# How to find the normalized coefficients?

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:

The normalized version of the difference equation is:

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

Is the actual result in this form:

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

The gain plays any special role?

• – Peter K. Apr 20 '13 at 16:02
• Oh, I see, you're taking it directly from the manual. I think that in the first sos array $b_{01} = bc_{1}$. – Peter K. Apr 20 '13 at 16:42

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 $b$.
• Yes, otherwise you would scale the whole filter by $g^2$ instead of by $g$. – Matt L. Apr 20 '13 at 20:17