The Uniqueness of a Multi-Dimensional Sequence in Terms of Its Phase or Magnitude.

A multi-dimensional sequence is not, in general, uniquely defined in terms of only the phase or magnitude of its Fourier transform. However, in this paper some conditions are developed under which a multi-dimensional sequence is uniquely defined by its phase. A similar set of conditions are then developed for the unique specification of a multi-dimensional sequence in terms of its Fourier transform magnitude. In both cases, it is initially assumed that either the phase or magnitude is known for all frequencies. The results are then generalized to the case in which the phase or magnitude is known only for a finite set of frequency values. (Author)