Hello Soongsc,
There is "by nature" a strong relation between group delay and acoustic impedance through the phase of the pressure wave. (GD resulting by derivation of the phase)
This is explicited by Ohm's acoustic law (better to consider it as complex ).
p = v × Z.
with
p = sound pressure
v = particle velocity
Z = acoustic impedance (acoustic resistance + j . acoustic reactance)
A pure resistive acoustical impedance leads to a pressure in phase with particle velocity
A pure reactive acoustical impedance leads to a pressure in phase quadrature with particle velocity
Best regards from Paris, France
Jean-Michel Le Cléac'h
There is "by nature" a strong relation between group delay and acoustic impedance through the phase of the pressure wave. (GD resulting by derivation of the phase)
This is explicited by Ohm's acoustic law (better to consider it as complex ).
p = v × Z.
with
p = sound pressure
v = particle velocity
Z = acoustic impedance (acoustic resistance + j . acoustic reactance)
A pure resistive acoustical impedance leads to a pressure in phase with particle velocity
A pure reactive acoustical impedance leads to a pressure in phase quadrature with particle velocity
Best regards from Paris, France
Jean-Michel Le Cléac'h
Hello Soongsc,
In a first time if I were you, I would not care about the non zero group delay at high frequency.
This non zero value is generally due to to a bad estimation of the mean "travelling time" of the wave. The error thus created by the bad compensation of the mean travelling time during phase compensation and unwrapping is then reflected as a constant error added to the GD at every frequency.
If the derivation of the phase (versus pulsation ) is correctly done (this means also that the unwrapping of the phase is correctly done...), what is more important than the absolute values of GD is the difference between the GD at 2 frequencies.
For myself I find more convenient also to express the GD as its equivalent distance travelled at the speed of sound (c = 344m/s).
Best regards from Paris, France
Jean-Michel Le Cléac'h
P.S. (David McBean has a very clever method to obtain the GD curve in Hornresp, which gives accurate results, may be if you contact him he will help you on that.)
In a first time if I were you, I would not care about the non zero group delay at high frequency.
This non zero value is generally due to to a bad estimation of the mean "travelling time" of the wave. The error thus created by the bad compensation of the mean travelling time during phase compensation and unwrapping is then reflected as a constant error added to the GD at every frequency.
If the derivation of the phase (versus pulsation ) is correctly done (this means also that the unwrapping of the phase is correctly done...), what is more important than the absolute values of GD is the difference between the GD at 2 frequencies.
For myself I find more convenient also to express the GD as its equivalent distance travelled at the speed of sound (c = 344m/s).
Best regards from Paris, France
Jean-Michel Le Cléac'h
P.S. (David McBean has a very clever method to obtain the GD curve in Hornresp, which gives accurate results, may be if you contact him he will help you on that.)
Hello Soongsc,
eventually you could adopt some kind of presentation of GD / angle like a polar map.
Best regards from Paris, France
Jean-Michel Le Cléac'h
eventually you could adopt some kind of presentation of GD / angle like a polar map.
Best regards from Paris, France
Jean-Michel Le Cléac'h
Had some time to do home work
Here are how high pass filters perform.
Instead of group delay, I show cumulative spectrum decay in the common form and also in its sonogram variant.
This to me – is in a first step - more intuitively to grasp as a difference in behaviour though I do not forget about GD at all.
The idea behind is that we might be as sensible to shift of origin from GD as we are possibly for a long decay in the time domain.
I know, electrically this is quasi "one and the same" or maybe better put "two sides of the same coin" but nevertheless I would like to bring in this additional aspect .
Basically the following plots show my measurements of all filters available from DCX at 1kHz - in lack of a versitale analog filter source.
All plots are what the text says, starting out with Gaussian 6dB over Bessel Butterworth and Linkwitz Riley up to 48dB
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Sadly we do not have Chebyshev filters with DCX
We clearly see that there is a huge difference in the time domain regarding decay at HP (XO) frequency.
The sharper and the steeper the HP filter is chosen the more pronounced and prolonged is decay time.
If we now look at the cut off of a horn with an XO set ~1 octave higher – it might be obvious that this "ringing" still will be audible and contribute to horn honk as its by no way compensated by a mating low pass (as is in XO application) – what you think ?
PS:
By the way, I digged up John Kreskovky's page on the matter (related to XO only):
http://www.musicanddesign.com/Stored_energy_2.html
Michael
Here are how high pass filters perform.
Instead of group delay, I show cumulative spectrum decay in the common form and also in its sonogram variant.
This to me – is in a first step - more intuitively to grasp as a difference in behaviour though I do not forget about GD at all.
The idea behind is that we might be as sensible to shift of origin from GD as we are possibly for a long decay in the time domain.
I know, electrically this is quasi "one and the same" or maybe better put "two sides of the same coin" but nevertheless I would like to bring in this additional aspect .
Basically the following plots show my measurements of all filters available from DCX at 1kHz - in lack of a versitale analog filter source.
All plots are what the text says, starting out with Gaussian 6dB over Bessel Butterworth and Linkwitz Riley up to 48dB
######
######
######
######
#######
#######
#######
#######
#######
Sadly we do not have Chebyshev filters with DCX
We clearly see that there is a huge difference in the time domain regarding decay at HP (XO) frequency.
The sharper and the steeper the HP filter is chosen the more pronounced and prolonged is decay time.
