  The spectral analysis with stochastic significance cannot distinguish the
spurious cycles effectively, because a non-stationary signal can make a
significant peak in spectrum. I show that the random separation between the
grand extremes such as grand maxima and minima in solar activity can make a
spurious but significant peak in spectrum. And it is possible to pick even the
weak stable cycle by applying an averaging down-sampling and the differencing
to a random signal. This is because both operations variously change the height
of peak in spectrum and the spurious cycle is in turn unstable in both
operations. I introduce a samplogram showing these operations and stability
intuitively.
