Co-prime arrays with compressed inter-element spacing (CACIS) is one of the generalizations of the co-prime array. The inter-element spacing can be varied in this case. The prototype co-prime arrays and nested arrays are a special case of the CACIS scheme. The problems that were not addressed previously are considered in this paper. The fundamentals of the difference set for the CACIS configuration are developed for low latency. In addition, the closed-form expressions for the weight function (number of samples that contribute to estimate the autocorrelation) and bias window of the correlogram estimate, which were previously unknown, are derived. Ideally, the bias window should be an impulse. Several examples are provided along with simulations to verify the claims made. All possible sample pairs are used for estimation, which provides for low latency. As an application, temporal spectrum is considered for simulations.