  The co-prime array is a sub-Nyquist acquisition scheme for the estimation of
second order statistics. It cannot generate all the difference values in the
co-prime range and hence, one of the sub-array is extended to enable the
estimation of the second order statistics at each difference value in the
co-prime range. Recently, the difference set for the co-prime array was studied
and low latency temporal spectrum estimation was demonstrated. In this paper,
the fundamentals of the difference set of the extended co-prime array, also
known as the conventional co-prime array, is developed. The closed-form
equations for the weight function, correlogram bias window, and the variance
are described. This is provided for the entire difference set, continuous
difference set and for the prototype co-prime period. It is shown that the
choice of $M\approx \frac{N}{2}$ generates a bias function with a large
relative amplitude between the main-lobe and side-lobe peaks, where $M$ and $N$
are co-prime pairs. The expressions for the number of multiplications and
additions required to compute the autocorrelation for the entire, continuous,
and prototype range is derived. Simulation results demonstrate low latency
spectrum estimation using the correlogram method.
