ESDU 86037 introduces the representation of a continuous signal by a sequence of equally spaced pulses each of which provides the value of the continuous signal at the particular sampling instant. The relationship of such a sequence to the Z-transform is established, and properties of the transform are given. The Z-transform is related to the Laplace transform and the relationships between poles and zeros in the complex s-plane to those in the complex z-plane are provided. Using the Z-transform the relationship between the sampled input and output of a system element, the pulse transfer function, is found and the method of combining such functions for individual elements to obtain a pulse transfer function for certain complete systems of cascaded elements in open or closed loop form is illustrated. The delayed Z-transform and multirate sampling, which allow signal information to be obtained between sampling instants, are described. The use of the data hold filter for reconstitution of the continuous signal is explained, and methods of obtaining the original sampled signal by inverting the Z-transform are given and illustrated.