Detailed calculations of the root‐mean‐square value of the output noise of correlators with an exponentially weighted average and an arbitrarily chosen weighting function for three commonly used mathematical models of white noise are derived. A comparative analysis has been made of noise properties of correlators with exponentially weighted average and true average based on two figures of merits: the output signal‐to‐noise ratio and the signal‐to‐noise improvement ratio. An analysis of noise properties of a boxcar averager for any gate width is performed. Expressions for the output signal‐to‐noise ratio and the signal‐to‐noise improvement ratio of a boxcar averager are derived.