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As mentioned in the comments, you have to choose a frequency $\omega_0$ at which you want to normalize the gain. This could be DC (i.e., $\omega_0=0$) or any other frequency, depending on the filter's characteristic. You have two filters in series, each with transfer function $$H_i(z)=\frac{1}{1-a_iz^{-1}+b_iz^{-2}},\qquad i=1,2\tag{1}$$ The total ...


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You can't implement the transfer function H(z) directly, you need to convert it to a difference equation. However, the process is trivial, so once you understand it you'll see the connection between the diagram and transfer function better. First, we need to unroll the summation. For example, we get this with m=2, for a second-order equation: $H(z) = \...


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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 ...


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