The effect of a linear filter with monotone gain on the first-order autocorrelation of a weakly stationary time series is discussed. When the gain is monotone increasing, the first-order autocorrelation cannot increase. Otherwise, when the gain is monotone decreasing, the correlation cannot decrease. Further, when the gain is strictly monotone, the first-order autocorrelation is unchanged if and only if the process is a pure sinusoid with probability 1. Under the Gaussian assumption, the zero-crossing rate moves oppositely from the first-order autocorrelation.
"Monotone Gain, First-Order Autocorrelation and Zero-Crossing Rate." Ann. Statist. 19 (3) 1672 - 1676, September, 1991. https://doi.org/10.1214/aos/1176348271