First- and second-order cyclostationary signal separation using morphological component analysis

A new algorithm is proposed to decompose a cyclostationary (CS) signal into its periodic and random sources within the MCA framework.This MCACS2 algorithm is composed of two dictionaries; each specialized in sparsifying and representing a CS component.The first-order CS component can be represented by means of the DCT basis.The second-order CS component is represented by means of a new proposed dictionary based on the envelope spectrum analysis.The algorithm was applied to simulated signals as well as to real biomechanical signals. Cyclostationarity (CS) has proven to be effective in the treatment and identification of signal components for diagnostic and prognosis purposes. CS research has focused on algorithms, in terms of simplicity and computational efficiency. The performance of algorithms largely depends on the signals being analyzed.The objective of this research paper is to exploit the CS characteristics of signals in the context of morphological component analysis (MCA) method. It proposes a novel methodology used for separating between the periodic (First-Order Cyclostationarity: CS1) and random (Second-Order Cyclostationarity: CS2) sources by means of one sensor measurement. This MCACS2 methodology is based on MCA, where each of the two sources is sparsely represented by a special dictionary: i) the CS1 periodic structure is sparsely represented by means of the Discrete Cosine Transform dictionary, and ii) the CS2 random component is sparsely represented by a new proposed dictionary derived from Envelope Spectrum Analysis. Subsequently, a simulation study is performed in order to validate the proposed new MCACS2 method followed by tests on real GRF biomechanical signals. The result concludes by stating that such a novel algorithm provides an additional way for the exploitation of cyclostationarity and may be useful in other domain applications.