Time-Domain Approximation by Iterative Methods

An iterative procedure is presented which permits the determination of a rational transfer function in the Laplace transform variable s which is optimal with respect to given input and output time-functions. The optimal system of a particular order is defined as the one whose output when subjected to the known input function is nearest in the time integral square sense to the desired output function. The method is thus applicable to a number of problems involving the minimization of an integral square error. To illustrate the technique, a set of optimal lumped-parameter delay lines is synthesized and their characteristics investigated; the behavior and convergence of the iteration in these problems is also studied. A comparison of other iterative methods applicable to the same problems leads to the conclusion that the proposed procedure has real advantages in computational simplicity and speed of convergence.