Is 'Bessel' digital lowpass filter standard?

On 24 Aug, 18:29, "gretzteam" <gretzteam@n_o_s_p_a_m.yahoo.com> wrote:
> >Two reasons:
>
> >1) Overshoot is not a design criterion often used in DSP. Maybe it
> > &#4294967295; is in control theory, that traditionally deals with transients.
> > &#4294967295; In DSP the focus is on frequency domain, not time domain.
>
> >2) In the olden days of analog filters, the Bessel filter was a
> >device
> > &#4294967295; useful to obtain approximately linear phase, but that had poor
> > &#4294967295; magnitude characteristics. In the realm of DSP one can obtain
> > &#4294967295; exact linear phase *and* total control of the magnitude by
> > &#4294967295; using FIRs. In the digital world the Bessel is more or less
> > &#4294967295; obsolete.
>
> >Rune
>
> Interesting!
> However I would say that some applications also care a lot about the time
> domain and transients, even when done in DSP. For example, the filtering of
> ECG signals in medical applications are very sensitive to transients.

Then don't use the DSP techniques for analyzing those signals.

> I guess a FIR filter could do exactly what I want. However, the processing
> power required would be huge.

No, it wouldn't. FIRs are standard DSP tools.

> The ratio of sampling rate to cutoff
> frequency is large in some mode of operation. This has to be small/low
> power.
>
> I'm not so sure that some Bessel-type approximation are really obsolete. So
> far it's giving me the best trade-off of processing power, overshoot and
> magnitude response.

It seems you have set your mind on the Bessel. If so, start
digging in the ancient references.

Rune

gretzteam wrote:


> I'm not so sure that some Bessel-type approximation are really obsolete. So
> far it's giving me the best trade-off of processing power, overshoot and
> magnitude response.

There is a common misconception that overshoot and linear phase are 
related. They actually aren't. If you need a filter with a given amount 
of overshoot, you should design a filter to a given amount of overshoot.

VLV

On 08/24/2010 09:29 AM, gretzteam wrote:
>> Two reasons:
>>
>> 1) Overshoot is not a design criterion often used in DSP. Maybe it
>>    is in control theory, that traditionally deals with transients.
>>    In DSP the focus is on frequency domain, not time domain.
>>
>> 2) In the olden days of analog filters, the Bessel filter was a
>> device
>>    useful to obtain approximately linear phase, but that had poor
>>    magnitude characteristics. In the realm of DSP one can obtain
>>    exact linear phase *and* total control of the magnitude by
>>    using FIRs. In the digital world the Bessel is more or less
>>    obsolete.
>>
>> Rune
>>
>
> Interesting!
> However I would say that some applications also care a lot about the time
> domain and transients, even when done in DSP. For example, the filtering of
> ECG signals in medical applications are very sensitive to transients.
>
> I guess a FIR filter could do exactly what I want. However, the processing
> power required would be huge. The ratio of sampling rate to cutoff
> frequency is large in some mode of operation. This has to be small/low
> power.
>
> I'm not so sure that some Bessel-type approximation are really obsolete. So
> far it's giving me the best trade-off of processing power, overshoot and
> magnitude response.

I think that part of the reason that the world came up with "named" 
filters like the Bessel and the Tshebyschev is because the chief 
advantage of all the "named" filters is that they are easy to calculate 
for the continuous-time case and they are often good enough 
approximations to what you really want to get the job done.

That was great from 1950 to 1970 or 1980, when the tools you had at your 
disposal were books with tables, and a slide rule or a hand-held 
calculator.  It was particularly good when you were going to implement 
the filter with a pile of resistors, caps, amplifiers and maybe some coils.

But the filters often weren't the _best_ fit to what you really needed 
-- if you were lucky they were good enough, and didn't require six 
months of tweaking in the lab to get them working.  Furthermore, when 
you take one of those filters as a continuous-time prototype and 
translate it to the digital world you lose some of the special qualities 
that makes the filter desirable.

On the other hand, with todays computers, if you have nimble fingers and 
a copy of Matlab, Octave or Scilab you can specify what you _really_ 
want out of a filter and turn your math package loose on finding an 
optimal solution for you.  There aren't any nice closed-form solutions, 
and you can't name the filter (unless you want to name it after 
yourself), but you may well get something that's a lot better for your 
purposes than some digital approximation to a named filter.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

On 08/24/2010 09:39 AM, Vladimir Vassilevsky wrote:
>
>
> gretzteam wrote:
>
>
>> I'm not so sure that some Bessel-type approximation are really
>> obsolete. So
>> far it's giving me the best trade-off of processing power, overshoot and
>> magnitude response.
>
> There is a common misconception that overshoot and linear phase are
> related. They actually aren't. If you need a filter with a given amount
> of overshoot, you should design a filter to a given amount of overshoot.

Think of a brick-wall (in frequency) filter as a good counter-example.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott wrote:
> On 08/24/2010 09:39 AM, Vladimir Vassilevsky wrote:

>> There is a common misconception that overshoot and linear phase are
>> related. They actually aren't. If you need a filter with a given amount
>> of overshoot, you should design a filter to a given amount of overshoot.
> 
> 
> Think of a brick-wall (in frequency) filter as a good counter-example.

