Michel,
> I've designed an bandpass IIR filter of order 8, composed with 4 Biquad
> filters. Now when I try to plot the frequency response of the filter
> with Ptolemy, I get wrong results
One rule of thumb is to put the biquad filters in ascending order
of their quality factors.
Each biquad will two conjugate poles, a +/- j b. A quality factor
can be defined as
sqrt(a^2 + b^2)
Q = ---------------
- 2 a
assuming that a < 0 for stability. Note that Q >= 1/2. A value of
1/2 corresponds to a real pole. Infinite Q corresponds to an imaginary
pole (pure oscillator). The higher the quality factor, the more likely
it is to oscillate. So, by putting the Biquads with lower Q values
first, the output is dampened before other sections process it.
Eighth-order elliptic filters designed by conventional formulas
(e.g. Matlab) have artificially high quality factors (three times
what they need to be). This is because the conventional formulas
pick one possible solution from an infinite collection of possible
solutions. Unfortunately, they pick one with very high quality
factors.
We have worked extensively on the topic of optimizing filter designs
for implementation. We have developed closed-form algebraic
solutions for minimizing the maximum Q factor for analog and digital
IIR filters, including IIR filters with dyadic coefficients. We
have also developed numerical optimization frameworks for multicriteria
filter design. We have used the numeric frameworks to optimize
phase response, step response, and quality factors simultaneously.
Both frameworks are available on the Web:
numeric (analog IIR filters only)
http://www.ece.utexas.edu/~bevans/projects/syn_filter_software.html
symbolic
http://galeb.etf.bg.ac.yu/~lutovac/afdhome.htm
Regards,
Brian
--
Prof. Brian L. Evans, Dept. of ECE Voice: (512) 232-1457
Engineering Science Building Fax: (512) 471-5907
The University of Texas at Austin E-mail: [EMAIL PROTECTED]
Austin, TX 78712-1084 USA Web: http://www.ece.utexas.edu/~bevans
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