Simplest Frequency-Dependent Loop Filter

$$\zbox{H_l(z) = b_0 + b_1z^{-1}}$$

• Linear phase $\Rightarrow b_0=b_1$ ( $\Rightarrow$ delay = 1/2 sample)
• Zero damping at dc $\Rightarrow b_0+b_1=1$
  $\Rightarrow b_0 = b_1 = 1/2$
  $\Rightarrow$
  $$\zbox{H_l(e^{j\omega T}) = \cos\left({\omega T/ 2}\right),\quad\left\vert\omega\right\vert\leq \pi f_s}$$