Improved Wavenumber Resolution for Small Arrays

The objective of the method described is to compute the Fourier transform of a function of space and time with a significant improvement in the resolution of spatial frequencies, particularly in the case of small arrays for which the size of the array is on the order of one wavelength (or less). This improvement is initially developed by considering the conversion of spatial frequency into temporal frequency through the oscillatory motion of a single receiver. A more practical scheme is next presented in which the oscillatory motion is created synthetically by the appropriate sequential sampling of individual elements in a receiving array. Both forms of this method (realand synthetic motion) besides providing some degree of "super-resolution" are linear and indicative of amplitude as well as phase.