Delta-operator formulated discrete-time approximations of continuous-time systems

Given a continuous-time system, a technique to directly obtain an approximate delta-operator formulated discrete-time system (/spl delta/-system) is presented. For this purpose, the analog of the well known Boxer-Thaler integrators (q-forms) applicable to shift-operator formulated discrete-time systems (q-systems) are derived for /spl delta/-systems. Next, using these /spl delta/-forms, a method to obtain an approximate /spl delta/-system of a given continuous-time system is derived. This algorithm is easily implementable in a computer with little computational burden. It is shown that, as sampling time decreases, the /spl delta/-system thus obtained yields the given continuous-time system further verifying the close equivalence between this formulation and continuous-time systems. Two examples illustrating advantages that may be gained by utilizing these /spl delta/-forms in digitizing analog systems are also included.<
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