Abstract
This paper showes that conventional z transform of time functions is not an extention of one of number sequences, and reformulates z transform pair to such an integral transformation that converts impulse train to power series of z-1.
Applying new z transform to sampled-data systems, it is convenient to make preliminary introduction for a double transformation made from ideal sampling and z transform. The double transformation, named here sz transform, not only corresponds to conventional z transform, but also has the following features.
(1) sz transform can analyse exactly such sampled-data systems in which the input of sampler jumps at sampling instants.
(2) sz transform plays the same role as modified z transform.
