained with 4th , 5th or more sliding means but I found that the precision and lack of artifacts obtained with 3 sliding means as in Hornresp is far sufficient.

No exponential calculation, no convolution is then needed. Further refinement lies in algorithms tricks in order to reduce at minimum the number of logical tests ( on indexes in order to verify they are in the correct range). The way the sliding mean is performed on both the imaginary and the real parts ( Re(t) = y(t).sin(at) and Im(t) = y(t).cos(at) ) is also original as we compute first the cumulative of Re(t) and Im(t) and then for every value of t we can easily obtain the mean value of Re and Im in the interval t1 t2 around t ( t1 a,d t2 = limits of the rectangular window) just using a single subtraction and dividing by the number of values between t1 and t2… This reduces a lot the run time. Then after the 3 sliding means has been performed a last refinement of the algorithm consists to calculate the magnitude in dB (which requires slow opeartions as power, square root, log...) of the spectrogram only for the t values corresponding to the displayed time values of the spectrogram window.


Best regards from Paris, France

Jean-Michel Le Cléac'h

[mige0]

Thanks for your additional infos Jean-Michel.
I'd have to seriously brush up my math before wrapping my head around, I'm afraid
I've noticed the more "smooth" shape in the time scale though - or at least what I though it may be..
Again, this spectrogram is a gorgeous feature.

One thing I miss (or have not focused too much until now) - but it would probably be better to discuss that in more detail in the wavelet thread, as we are getting even more OT in David's thread with this - is the possibility to optionally equalize to flat FR before performing a wavelet / spectrogram analysis.

This would highlight the differences in CMP behaviour for different designs even better IMO. I mean - a pretty good straight horn shows (in theory) negligible CMP whereas a TM or tapped horn always shows distinct CMP due to the standing wave mechanism needed for its operation.

I mean - the most natural thing done until now and being done in the future is to equalize for flat FR (or any house curve of desire), and it might be pretty revealing to have a tool at hand that shows to what extend the results still differ from ideal in the time domain (spectrogram) due to CMP.

Michael