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Old 29th July 2012, 01:13 PM   #131
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Quote:
Originally Posted by steph_tsf View Post
Between the early eighties and the late nineties, there must have been dozens of people having tweaked the Lipshitz-Vanderkooy, putting a Bessel as lowpass kernel, concluding that the poor highpass slope that's resulting transforms it into something barely usable.
With a subtractive filter can't the high pass section be used as the initial transfer function and then the low pass section derived from subtracting, instead of the other way around ?

If the tweeter requires a steeper slope (which is often necessary, or at the least, a very good idea even if the tweeter would "survive" without it) you can choose an arbitrary steeper slope for the tweeter, then accept the shallower rolloff for the woofers derived low pass filter.... provided that the woofer has a well controlled breakup region, or the breakup is also corrected in the filter sufficiently far into the stop band.

Or have I missed something ?
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Old 29th July 2012, 01:56 PM   #132
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Hi,

Very interesting discussion going on here...

Back to FIR filtering, what do you think about linear-phase Neville-Thiele kernels as target functions?

I found that those (notably, 1st order NT) give a good overall compromise :
- compact kernels with low overshoot and low ringing
- sort of a "continuously rising filter order"-type of magnitude response

Attached a four-pic screenshot detailing the properties of a 1st oder NT at 215Hz.
Observations from top left graph, then clockwise :
- magnitude response, course. The restricton of the XO range to one octave left and right of center is clearly visible
- step responses of LP(red), HP(green), SUM(blue), delayed HP(brown) and finally sum(black) of the latter with the LP. In the mag plot we can see the delay causes a small broadband dip.
- the LP kernel impulse reponse. Has some kind of smooth "gaussianess", only a slight, 7% overshoot. Now, note the similarity of this kernel impulse to the "error shape" seen on top of the ideal step for the LP + delayed_HP case. That's why the kernel properties may be heard in some way (off-axis)**1. A Gaussian Pulse will not have a tonal character, rather it will sound like "noise pulse" (with a pitch sensation, still). The skewed, off-axis NT sum step shows some slight tonal ringing but still looks benign (try other XO functions to see). One might identify three periods of a shaped "215Hz" pulse with a fast decay at the skirts.
- close-up of the XO region, with 6dB, 12dB and 18dB slopes added for illustration, tangential to the LP response.

**1 : In minphase XOs the ringing (and it's complementary, "destructive interference" time sections in the step response) is also there, but it is masked off much better because it only post-rings.
Attached Images
File Type: png NT1@215.png (93.3 KB, 79 views)

Last edited by KSTR; 29th July 2012 at 01:59 PM.
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Old 29th July 2012, 03:49 PM   #133
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Originally Posted by DBMandrake View Post
With a subtractive filter can't the high pass section be used as the initial transfer function and then the low pass section derived from subtracting, instead of the other way around ?
Unfortunately, that won't work well. When the Gaussian is centered at half the sampling frequency, its impulse response has a Gaussian envelope but every other sample changes algebraic sign -- it oscillates at the sampling frequency. See the attached graphs.
Attached Images
File Type: png Gaussian Highpass Spectrum.png (5.5 KB, 74 views)
File Type: png Gaussian Highpass Impulse.png (3.8 KB, 70 views)
File Type: png Derived Gaussian Lowpass Impulse.png (3.9 KB, 64 views)
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Old 29th July 2012, 04:03 PM   #134
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Originally Posted by KSTR View Post
Back to FIR filtering, what do you think about linear-phase Neville-Thiele kernels as target functions?
Very interesting, and certainly viable. And demonstrative of the huge variety of design decisions to be made. Does one sacrifice frequency response for impulse response? Does one opt for linear phase or minimum phase (or something in-between)? Does one worry about spatial lobing due to non-coincident drivers and non-identical phase in the crossover sections? Does one worry about attenuation rates and driver overload? Does one worry about perfect reconstruction?

