Higher order Bessel filter

Dear All,

Thank u very much for the help. 

Hi Vladimir, Can u please explain me in little detail how i can proceed
further meanwhile i get the book u suggested. 

I need this higher order bessel filter implementation for the design of
cross over application. I have designed for 24th order Butterworth and
Linkwitz Riley filters but i am stuck up at 24th order Bessel filter
implementation.

Your guidance is very much appreciated.

Gangadhar


>
>
>Tim Wescott wrote:
>
>
>> Now that we have powerful enough computers that exhaustive searches are

>> only exhausting for the electrons involved, I've become a big fan of 
>> dropping a close approximation into a nonlinear optimizer, such as the

>> one in Scilab, and letting it do the heavy lifting. 
>
>I am guilty of that too. Quite often a brute force is the shortest way 
>to a solution, and it also helps better understanding of the problem.
>
>Not too long ago, I managed to find the closed form solution to the 
>system of nonlinear equations which I used to solve numerically. That 
>reduced the computing time from a second to several milliseconds in the 
>practical application. What is more important, the numerical algorithms 
>can go wild on the occasions, and the great care should be taken about
that.
>
>
>  This has served me
>> well for problems in robust control and curve fitting, and I suspect 
>> it'd do fairly well for designing filters to specification.
>
>The high order IIR filter design by optimization is known to be 
>complicated. You have to define a filter in the way the stability is 
>guaranteed and the dependencies are continuous.
>
>   The two big
>> questions you have to answer before you start are "can I gin up an 
>> adequate cost function" and "will my algorithm avoid the local
minima?". 
>>   If the answers to those questions are both "yes", then you can do a 
>> pretty good job.
>
>Those conditions are the strong restrictions of what you can do already;

>besides, there are the ill-behaviors, the numerical problems and the 
>discontinuities.
>
>> Speaking about approximations that don't work, do you know of a good 
>> reference that gives a clean expression for a working notch filter in 
>> the sampled-time domain?
>> The various approximations don't work well, because they move the zeros

>> around and mess up the null.  I know how to do this by direct design, 
>> but the resulting expressions for the numerator coefficients are about

>> as messy as can be -- it's good enough for me, but I'd like something 
>> that I can include in a publication for beginner or intermediate 
>> practitioners, which means that the derivation of the numerator 
>> coefficients should be smaller than the derivation of the propagation
of 
>> electromagnetic radiation from Maxwell's equations.
>
>A basic notch is FIR with 3 taps. This looks like a simple trigonometry 
>problem:
>
>fi = 2 PI Fc/Fs
>A1 cos(fi) + A2 cos(2fi) = -A0
>A1 sin(fi) = A2 sin(2fi) = 0
>
>If I did not make a mistake somewhere:
>
>A2 = A0
>A1 = - 2 A0 cos(fi)
>
>
>Vladimir Vassilevsky
>
>DSP and Mixed Signal Design Consultant
>
>http://www.abvolt.com
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