EMD performance comparison: single vs double floating points

Empirical mode decomposition (EMD) is a data-driven method used to decompose data into oscillatory components. This paper examines to what extent the defined algorithm for EMD might be susceptible to data format. Two key issues with EMD are its stability and computational speed. This paper shows that for a given signal there is no significant difference between results obtained with single (binary32) and double (binary64) floating points precision. This implies that there is no benefit in increasing floating point precision when performing EMD on devices optimised for single floating point format, such as graphical processing units (GPUs).

On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.