As a user of Acourate (a software audio toolbox) Neville Thiele (NT) filters are quite familiar to me, and I thought that NT filters were broadly used because of their elegance and efficiency. Therefore, I was puzzled to realize, that in this forum, these filters have only marginally been discussed yet: A search for Neville Thiele leads to very few results, and some of the posts contain a warning because of theirs supposedly bad ringing behavior (which might not be a problem at all, as shown in the examples below). I like NT’s. I even dare the statement that well parametrisized NT linear phase filters can overall outperform LR4 and BES2. Nota bene and be aware then that unlike LR4 and BES2, NT filters rely on DSP. They cannot correctly be implemented using analog circuitry.
Neville-Thiele (NT) filters can come in different flavors, and they all have the same, interesting characteristic: Inside the passband, they have a smoothly steepening slope, then run steeper and steeper trough a limited transition area and end up with a final, vertical brickwall cutoff characteristic. Because of this final brickwall cutoff, the term "steepness" does not really apply for NT filters. Nevertheless, like in traditional Bessel, Butterworth and Linkwitz-Riley filters, where the steepness can be defined by a parameter (the “order”, e.g. as LR4 or BES2), NT filters of a given passband allow the variation of the width of the limited transition area by a parameter. This parameter of any suitable decimal value allows to fine tune the filters width to specific needs. A high value for the width results in a narrow limited transition area and vice versa. Like a high order in traditional filters will result in steep filter slopes.
In the following examples, a three way xover with f_-6dB points at 400Hz and 2.5kHz using linear phase NT filters of different widths will be examined. First, the influence of the width parameter is shown using values of 0.4, 0.5, 0.7071, 1 and 2. For the passband filter, these values will result to a total filter width, including the passband and both limited transition areas of 70Hz/14.1kHz, 100/10kHz, 150Hz/6.7kHz, 200Hz/5kHz, 283Hz/3.5kHz.
Fig. 1
Fig. 2
And how do NT filters compare against traditional filters, like eg LKR4?
NT1.0 vs. LR4:
Fig. 3
Fig. 4
In the frequency domain, NT1.0 has quite a sharper charactreristic than LR4, it’s behavior in time domain is potentially a bit more critical (pre- and postringing) than LR4
NT0.5 vs. LR4:
Fig. 5
Fig. 6
NT0.5 has a broader charactreristic in frequency domain than LR4, it’s behavior in time domain is a bit tamer than LR4’s.
NT0.7 vs. LR4:
Fig. 5
Fig. 6
In frequency domain, NT0.7 initially more or less follows the characteristic of LR4 inside the passband and further to approx. -22dB. Beyond this level, NT0.7 gently dives into the brickwall cutoff characteristic. In time domain it’s behavior seems much the same as for the LR4 filter.
The time domain shows much the same, but or course not exactly the same:
Fig. 7
NT0.7 shows some “bumps” at a level of 0.000025, whereas LR4 remains more or less at level 0. Given the main impulse value of the filters peaking at 0.887, this results in a corrected value of
28.2 E-6 for the adddtional pre- and postimpulse oscillations of the NT0.7 filter compared to the LR4 filter… Guess if anyone would be able to hear the effects of the resulting ringing that may result under worst-case conditions. So there is not exactly a lunch for free. But quite a huge one in frequency domain for quite a small price in time domain:
Fig. 8
Second set of examples: Bessel2 vs. NT0.4
NT0.4 vs. BES2:
Fig. 9
Fig. 10
Fig. 11
Fig. 12
BES2 is not widely used, because of it’s demanding broadband’s requirements to the driver. With nearly the same characteristics in the passband, NT04 provides some headroom beyond the approx. -22dB threshold.
Example of a minimum width brickwall NT16 filter (width parameter=16.0)
Fig. 13
Fig. 14
Nobody will generate such a filter for regular audio use...
This might be a brief insight into NT filters. I think it’s worth having a closer look into all options of these smooth filters for all those interested in DSP and xover filters. NT filters can be especially useful when encountering drivers - filters characteristics mismatches (in terms of max. SPL, drivers distortion figures, thermal and Vd limits) along with traditional filters like LR4. For most audio uses, the width range between 0.4 … 2.0 might be most relevant. Acourate in it’s most recent implementation generates NT filters with width parameters of any decimal values between 0.25 … 16. My actual speaker project is a 4-way dipole relying on NT filters - what else? I am currently tweaking with width parameter values ranging from 0.6 … 0.9. And I am delighted by the smoothness and acoustic results of these NT filters.
Statement of non-conflicting interests: My primary insterest is to share my delight for NT filters, and maybe to get some evolutive feedback. That’s all. I am a completely independent hobbyist owning a regular licence for Acourate. Although recommending Acourate (AudioVero) to every audio enthousiast and hobbyist, I have absolutely no financial interests to do so.
Neville-Thiele (NT) filters can come in different flavors, and they all have the same, interesting characteristic: Inside the passband, they have a smoothly steepening slope, then run steeper and steeper trough a limited transition area and end up with a final, vertical brickwall cutoff characteristic. Because of this final brickwall cutoff, the term "steepness" does not really apply for NT filters. Nevertheless, like in traditional Bessel, Butterworth and Linkwitz-Riley filters, where the steepness can be defined by a parameter (the “order”, e.g. as LR4 or BES2), NT filters of a given passband allow the variation of the width of the limited transition area by a parameter. This parameter of any suitable decimal value allows to fine tune the filters width to specific needs. A high value for the width results in a narrow limited transition area and vice versa. Like a high order in traditional filters will result in steep filter slopes.
