Multifractal processing of speech signals

This paper describes a novel framework in processing speech signals using multifractality concepts, and shows that multifractality could be a new fundamental tool for speech processing. New approaches using the self-similarity model of complexity have been developed to simplify processing of complicated speech signals. The approaches associate signals with fractal sets and then characterize the sets using real numbers called fractal dimensions. This paper extends the approaches by associating speech signals with measures and then characterizing the measures with multifractal curves such as Mandelbrot dimensions (denoted as f(α)) or Renyi dimensions D_q. Such curves (also known as singularity curves) are the characterization of speech signals. This paper shows that multifractal (or singularity) processing of speech is capable of providing important processing aspects: decomposition, representation, and spectrum characterization-a capability that makes Fourier processing of signals is fundamental. The multifractal approach can decompose speech into various segments based on variations of the segment´s Holder exponents. The results can be used for new speech segmentation schemes. The multifractal approach is also used in characterizing speech through singularity spectrum. This can be used to develop better accuracy speech recognition schemes. Finally, the paper describes a process to reconstruct speech signals from their singularity representation, by the means of the so-called wavelet maxima