On the N-dimensional extension of the discrete prolate spheroidal window

The optimal one-dimensional (1-D) window, an index-limited sequence with maximum energy concentration in a finite frequency interval, is related to a particular discrete prolate spheroidal sequence. This letter presents the N-dimensional (N-D) extension, i.e., the N-D window with limited support and maximum energy concentration in a general nonseparable N-D passband. These windows can be applied to multidimensional filter design and the design of optimal convolution functions. We show the three-dimensional (3-D) optimal window based on a rhombic dodecahedron as a passband region.