Nonseparable Nth-band filters as overlapping-subarray tapers

In a receive array "overlapped subarrays" refers to an array output formed as a weighted sum of subarray outputs themselves formed as identically weighted combinations of the outputs of overlapping element subsets. The system array factor becomes a product of two array factors with different periods, one associated with each sum, just as the frequency response of a two-stage IFIR filter in a DSP system is the product of two frequency responses with different periods. It is well known that an Nth-band filter can be the most efficient choice for an IFIR filter's first stage, but the corresponding array idea appears unknown. Design examples apply modern optimization to nonseparable tapers, with three of four examples featuring Nth-band subarray tapers. Whether an Nth-band approach is best is not settled here and is properly context dependent: designs should be carried out both ways and compared. Further, a very small subarray taper can easily be Nth-band entirely by accident, so designers should be aware of the associated array-factor features that necessarily result and cannot be optimized away.