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The problem of determining the first-order probability density of a filtered version of hard-limited noise is considered. An integral equation for the density is derived by using Siegert's results on zero-crossing distributions for noise. We also show how the integral equation can be obtained from a two-dimensional Fokker-Planck equation. The exact solution of the integral equation has not been found, but some general information is available. An iterative scheme for determining the moments has been found, and some information has been obtained regarding the behavior of the density as the variable approaches the ends of its range. One result of this portion of the investigation is a disproof of au expression for the density conjectured by Pawula and Tsai. Finally, curves for the density are obtained by solving the integral equation numerically.