An algorithm for generating finite two‐dimensional real number sequences with low autocorrelation sidelobes

Abstract

AbstractWhen the spread‐spectrum technique or smear technique is applied to the two‐dimensional data such as the image data, which have the two‐dimensional array structure, it is important to apply the two‐dimensional numerical sequence that minimizes the sidelobe component of the autocorrelation function.This paper proposes a new method of generation, where the two‐dimensional complex exponential function is used as the generating function and a finite two‐dimensional real‐number sequence with a sharp autocorrelation function is derived from the two‐dimensional Fourier expansion coefficients.As the first step, the phase condition is derived for the Fourier expansion coefficients of the generating function to be real. It is shown that the infinite two‐dimensional real‐number sequence constructed by the forementioned infinite number of Fourier expansion coefficients is an uncorrelated sequence. Then it is shown that by using the proportional constant of the phase function as the parameter, a finite two‐dimensional real‐number sequence with the autocorrelation function with arbitrary evaluation function value can be derived.Finally, a generation example of the finite two‐dimensional real‐number sequence is shown, demonstrating that the finite two‐dimensional real‐number sequence with a very sharp autocorrelation can be generated by the proposed method.