  One-bit quantization, which relies on comparing the signals of interest with
given threshold levels, has attracted considerable attention in signal
processing for communications and sensing. A useful tool for covariance
recovery in such settings is the arcsine law, that estimates the normalized
covariance matrix of zero-mean stationary input signals. This relation,
however, only considers a zero sampling threshold, which can cause a remarkable
information loss. In this paper, the idea of the arcsine law is extended to the
case where one-bit analog-to-digital converters (ADCs) apply time-varying
thresholds. Specifically, three distinct approaches are proposed, investigated,
and compared, to recover the autocorrelation sequence of the stationary signals
of interest. Additionally, we will study a modification of the Bussgang law, a
famous relation facilitating the recovery of the cross-correlation between the
one-bit sampled data and the zero-mean stationary input signal. Similar to the
case of the arcsine law, the Bussgang law only considers a zero sampling
threshold. This relation is also extended to accommodate the more general case
of time-varying thresholds for the stationary input signals.