If we now look at the cut off of a horn with an XO set ~1 octave higher – it might be obvious that this "ringing" still will be audible and contribute to horn honk as its by no way compensated by a mating low pass (as is in XO application) – what you think ?
PS:
By the way, I digged up John Kreskovky's page on the matter (related to XO only):
http://www.musicanddesign.com/Stored_energy_2.html
Michael
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LOL
Who wouldn't , oh boy , who wouldn't !
Already forgot about :
Hy doug20
....
So it may take a while until you get some "cook book" suggestions here.
LOL - if at all !
Michael
But if you are in a hurry / simply cant await :
maybe you just try to go response shaping via PC ? - for the issue presented this should do fine - and the goals are named clearly yet...
Don't forget to report back !
Michael
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I wouldn't say it's the law of physics because this a really a "control system" problem, and surely it's possible to shift parameters around. I have shown in another thread that even real components react differently from theoretical components, to be more specific, the impedance phase is different between solid core inductor and air core inductor; the impedance shape will also change based on core design.
What you have shown is similar to the measurements presented in Newell and Holland's book on Loudspeakers. The issue is how we shift the parameters around during design to get the effect we desire.
Hello Michael,
A quasi general feature of LP filters and Hp filters is that in both cases the GD delay at HF is smaller than at LF.
All pass filters behave the same too.
That'why to try to compensate the GD rise of a horn cannot be based on using a classical LP filter.
I indicated my method who consist in designing a subtractive filter+ delay GD compensator in order to obtain a compensation transfer function for which the GD is larger at HF than at LF.
The result can be seen in the graph:
http://www.diyaudio.com/forums/atta...6483025-geddes-waveguides-gd_compensation.jpg
The curves in red are the frequency response curve (top) and the GD cruve (bottom). Original measured curves before compensation are in blue. As you can see the "compensated" response curve is quasi similar to the "uncompensated" but the main difference is see when we compare the GD curves. There is an efficient decrease in GD between 650Hz and 1500Hz after compensation and this allows us to use a HP cut-off one octave below the one we should use for the original uncompensated driver+horn.
See also:
http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted.html#post2091097
Best regards from Paris, France
Jean-Michel Le Cléac'h
P.S. (I think it is possible to ameliorate your CSDs, please send me your PIRs and I'll see what I can do.)
A quasi general feature of LP filters and Hp filters is that in both cases the GD delay at HF is smaller than at LF.
All pass filters behave the same too.
That'why to try to compensate the GD rise of a horn cannot be based on using a classical LP filter.
I indicated my method who consist in designing a subtractive filter+ delay GD compensator in order to obtain a compensation transfer function for which the GD is larger at HF than at LF.
The result can be seen in the graph:
http://www.diyaudio.com/forums/atta...6483025-geddes-waveguides-gd_compensation.jpg
The curves in red are the frequency response curve (top) and the GD cruve (bottom). Original measured curves before compensation are in blue. As you can see the "compensated" response curve is quasi similar to the "uncompensated" but the main difference is see when we compare the GD curves. There is an efficient decrease in GD between 650Hz and 1500Hz after compensation and this allows us to use a HP cut-off one octave below the one we should use for the original uncompensated driver+horn.
See also:
http://www.diyaudio.com/forums/multi-way/161627-horn-honk-wanted.html#post2091097
Best regards from Paris, France
Jean-Michel Le Cléac'h
P.S. (I think it is possible to ameliorate your CSDs, please send me your PIRs and I'll see what I can do.)
Hello everyone,
Some measurement on the group delay issue. Here's a 18sound horn XD125 crossed at 2kHz to 8" driver with 2nd order LR filter.
Picture is a wavelet transform of the impulse response, showing the 'burst envelope' at the given frequency as a function of time.
One can clearly see the heavy twist between 2-4kHz. Notice that only part of the group delay is coming from the cross over filter - The horn itself has a non constant group delay! (I couldn't find measurement of the horn alone.. have to look for it and post later).
- Elias
Some measurement on the group delay issue. Here's a 18sound horn XD125 crossed at 2kHz to 8" driver with 2nd order LR filter.
Picture is a wavelet transform of the impulse response, showing the 'burst envelope' at the given frequency as a function of time.
One can clearly see the heavy twist between 2-4kHz. Notice that only part of the group delay is coming from the cross over filter - The horn itself has a non constant group delay! (I couldn't find measurement of the horn alone.. have to look for it and post later).
- Elias
Attachments
Hello Elias,
You example is typical of
1) the choice of a too much low -3dB frequency for the high pass filter
2) the choice of a crossover having quite large phase distortion
Things may be improved a lot if:
a) we choose an -3dB frequency of the high pass filter one octave above the acoustical cut-off of the horn.
b) we choose a crossover having a lower phase distortion (by example a Le Cléac'h quasioptimal crossover).
Best regards from Paris, France
Jean-Michel Le Cléac'h
You example is typical of
1) the choice of a too much low -3dB frequency for the high pass filter
2) the choice of a crossover having quite large phase distortion
Things may be improved a lot if:
a) we choose an -3dB frequency of the high pass filter one octave above the acoustical cut-off of the horn.
b) we choose a crossover having a lower phase distortion (by example a Le Cléac'h quasioptimal crossover).
Best regards from Paris, France
Jean-Michel Le Cléac'h
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