Higher order crossings spectral analysis of an almost periodic random sequence in noise

The precise effect of noise on HOC (higher-order crossing) sequences is examined, settling some issues not dealt with previously. It is shown that it is possible to construct HOC sequences that converge to true discrete frequencies in a mixed spectrum even for very low signal-to-noise ratios. The availability of the correlation function is then assumed. When the expected HOCs (from repeated differences) are known, the correlation function is automatically known as well. However, other quantities, not just the expected HOC, can serve the same purpose. For example, under the Gaussian assumption, the correlation function can be obtained from that of the binary process derived by clipping the original process at any level