It is known that, if an equilibrium of a nonlinear system has a stability property when an external input is frozen, then the property is maintained under the input being slowly varying. In this paper, we show that the same stability property is preserved not only under slowly varying input but also under slowlyvarying-average input (which is not actually slowly varying but its ‘average’ is slo...

The Empirical Mode Decomposition (EMD) is a popular algorithm used for the processing of non-linear and non-stationary signals. In this paper we implemented the EMD algorithm and study the use of EMD in broad range of applications for extracting data from the signals. It decomposes the signal into highly varying Intrinsic Mode Functions (IMF) and slowly varying residues. Finally the results are...

We assume that the sequence ck, k ≥ 0, is regularly varying with index −β, β ∈ (1/2, 1) (written as ck ∈ RV−β). This means that ck ∼ k L0(k) as k → ∞, where L0 is slowly varying at infinity (see e.g. [2, Sections 1.4, 1.5] for the definition of slowly varying functions). We shall refer to all such models as long range dependent (LRD) linear processes. In particular, by the Karamata Theorem, the...