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This paper studies the impact of the spatial sign function on the cyclic features of communication signals and thereby on the performance of cyclic-feature detectors. It extends the existing results obtained for Gaussian signals and provides new insights into the interactions between the cyclic features of a cyclostationary signal sent through a spatial sign filter, which lead to the modified cyclic features at the output. We apply these results to analytically derive the performance of the spatial sign cyclic correlation (SSCC) detector, which filters a received signal by the spatial sign function prior to its processing using a cyclic-feature detector. These results are extended to variations of the spatial sign function and we further motivate their application to general zero-memory non-linear (ZMNL) functions.