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Letting $\mathbf{F}$ and $\mathbf{F}^{-1}$ be the forward and inverse discrete Fourier transform, the cyclic autocorrelation of a signal $A$ is given by $$S(A)=\mathbf{F}^{-1}\left[\mathbf{F}(A)\mathbf{F}(A)^*\right].$$ Let the low-passed signal $A_L$ be $$A_L=\mathbf{F}^{-1}\left[\mathbf{F}(A)\mathbf{F}(L)\right]$$ where $L$ is the low-pass filter in the ...