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I use the below matlab function to design the unquantised coefficient set:

[b,a]=ellip (4,2,60,2*[0.2,0.3]);

and then i use the matlab finction "tf2sos" to convert the direct form coefficients to a set of a factorized second-order sections:

[sos,g]=tf2sos(b,a);

My result is:

enter image description here

The normalized version of the difference equation is:

enter image description here

How i can find the b and the c1,c2,...

Is the actual result in this form:

enter image description here

or factorized means normalized and the result is in this form:

enter image description here

The gain plays any special role?

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  • $\begingroup$ Doesn't the manual tell you? $\endgroup$ – Peter K. Apr 20 '13 at 16:02
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    $\begingroup$ Oh, I see, you're taking it directly from the manual. I think that in the first sos array $b_{01} = bc_{1}$. $\endgroup$ – Peter K. Apr 20 '13 at 16:42
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I'm not sure how you define your normalized difference equation, but in any case you can equate the $b_{ij}$ coefficents in the sos matrix with your $c$ coefficients, and the gain that tf2sos returns would then be your normalization constant $b$.

I think you already know, but just to be clear: every row of the sos matrix contains the coefficients for one second-order section, starting with the 3 numerator coefficients, and then the denominator coefficients (the first of which is always 1). You can incorporate the gain into the first section.

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  • $\begingroup$ You mean that my normalized coefficients are: first line: 0.005 ,0.0087635, 0.005, 0.005, 0.001252,0.0042305 etc for the rest of them? $\endgroup$ – 20317 Apr 20 '13 at 19:43
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    $\begingroup$ No, the gain only applies to the b coefficients (of the first row), the a coefficients remain unchanged. $\endgroup$ – Matt L. Apr 20 '13 at 19:50
  • $\begingroup$ Yes, you are right.Stupid question... This applies only in the first row? In the second the coefficients remains unchanged? $\endgroup$ – 20317 Apr 20 '13 at 20:09
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    $\begingroup$ Yes, otherwise you would scale the whole filter by $g^2$ instead of by $g$. $\endgroup$ – Matt L. Apr 20 '13 at 20:17

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