Spectral Correlation of the embolic blood Doppler signal

In a previous study we have shown that take into account the quasi-cyclostationary properties of the blood Doppler signal is useful to detect embolus (red blood cell aggregates). In this latter approach, we have first considered a simple "off-line" synchronous detector. As results were very interesting, we have thought that the correlation spectrum could be an interesting alternative to the synchronous detection. As the correlation spectrum of in vivo signal seems to be too complicated, we propose here to elucidate this apparent complexity by analytically computing the correlation spectrum of Doppler signal model with or without embolus