A faster algorithm for the calculation of the fast spectral correlation. (October 2018) - Borghesani, P.; Antoni, J.
Highlights: The Spectral Correlation is the main target of cyclostationary analysis. The Fast Spectral Correlation (FSC) is the fastest algorithm for its estimation. A faster algorithm for the computation of the FSC is here proposed. The algorithm also has a simpler implementation procedure. Gains of 2–3 orders of magnitude are achieved in terms of computational complexity. Abstract: One of the main aims of second order cyclostationary (CS2) analysis is the estimation of the full spectral correlation, allowing the identification of different CS2 components in a signal and their characterisation in terms of both spectral frequency f and cyclic frequency α . Unfortunately, traditional estimators of the full spectral correlation (e.g. averaged cyclic periodogram) are highly computationally expensive and hence their application has been quite limited. On the other hand, fast envelope-based CS2 indicators (e.g. cyclic modulation spectrum, CMS) are bound by a cyclic-spectral form of the uncertainty principle, which limits the extent of the cyclic frequency axis α max at approximately the value chosen for the spectral frequency axis resolution Δ f . A recent work has however introduced a ground-breaking approach resulting in a fast algorithm for the calculation of the spectral correlation. This approach is based on the calculation of a series of CMS-like quantities, each scanning a different cyclic-frequency band, given a certain spectral frequency resolution. The superposition of all these quantities allows covering a larger α -band breaking the constraint between maximum cyclic frequency α max and spectral frequency axis resolution Δ f, at a limited computational cost. In this paper a new algorithm for the calculation of the same fast spectral correlation is introduced, resulting in a further computational efficiency gain, and a simplification of the computational procedure.