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On Thu, 15 Dec 2005 02:23:25 GMT, Vladimir Vassilevsky
<a...@hotmail.com> wrote:

>Perhaps we did not quite understand each other.
>
>1. Âuild a biquad HPF with Fc = 20Hz and Fs = 48kHz.
>2. Apply a small signal to the input.
>3. Observe the amount of trash at the output.

20Hz?  I thought that we were talking about 100Hz.

>This is a problem I am talking about. Not much can be done about it 
>unless noise shaping is used or the numeric precision is increased.

The techniques that I mentioned ARE ways to increase numeric precision,
but they don't require construction of traditional double precision
operations.

>> As a simple example,
>> consider that if one of the feedback coefficients is "4.19754",
>
>How could it be?
>For the stability of the biquad it is required that  -2 < A1 < +2,
>  -1 < A2 < +1

Okay, so I pulled a number out of thin air, without really thinking
about the resulting locations of the poles.  It was a poor example of a
good idea.

>The 24dB/oct Xovers are "good enough" for most practical purposes. 

That's a sweeping generalization about something that requires
consideration on a case-by-case basis.  

>It 
>does not really matter if it is FIR or IIR and what is the particular 
>type of the response. The 24dB slope is not going to produce much ripple 
>in the transient anyway.

The transition band slope is only half the problem.  The other half is
the flatness in the passband.  A 4th order Bessel will have essentially
no ringing at all, while a 4th order Chebyshev might ring excessively.

Greg

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Greg Berchin wrote:

>>1. =C2uild a biquad HPF with Fc =3D 20Hz and Fs =3D 48kHz.
>>2. Apply a small signal to the input.
>>3. Observe the amount of trash at the output.
>=20
>=20
> 20Hz?  I thought that we were talking about 100Hz.

I suggested to try lower frequency just to make the artifacts more=20
pronounced. It will be also very noticeable at 100Hz. The 24bit=20
precision at Fs =3D 48kHz without noise shaping allows to build biquads=20
with Fc no lower then about 500Hz. If the Fc is lower the performance is =

  likely to be insufficient for the quality audio.


>>This is a problem I am talking about. Not much can be done about it=20
>>unless noise shaping is used or the numeric precision is increased.
>=20
> The techniques that I mentioned ARE ways to increase numeric precision,=

> but they don't require construction of traditional double precision
> operations.

The problem is that you have to increase the precision significantly. At =

the 100Hz cutoff the loss of precision can be as high as 16 bits. Small=20
tricks can save one or two bits however it is not going to help much.=20
Noise shaping in biquad is good and simple solution.

>>The 24dB/oct Xovers are "good enough" for most practical purposes.=20
> That's a sweeping generalization about something that requires
> consideration on a case-by-case basis. =20

This is the engineering approach and also my observation from the=20
practice. In most cases, steep slopes do not really make noticeable=20
improvement.


>>It=20
>>does not really matter if it is FIR or IIR and what is the particular=20
>>type of the response. The 24dB slope is not going to produce much rippl=
e=20
>>in the transient anyway.
>=20
>=20
> The transition band slope is only half the problem.  The other half is
> the flatness in the passband.  A 4th order Bessel will have essentially=

> no ringing at all, while a 4th order Chebyshev might ring excessively.

The reasonably designed 24dB IIR filter will have relatively mild=20
ringing. High Q stages are very sensitive to the problems with numeric=20
precision and the overflows, therefore I wouldn't recommend Chebyshev.=20
Old good Butterworth will work just fine.


Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

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