Linkwitz-Riley bandpass filter design

Hi Everyone,

I have read a lot about the good phase response of the Linkwitz-Riley
filter and would like to design a 3 band equalizer using it. I will
primarily be coding in C++. Most of the Linkwitz-Riley design guides that
I have found online help one to design for analog circuitry. 

Could anyone could point me towards material that would help me to
translate my 3 band eq from cut-off frequencies to code or an H(z)
equivalent that I that can then implement using a Direct Form structure.

Thanks.  

carleeto wrote:
> Hi Everyone,
> 
> I have read a lot about the good phase response of the Linkwitz-Riley
> filter and would like to design a 3 band equalizer using it. I will
> primarily be coding in C++. Most of the Linkwitz-Riley design guides that
> I have found online help one to design for analog circuitry. 
> 
> Could anyone could point me towards material that would help me to
> translate my 3 band eq from cut-off frequencies to code or an H(z)
> equivalent that I that can then implement using a Direct Form structure.

A Linkwitz-Riley crossover is an analog filter whose phase response can 
be only approximated by a digital model, and the approximation is likely 
to be poor unless the sampling frequency is up around 80 KHz or more.

The phase response of a crossover is a critical property and needs to 
work with proper speaker placement. Maybe the aberrations cause by a 
digital implementation can be corrected by a novel speaker arrangement.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

carleeto wrote:

> Hi Everyone,
> 
> I have read a lot about the good phase response of the Linkwitz-Riley
> filter and would like to design a 3 band equalizer using it.

????
LR as equalizer does not make sense.

LR is a hipass/lopass crossover arrangement made of four Butterworth 
stages (two as lowpass, another two as highpass). There is nothing 
particularly good about the phase response. The feature of LR is that 
the sum of the highpass and the lowpass channels makes for the perfect 
allpass; although it is largely unimportant in practice.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Jerry Avins wrote:
> carleeto wrote:
>> Hi Everyone,
>>
>> I have read a lot about the good phase response of the Linkwitz-Riley
>> filter and would like to design a 3 band equalizer using it. I will
>> primarily be coding in C++. Most of the Linkwitz-Riley design guides that
>> I have found online help one to design for analog circuitry.
>> Could anyone could point me towards material that would help me to
>> translate my 3 band eq from cut-off frequencies to code or an H(z)
>> equivalent that I that can then implement using a Direct Form structure.
> 
> A Linkwitz-Riley crossover is an analog filter whose phase response can 
> be only approximated by a digital model, and the approximation is likely 
> to be poor unless the sampling frequency is up around 80 KHz or more.
> 
> The phase response of a crossover is a critical property and needs to 
> work with proper speaker placement. Maybe the aberrations cause by a 
> digital implementation can be corrected by a novel speaker arrangement.

There is an excellent discussion of Linkwitz-Riley crossovers at 
http://www.rane.com/note160.html which explains, among other things, 
what is so nice about my Tannoy coaxial speakers.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

On Feb 18, 12:29&#4294967295;pm, Jerry Avins <j...@ieee.org> wrote:

> A Linkwitz-Riley crossover is an analog filter whose phase response can
> be only approximated by a digital model, and the approximation is likely
> to be poor unless the sampling frequency is up around 80 KHz or more.

Entirely true for the actual phase vs. frequency values.  However, an
important aspect of the phase response of a Linkwitz-Riley pair is
that the lowpass response and the highpass response are in-phase at
all frequencies.  I believe that THIS attribute is preserved by the
Bilinear Transform.

Proper implementation of a 3-(or more)-way Linkwitz-Riley crossover
requires additional allpass sections.  See "Active Realization of
Multiway All-Pass Crossover Systems" by Joseph A.D'Appolito; Journal
of the Audio Engineering Society, Volume 35, Number 4, April 1987.

Greg

>A Linkwitz-Riley crossover is an analog filter whose phase response can 
>be only approximated by a digital model, and the approximation is likely

>to be poor unless the sampling frequency is up around 80 KHz or more.

Could you please explain further? 

 

>>A Linkwitz-Riley crossover is an analog filter whose phase response can 
>>be only approximated by a digital model, and the approximation is
likely
>>to be poor unless the sampling frequency is up around 80 KHz or more.

I guess what I'm looking for is to design an equalizer that gracefully
transitions from an all-pass (EQ set to not do anything) to something
where the response is controller by the EQ parameters and I was under the
impression that an EQ based on LR filters would be the best one for the
job. Is there something better I could use? 

