A Fast Method of Transforming Relaxation Functions Into the Frequency Domain

National Institute of Standards and Technology, Gaithersburg, MD 20899-0001 The limits to the error due to truncation of the numeric integration of the one-sided Laplace transform of a relaxation function in the time domain into its equivalent frequency domain are established. Separate results are given for large and small v . These results show that, for a given v , only a restricted range of time samples is needed to perform the computation to a given accuracy. These results are then combined with a known error estimate for integration by cubic splines to give a good estimate for the number of points needed to perform the computation to a given accuracy. For a given data window between t1 and t2, the computation time is shown to be proportional to ln(t1/t2).