  Co-prime sensing is a sub-Nyquist technique for signal acquisition. Several
modifications to the prototype co-prime array have been proposed in the
literature. Researchers have also demonstrated low latency estimation. This
paper describes the functioning of a Family of Adjustable Pivot Co-Prime
Arrays. However, the main focus is to introduce the reader to a concept called
Extremely Sparse Co-Prime Arrays and Samplers. Adjustable pivot co-prime arrays
are a special case of the extremely sparse arrays. The closed-form expressions
for the weight function and the correlogram bias window are derived. Low
latency estimation is demonstrated using the extremely sparse co-prime scheme.
Furthermore, a multidimensional and a hybrid extremely sparse co-prime array is
proposed as a straightforward extension of the 1D-theory. Finally, a
generalized extremely sparse structure is developed with several design
parameters. Most existing structures may be viewed as a special case of the
generalized scheme.
