Some New Developments on the Al-Alaoui and the Pei and Hsu s-to-z Transforms

This brief refocuses on three classes of s-to-z transforms. For each class, a closed-form expression is proposed, and a particular element, having an imaginary part of its frequency response very close to the ideal value, is presented. These s-to-z transforms are then related to all-pass infinite-impulse-response fractional delay filters, allowing another way to choose their degree of freedom.