Direct form 2 iir filter

I am trying to write a code for implementing a direct form 2 based iir filter (without using the filter command), the problem is that i am confused about the intermediate variable (let's call it "w"), isn't "w" just a delayed version of x (x being the input signal), if not, could you help clarify the doubt of how to fill up the intermediate variable i.e "w".

These are the two equations i use to implement the IIR filter in direct form 2, where "b" and "a" represent the filter coeffecients pertaining to the numerator and the denominator of the transfer function.

i went through your function file as well, it works just fine, but i am having a hard time understanding the role of "w(n)".

[Jan]

If I guess, that your a is defined such, that a(0) is set to 1, your w is the vector of the last M+1 elements of the input scaled by a.

It might get clear, if you write down the equations for a specific |M| and a, b. Then the equivalence between these two equations and the Direct Form II approach in my code gets visible. See this form also:

           N                   M
 y(n) = - SUM a(k+1) y(n-k) + SUM b(k+1) x(n-k)  for 1<=n<=length(x)
          k=1                 k=0

Answer 1

[Jan]

See https://www.mathworks.com/matlabcentral/answers/9900-use-filter-constants-to-hard-code-filter#answer_13623 for a Matlab function, which calculates the same as filter().

All you have mentioned yet is the name of the "intermediate" variable "w", but without seeing the definition you use or the code, we cannot guess, what it is.