I can make a filter as close to a brick wall as required without any 
overshoot or ringing. It could be done with linear or nonlinear phase; 
there is no connection.

VLV

>> I guess a FIR filter could do exactly what I want. However, the
processin=
>g
>> power required would be huge.
>
>No, it wouldn't. FIRs are standard DSP tools.

Of course they are standard DSP tools. But whether you can use it or not
really depends on what world you live in. If you're used to do DSP with a
700MHz Sharc DSP, yeah you can do what you want. If you're implementing
this directly in hardware where every gate counts (yes this world still
exists), then you have to try something else. 

I'm now trying to find a good-enough solution, that solves the problem. I
don't know what is wrong with that. Bessel gets me pretty much there, and I
wonder if there could potentially be better. FIR isn't.

Dave

> I believe the input to the system
> will contain squarish wave and an overshoot/ringing is not tolerable.

Bessel has traditionally been used in analog filters in
similar applications, typical for communications.
A digital IIR based on an analog filter
catalogues will be possible, but probably not ideal
for order >3.
There are variations on Bessel:
AN56 "Better than Bessel" Linear Phase Filters for Data Communications
http://cds.linear.com/docs/Application%20Note/an56.pdf

A digital linear phase filter would typical be a FIR.

If the job is to remove spikes a median filter works well
preserving squarewaves.

MfG   JRD

>> I believe the input to the system
>> will contain squarish wave and an overshoot/ringing is not tolerable.
>
>Bessel has traditionally been used in analog filters in
>similar applications, typical for communications.
>A digital IIR based on an analog filter
>catalogues will be possible, but probably not ideal
>for order >3.
>There are variations on Bessel:
>AN56 "Better than Bessel" Linear Phase Filters for Data Communications
>http://cds.linear.com/docs/Application%20Note/an56.pdf
>
>A digital linear phase filter would typical be a FIR.
>
>If the job is to remove spikes a median filter works well
>preserving squarewaves.
>
>MfG   JRD
>

Thanks for this. I'm actually not too concerned about phase response (and
I'm not association linear phase with overshoot either). The 'good' thing
about this Bessel approximation is that it has low overshoot and somewhat
linear phase so I'll take it.

Maybe this Bessel approximation is a 'named' filter that come close to a
un-named fully optimized filter for my application. If it's the case I'll
take it and move on...

thanks!
Dave

On Aug 24, 1:33&#4294967295;pm, "gretzteam" <gretzteam@n_o_s_p_a_m.yahoo.com>
wrote:
> >> I believe the input to the system
> >> will contain squarish wave and an overshoot/ringing is not tolerable.
>
> >Bessel has traditionally been used in analog filters in
> >similar applications, typical for communications.
> >A digital IIR based on an analog filter
> >catalogues will be possible, but probably not ideal
> >for order >3.
> >There are variations on Bessel:
> >AN56 "Better than Bessel" Linear Phase Filters for Data Communications
> >http://cds.linear.com/docs/Application%20Note/an56.pdf
>
> >A digital linear phase filter would typical be a FIR.
>
> >If the job is to remove spikes a median filter works well
> >preserving squarewaves.
>
> >MfG &#4294967295; JRD
>
> Thanks for this. I'm actually not too concerned about phase response (and
> I'm not association linear phase with overshoot either). The 'good' thing
> about this Bessel approximation is that it has low overshoot and somewhat
> linear phase so I'll take it.
>
> Maybe this Bessel approximation is a 'named' filter that come close to a
> un-named fully optimized filter for my application. If it's the case I'll
> take it and move on...
>
> thanks!
> Dave- Hide quoted text -
>
> - Show quoted text -

Hello Dave,

The Butterworth filter arises from maximizing the number of
derivatives in the magnitude response being equal to zero at DC and
the Bessel filter arises from maximizing the number of terms that
yield linear phase at DC. It is called a Bessel filter since the coefs
for the s form of the transfer equation result from Bessel polynomials
which may be derived from Bessel functions.  It could be that the
Bessel filter is good enough for your application. If need be, just
increase the filter order to get the overshoot under control. The
magnitude response of Bessel filters (also called Thompson filters) is
described by some as sort of "droopy." So you don't see them often,
but I do know of some protocols where they are speced in. For example,
Flex and ERMES specify 10th order Bessel filters for intersymbol
interference rejection! Probably not the best answer by the protocol
committee but it was its simplicity to specify as opposed to some
optimized numerical result that made it get speced that way.

Clay

Clay wrote:



> It could be that the
> Bessel filter is good enough for your application. If need be, just
> increase the filter order to get the overshoot under control.

The Bessel filters of the higher orders have higher overshoot.

> The
> magnitude response of Bessel filters (also called Thompson filters)

IIRC the Thompson filter is some kind of compromise between Butterworth 
and Bessel responses.

> is
> described by some as sort of "droopy." So you don't see them often,
> but I do know of some protocols where they are speced in. For example,
> Flex and ERMES specify 10th order Bessel filters

9th order, Fc = 3.9kHz. Just advised as an example, not prescribed.

> for intersymbol interference rejection!

for adjacent channel spillage reduction.

> Probably not the best answer by the protocol
> committee but it was its simplicity to specify as opposed to some
> optimized numerical result that made it get speced that way.

I was surprised by such an advice also; actually, I used FIR filter.


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