Thanks.

Vladimir Vassilevsky wrote:
> 
> 
> carleeto wrote:
> 
>> Hi Everyone,
>>
>> I have read a lot about the good phase response of the Linkwitz-Riley
>> filter and would like to design a 3 band equalizer using it.
> 
> ????
> LR as equalizer does not make sense.
> 
> LR is a hipass/lopass crossover arrangement made of four Butterworth 
> stages (two as lowpass, another two as highpass). There is nothing 
> particularly good about the phase response. The feature of LR is that 
> the sum of the highpass and the lowpass channels makes for the perfect 
> allpass; although it is largely unimportant in practice.

You know, Vlad, you are the only one who picked up on carleeto's 
fundamental misconception. The rest of read "Linkwitz-Riley" and just 
assumed he _meant_ crossover. Good catch!

The important fearure od LR crossovers is that there is no cancellation 
of frequencies in the crossover region anywhere in a typical auditorium. 
Although a LY is allpass for voltage, it has a 3 dB power dip, which I 
think is more important -- as a defect -- in a typical living room.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:

> Vladimir Vassilevsky wrote:
>> carleeto wrote:
>>
>>> I have read a lot about the good phase response of the Linkwitz-Riley
>>> filter and would like to design a 3 band equalizer using it.
>>
>>
>> ????
>> LR as equalizer does not make sense.
>>
>> LR is a hipass/lopass crossover arrangement made of four Butterworth 
>> stages (two as lowpass, another two as highpass). There is nothing 
>> particularly good about the phase response. The feature of LR is that 
>> the sum of the highpass and the lowpass channels makes for the perfect 
>> allpass; although it is largely unimportant in practice.
> 
> 
> You know, Vlad, you are the only one who picked up on carleeto's 
> fundamental misconception. The rest of read "Linkwitz-Riley" and just 
> assumed he _meant_ crossover. Good catch!

Actually, Greg made a good point about the in-phase addition of the 
different bands. If the equalizer is made as the parallel combination of 
the bandpass filters, the LR-like arrangement avoids the possible dips 
in the areas of overlap.

> The important fearure od LR crossovers is that there is no cancellation 
> of frequencies in the crossover region anywhere in a typical auditorium. 
> Although a LY is allpass for voltage, it has a 3 dB power dip,

Yes! Although it took me a minute to figure out why :)

> which I 
> think is more important -- as a defect -- in a typical living room.

I'd say the crossover filter response is not very important. The 
arrangement and the response of the speakers and the acoustics of the 
room have much higher influence. As for the crossover, Bessel, 
Butterworth, LR or any other kind of filter with the slope of ~24dB/oct 
will do about equally as good.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Mon, 18 Feb 2008 16:35:31 -0600, Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote:

>> You know, Vlad, you are the only one who picked up on carleeto's 
>> fundamental misconception. The rest of read "Linkwitz-Riley" and just 
>> assumed he _meant_ crossover. Good catch!

I have actually designed multiband dynamics processors using crossover topologies.  Extension of the concept to EQ was not
difficult.  I figured the OP wanted something akin to the Bass/Presence/Treble controls on old-time preamplifiers.

>> The important fearure od LR crossovers is that there is no cancellation 
>> of frequencies in the crossover region anywhere in a typical auditorium. 
>> Although a LY is allpass for voltage, it has a 3 dB power dip,
>
>Yes! Although it took me a minute to figure out why :)

I had never thought of it that way before, Jerry.  For those who haven't figured out why:

Power output from lowpass section (limiting case; assume highpass output = 0):  
V&#4294967295;/R.

Power output from highpass section (limiting case; assume lowpass output = 0):  
V&#4294967295;/R.

Combined power output at crossover, LP and HP section each receiving V/2:  
(V/2)&#4294967295;/R + (V/2)&#4294967295;/R = V&#4294967295;/4R + V&#4294967295;/4R = V&#4294967295;/2R.

>I'd say the crossover filter response is not very important. The 
>arrangement and the response of the speakers and the acoustics of the 
>room have much higher influence. As for the crossover, Bessel, 
>Butterworth, LR or any other kind of filter with the slope of ~24dB/oct 
>will do about equally as good.

In the living room the differences are not nearly as important as they are in the auditorium, where phase differences between LP
and HP sections lead to very audible lobing problems.

Greg