Wavenumber support regions for arbitrary arrays

Abstract

We set out a procedure for defining the region of wavenumber support relevant for maximum entropy spectral estimation of a noise field incident on a planar array. We consider first linear, nonequispaced arrays, and argue that the problem of defining a region of wavenumber support is only well-posed when either position uncertainty for the array elements is postulated, or phase uncertainty in the measurement of the signals at the array elements is postulated, or one acknowledges that a polar diagram that is almost periodic defines an aliasing frequency in virtually the same way as a polar diagram which is periodic. For planar arrays, the region of wavenumber support can be approximately circular but in general has to be defined with reference to the particular array.