Properties of the Weierstrass function in the time and frequency domains

The Weierstrass function is continuous everywhere and differentiable nowhere. It is used advantageously for modeling fractally coarse media. The frequency domain expression is analyzed using the Laplace transform of a truncated Weierstrass function. The poles of this function constitute a geometric sequence on the imaginary axis of the complex frequency plane. Computer calculations show that the zeros change little as the order is increased. Theoretical development reveals the nature of the dependence of the zeros on order and the parameters of the function. The effect of the scale of observation on the functionʹs properties is examined in both time and frequency domains.