The new arithmetical approach to Fourier analysis for a 2D signal

An arithmetical approach to Fourier analysis, called the arithmetic Fourier transform (AFT), is developed for a two-dimensional (2D) signal. This 2D AFT algorithm is based on the arithmetical approach that H. Bruns originated in 1903. It uses alternating arithmetic averages of 2n samples over a period. The use of alternating arithmetic averages yields an algorithm of low complexity. The number of multiply operations, which compose a major part of the architecture, is reduced. This algorithm features parallel processing which can be effectively implemented with VLSI techniques or optical processors. As a consequence, it is expected that this arithmetic algorithm can compete in complexity and speed with the conventional 2D fast Fourier transform algorithm. Simulation of the algorithm for equally space 2D data is accomplished by using zero-order interpolation. Computer simulation demonstrates that the errors in the Fourier coefficients are tolerable for many applications