A faster algorithm for the calculation of the fast spectral correlation

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 αmax at approximately the value chosen for the spectral frequency axis resolution Δf. 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 αmax and spectral frequency axis resolution Δf, 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.