In the following examples, a three way xover with f_-6dB points at 400Hz and 2.5kHz using linear phase NT filters of different widths will be examined. First, the influence of the width parameter is shown using values of 0.4, 0.5, 0.7071, 1 and 2. For the passband filter, these values will result to a total filter width, including the passband and both limited transition areas of 70Hz/14.1kHz, 100/10kHz, 150Hz/6.7kHz, 200Hz/5kHz, 283Hz/3.5kHz.
Fig. 1
An externally hosted image should be here but it was not working when we last tested it.
Fig. 2
An externally hosted image should be here but it was not working when we last tested it.
And how do NT filters compare against traditional filters, like eg LKR4?
NT1.0 vs. LR4:
Fig. 3
An externally hosted image should be here but it was not working when we last tested it.
Fig. 4
An externally hosted image should be here but it was not working when we last tested it.
In the frequency domain, NT1.0 has quite a sharper charactreristic than LR4, it’s behavior in time domain is potentially a bit more critical (pre- and postringing) than LR4
NT0.5 vs. LR4:
Fig. 5
An externally hosted image should be here but it was not working when we last tested it.
Fig. 6
An externally hosted image should be here but it was not working when we last tested it.
NT0.5 has a broader charactreristic in frequency domain than LR4, it’s behavior in time domain is a bit tamer than LR4’s.
NT0.7 vs. LR4:
Fig. 5
An externally hosted image should be here but it was not working when we last tested it.
Fig. 6
An externally hosted image should be here but it was not working when we last tested it.
In frequency domain, NT0.7 initially more or less follows the characteristic of LR4 inside the passband and further to approx. -22dB. Beyond this level, NT0.7 gently dives into the brickwall cutoff characteristic. In time domain it’s behavior seems much the same as for the LR4 filter.
The time domain shows much the same, but or course not exactly the same:
Fig. 7
An externally hosted image should be here but it was not working when we last tested it.
NT0.7 shows some “bumps” at a level of 0.000025, whereas LR4 remains more or less at level 0. Given the main impulse value of the filters peaking at 0.887, this results in a corrected value of
28.2 E-6 for the adddtional pre- and postimpulse oscillations of the NT0.7 filter compared to the LR4 filter… Guess if anyone would be able to hear the effects of the resulting ringing that may result under worst-case conditions. So there is not exactly a lunch for free. But quite a huge one in frequency domain for quite a small price in time domain:
Fig. 8
An externally hosted image should be here but it was not working when we last tested it.
Second set of examples: Bessel2 vs. NT0.4
NT0.4 vs. BES2:
Fig. 9
An externally hosted image should be here but it was not working when we last tested it.
Fig. 10
An externally hosted image should be here but it was not working when we last tested it.
Fig. 11
An externally hosted image should be here but it was not working when we last tested it.
Fig. 12
An externally hosted image should be here but it was not working when we last tested it.
BES2 is not widely used, because of it’s demanding broadband’s requirements to the driver. With nearly the same characteristics in the passband, NT04 provides some headroom beyond the approx. -22dB threshold.
Example of a minimum width brickwall NT16 filter (width parameter=16.0)
Fig. 13
An externally hosted image should be here but it was not working when we last tested it.
Fig. 14
An externally hosted image should be here but it was not working when we last tested it.
Nobody will generate such a filter for regular audio use...
This might be a brief insight into NT filters. I think it’s worth having a closer look into all options of these smooth filters for all those interested in DSP and xover filters. NT filters can be especially useful when encountering drivers - filters characteristics mismatches (in terms of max. SPL, drivers distortion figures, thermal and Vd limits) along with traditional filters like LR4. For most audio uses, the width range between 0.4 … 2.0 might be most relevant. Acourate in it’s most recent implementation generates NT filters with width parameters of any decimal values between 0.25 … 16. My actual speaker project is a 4-way dipole relying on NT filters - what else? I am currently tweaking with width parameter values ranging from 0.6 … 0.9. And I am delighted by the smoothness and acoustic results of these NT filters.
Statement of non-conflicting interests: My primary insterest is to share my delight for NT filters, and maybe to get some evolutive feedback. That’s all. I am a completely independent hobbyist owning a regular licence for Acourate. Although recommending Acourate (AudioVero) to every audio enthousiast and hobbyist, I have absolutely no financial interests to do so.
Nicely worked out, thanks! 
Did you already try out the new filters in Acourate, developed by Uli?
These are LTA (limited transition area) filters too, like Neville Thiele.
But as Uli states, they avoid some disadvantages of the NT filters. They are smoother and like Uli says the time response with respect to ringing is improved.
Best regards
Matthias
Did you already try out the new filters in Acourate, developed by Uli?
These are LTA (limited transition area) filters too, like Neville Thiele.
But as Uli states, they avoid some disadvantages of the NT filters. They are smoother and like Uli says the time response with respect to ringing is improved.
Best regards
Matthias
Yes, these LTA filters is very good and hot news:
These new jUB's (jerkless Uli Brüggemann's) filters as an unprecedented LTA filters class are indeed exciting and allow unlimited possibilities to tailor the filters behavior to the drivers characteristics. My actual dipole project is based on jUB jPol7 0.6 filters approaching a LR4 characteristic in the passband, but cutting steeply like brickwall filters in the outer TA. Early prototypes sound very smooth.
There is a discussion about these jUB filters (in german) going on here:
aktives-hoeren.de • Thema anzeigen - Eine neue Klasse von Frequenzweichen
Jerkless regards from a now jerkless filters world!
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