Analysis of linear sampled-data systems with finite pulse width: Open loop

An exact method for analysis of sampled-data systems with finite pulse width is presented. The results make it possible to obtain the output of such systems in a closed form, as a continuous function of time, and without recourse to any approximations. (The closed form is that which does not involve summation of series.) The analysis is based on introducing a new transform method, analogous to the z-transform, except that the actual pulse width and pulse shape are considered. This is called the p-transform where p denotes pulse width. Furthermore, by utilizing the modified z-transform, a method for obtaining the inverse Laplace transform of functions involving both ¿Ts and s is developed. This technique has been advantageously applied to evaluate the inverse p-transform in a closed form. (The term ¿modified z-transform¿ was introduced in reference 1.) The limiting cases of the p-transform are investigated. It is concluded that the p-transformation method provides a powerful technique for analysis of sampled-data systems with finite pulse width.