Real-time modulated IIR filter
okay, using the snipping tool, i tried to put in just the 2nd-order IIR lattice in the following drawing.  $x[n]$ is being input in the upper left.  the numbering for the $v_*$ coefficients is horrible, but i just cut this drawing out from somewhere else.



now the transfer function i get for this is

$$ H(z) = \frac{Y(z)}{X(z)} = \frac{v_4 + v_3(-k_1 + z^{-1}) + v_2\big(-k_2+k_1(k_2-1)z^{-1} + z^{-2}\big)}{1 + k_1(k_2-1) z^{-1} - k_2 z^{-2}}$$

and if you compare that to the standard direct form

$$ H(z) = \frac{b_0 + b_1 z^{-1} + b_2 z^{-2}}{1 + a_1 z^{-1} + a_2 z^{-2}} $$

you should have equivalence when

$$\begin{align}
k_2 &amp;= -a_2 \\
k_1 &amp;= -\frac{a_1}{a_2+1} \\
\\
v_2 &amp;= b_2 \\
v_3 &amp;= b_1 - a_1 b_2 \\
v_4 &amp;= b_0 - \frac{a_1}{a_2+1} b_1 + \left( \frac{a_1^2}{a_2+1} - a_2 \right)b_2 \\
\end{align}$$

i would appreciate it if someone else would check my work.  i could well have fucked up a sign or something.

so, wherever you get your five Direct Form $a_k$ and $b_k$ coefficients (e.g., the Cookbook, but remember to divide everything by $a_0$), you can convert them to the five Lattice Form coefficients with the above equations (assuming i didn't mess it up).