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?
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.