Draw a structure for IIR Filter given H(z) This is the transfer function for the Direct Form 1 of the IIR Filter:



I'm trying to understand the rules to convert $H(z)$ into its corrispondent structure



I've just understood how to draw $H_1(z)$, but i don't understand why $H_2(z)$ is drawed as such in diagram. Can you explain to me ?

ps: can i also implement a FIR filter using Direct Forms 1 and 2 ?
It would help to apply some specificity to the general equation:

$H(z) = \frac{b_0 + b_1z^{-1}+b_2z^{-2}}{1+a_1z^{-1}+a_2z^{-2}}$

Rearrange into a difference equation, skipping the steps for brevity:

$y[n] = b_0x[n] +b_1x[n-1]+b_2x[n-1]-a_1y[n-1]-a_2y[n-2]$

Does the difference equation form show now that the Direct Form structure is derived purely by inspection?