TIME TO FREQUENCY-DOMAIN TRANSFORMS

Recently, Weiss et al, proposed an improved computational method for transforming the stretched exponential function from the time domain to the frequency domain. In this work, we report another simpler and more general transform technique based on Schwarzl's methodology for transforming data from the time domain to the frequency domain. Rather than assume a doubling in the frequency spacing as does Schwarzl, the optimum spacing is determined by non-linear methods. This technique, or extended Schwarzl method, yields results on the stretched exponential that are comparable to the more standard high quality results obtained by Koizumi and Kita as well as Dishon et al. Comparisons show that the real parts of the complex numbers are within a few digits in the sixth decimal place, while the imaginary numbers are within a few digits in the fourth decimal place. One advantage to the method described herein is that it can be used to transform any smoothly decaying (or rising) time function on a personal computer of modest dimensions.