A correlator detector is considered which processes the outputs of two identical collinear arrays of uniformly spaced elements. When the input signal is sinusoidal, the mean system output is bounded by the product of the space factors of the arrays. Complex amplitude factors are introduced following each element, and it is shown how to choose them in order to optimize the main lobe‐width‐side‐lobe‐level relationship of the space‐factor product or envelope. In addition, it is proved that the use of amplitude factors for improving envelope resolution gives rise to a signal‐noise degradation relative to the corresponding uniform amplitude system. Various numerical results are given, including the fact that the optimum system provides an envelope main‐lobe‐width reduction of approximately thirty percent when twenty or fewer elements appear in each array.