Filter Designer coefficiants of IIR Filter

Hello,

I have a question regarding the computed coefficients of an IIR filter by the Filter Designer. My question relates to the Direct Form II structure. I have added the picture of a designed filter

The designed filter is a 6th order filter which is structured into three 2nd order filters of the direct Form II. So let's focus on the first section: I can see three numerator coefficiants and three denominator coefficiants, in addition to a gain factor.

I will add another picture of the Direct Form II structure. There we can see, that for a second order filter in direct Form II, we have three numerator coefficiants and three denominator coefficiants, whereas a_0 = 1. But Where do I put the additional gain factor? Is the Input x(k) multiplied with it?

[Alexander Letzel]

If the question remains unclear, please let me know

Answer 1

[Dinesh Yadav]

The additional gain factor is multiplied at input of each stage. That is, the input is multiplied by 1st section’s gain factor, then output of first section of 2nd order filter is multiplied by 2nd section’s gain factor, then output of second section of 2nd order filter is multiplied by 3rd section’s filter gain and finally output of third section 2nd order filter is multiplied by output gain.

I am attaching the documentation link below. In the left side panel in documentation go to Parameters-> scale values for visual clarity.

https://www.mathworks.com/help/dsp/ref/biquadfilter.html#mw_65ca1a69-59ea-43d7-accc-85056b0a6e5b