Examples

Half-sample delay:

$${\hat y}\left(n-\frac{1}{2}\right) \;=\;\frac{1}{2} \cdot y(n) + \frac{1}{2}\cdot y(n-1)$$

Quarter-sample delay:

$${\hat y}\left(n-\frac{1}{4}\right) \;=\;\frac{3}{4} \cdot y(n) + \frac{1}{4}\cdot y(n-1)$$