Next Simplest Case: Length 3 FIR Loop Filter

$$\zbox{H_l(z) = b_0 + b_1 z^{-1}+ b_2 z^{-2}}$$

• Linear phase $\Rightarrow b_0=b_2$ ( $\Rightarrow$ delay = 1 sample)
• Unity dc gain $\Rightarrow b_0+b_1+b_2 = 2b_0+b_1 = 1$ $\Rightarrow$
  $$H_l(e^{j\omega T}) = e^{-j\omega T}\left[(1-2b_0) + 2b_0 \cos(\omega T)\right]$$

• Remaining degree of freedom = damping control