Fast inverse Laplace transformation of functions containing one multiple pole

The letter introduces useful relations for the evaluation of the coefficients of a partial-fraction expansion. For rational functions containing a single multiple pole, repeated differentiation is replaced by simple arithmetic operations. This scheme greatly simplifies the determination of transient response in the case of one higher-order pole. Its outstanding feature is apparent in the computer-aided design of control systems when the accuracy is improved and the computational time is considerably reduced. Hence the name FILT which stands for fast inverse Laplace transformation.