Rational delay functions based on continued-fraction expansion of ex

Rational approximations to the ideal delay function e¿ts (where ¿ is the delay time, and s is the complex frequency) based on the continued fraction expansion (c.f.e.) of ex are studied in both the frequency and the time domains. Comparisons with other approximations show that the new approximations have the least ratios of rise time to delay time for the same order of the function and within certain tolerances of overshoot and undershoot in the step response.