I am very happy to see that the trend is away from simply designing filters completely in the frequency domain, without regard to time-domain effects. It remains to be seen what levels of compromise are ultimately deemed to be "acceptable".
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Old 29th July 2012, 08:52 PM   #135
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Originally Posted by gberchin View Post
I am very happy to see that the trend is away from simply designing filters completely in the frequency domain, without regard to time-domain effects. It remains to be seen what levels of compromise are ultimately deemed to be "acceptable".
FIRs can deliver interesting complementary phase-linear crossovers. They can be incredibly sharp and selective, but on the other hand they exhibit presoot and ringing, and their attenuation curves are not symmetric when represented in log frequency axis. Some other varieties are less spectacular (they exhibit smaller slopes), but in exchange they don't exhibit preshoot and ringing, and their attenuation curves are symmetric when represented in log frequency axis. See attached .jpg. Which one would you try in first place?
Attached Images
File Type: jpg FIR Lab Gauss.jpg (181.1 KB, 66 views)
File Type: jpg iDFT XO Bessel.jpg (181.0 KB, 18 views)
File Type: jpg iDFT XO Butterworth 2 double (=LR4).jpg (181.1 KB, 20 views)
File Type: jpg iDFT XO Asymptot 2nd order.jpg (179.6 KB, 24 views)
File Type: jpg iDFT XO Brickwall.jpg (171.8 KB, 23 views)
File Type: jpg iDFT XO CSRn 64th order.jpg (179.1 KB, 22 views)
File Type: jpg iDFT XO CSTBSi.jpg (177.1 KB, 24 views)
File Type: jpg iDFT XO CSTBSL.jpg (189.1 KB, 23 views)
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Old 29th July 2012, 10:40 PM   #136
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Originally Posted by steph_tsf View Post
Which one would you try in first place?
Well, as you know, I do genuinely like the look of the straight line transition band! In my earliest experiments I tried a sine-shaped transition band too, as it was intuitively more rounded than the straight line transition but, again relying on intuition, I'm thinking that slope steepness should be kept in reserve for the extremities of the crossover region, so the linear-ish transition gets closer to that.
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Old 30th July 2012, 12:37 AM   #137
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Originally Posted by CopperTop View Post
I'm thinking that slope steepness should be kept in reserve for the extremities of the crossover region, so the linear-ish transition gets closer to that.
Would be nice to listen at them, switching the FIR coefficients on the fly. Always the same FIR length.

I'm considering eliminating any crossover generating some annoying sound, when listening to the woofer alone or the tweeter alone.

I'm curious to listen to the "Asymptot 2nd-order" XO because the woofer certainly will deliver a natural sound (if using a quality 3 inch or 4 inch driver, possibly two in d'Appolito), and the tweeter may exhibit a pleasing texture, with such "round" amplitude curve between 3 kHz and 5 kHz.

The Linkwitz-Riley 4th-order (two cascaded 2nd-order Butterworth) seems to materialize the gravity centre of the constellation. It still looks interesting, now that the FIR implementation permits a perfect reconstruction.
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Old 30th July 2012, 10:34 AM   #138
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Might another graph be useful: a log representation of the magnitude of the impulse response vs. time? Using a linear display of the impulse response, it is not obvious that while some filters are good for ringing around the central impulse, they result in low level ringing that persists for longer.

I enclose some screenshots where this information is overlaid onto the normal impulse response images (I need to indicate dB etc. and I notice the frequency response dB markings next to the impulse responses are confusing.) Also, it might look better if only the peaks are used, joined into a smoother line.
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Old 30th July 2012, 12:55 PM   #139
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Originally Posted by CopperTop View Post
Might another graph be useful: a log representation of the magnitude of the impulse response vs. time?
Excellent! I was hoping that you would do this. It shows just how much ringing is actually occurring, even on waveforms that appear to be benign when viewed on a linear scale.

However, once again it appears that you are again referring to "Gaussian-like" waveforms (exp[-|x|^N], where N != 2) as "Gaussian". Please, to avoid misunderstanding, do not do that. It is only a Gaussian if N==2.

EDIT: Also, the difference between N==2 and N==4 is profound. Could you try N==3? Thanks.

Last edited by gberchin; 30th July 2012 at 01:04 PM.
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Old 30th July 2012, 01:16 PM   #140
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Originally Posted by gberchin View Post
However, once again it appears that you are again referring to "Gaussian-like" waveforms (exp[-|x|^N], where N != 2) as "Gaussian". Please, to avoid misunderstanding, do not do that. It is only a Gaussian if N==2.
Hi gberchin

Yes, sorry. What is the best description? "Gaussian-derived"?

Edit: I enclose the results for Gaussian-derived (not too late to change that wording) at 2.0 (indicated as "Gaussian"), 3.0 and 4.0. Even the difference between a true 2.0 and the previous example of order 1.98 (or was it 2.02?) is noticeable.

(I have changed my UI to give me fixed steps of 0.2 in the order rather than a multiplying factor as previously, which was good for going up to very high orders quickly but a bit arbitrary in the step size).

Last edited by CopperTop; 30th July 2012 at 01:30 PM.
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