Spectral analysis of the Weierstrass-Mandelbrot function

In this paper, the Weierstrass-Mandelbrot function on the Cantor set is presented, with an emphasis on possible applications in science and engineering. The one-sided Fourier transform of the Weierstrass-Mandelbrot function is computed and an asymptotic estimation, in accordance with the simulation results, is analytically derived. Additionally, a time-frequency analysis of the Weierstrass-Mandelbrot function is provided by the numerical computation of both continuous wavelet transform and wavelet scalogram.