Advanced Z-transform

Summary

The advanced Z-transform is a variant of the Z-transform of sampled signals. It samples a continuous-time signal at the instants $kT + m$, shifted by a part $m$ of the sampling period $T$. It is $F(z, m) = \sum_{k \ge 0} f(kT + m) z^{-k}$, with $0 \le m \le T$. It lets one describe delays that are not whole multiples of the sampling period, and the behaviour of a sampled system between sampling instants. For fixed $m$ it has the usual properties of the Z-transform.