The wavelet decomposition is used to generalize the multifractal formalism to singular signals. The singularity spectrum is directly determined from the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima. Illustrations on fractal signals with a recursive structure, e.g., devil’s staircases, are shown. Applications to fully developed turbulence data and Brownian signals are reported.

• Received 15 July 1991

DOI:https://doi.org/10.1103/PhysRevLett.67.3515