An efficent implementation of a hexagonal FFT

In pursuing the goal to represent and process 2-D signals more efficiently than with a rectangular matrix representation, the idea of minimal sampling on a hexagonal lattice coupled with Fourier interpolation is presented. Hexagonal sampling, a special case of a more general sampling strategy, inherently offers greater efficiency than rectangular sampling for many signals; and therefore requires fewer resources to be expended and/or allocated for the sampling and processing of these signals. Processing efficiency can be increased by using a minimal set of data and then interpolated to provide unambiguous resolution of the output signal. This paper introduces an efficient hexagonal FFT (HFFT) that provides for band limited interpolation of hexagonally sampled 2-D signals and compares the number of multiplications required by the "hexagonal pruning FFT" to a regular HFFT and to a rectangular FFT that operates on a rectangularly sampled data set of the waveform. A simple application to antenna modeling is shown and areas for further applications are indicated.