A general method for generating odd‐shift orthogonal sequences
Kenji Ohue · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract In general, it is difficult to derive a finite sequence which minimizes the sidelobe of the autocorrelation function. However, it is shown that there exist the evenshift orthogonal sequences, i.e., the finite sequences for which the even‐shift autocorrelation function takes the zero value. the generation method also is shown. On the other hand, there has not been known the general method for generating the odd‐shift orthogonal sequences, for which the odd‐shift autocorrelation takes the zero value. Neither have the properties of such sequences been analyzed. This paper presents the general method for deriving the odd‐shift orthogonal sequences, using the complex function as the generating function and constructing the numerical sequence from the Fourier expansion coefficients. First, the one‐ and two‐dimensional odd‐shift orthogonal complex sequences and odd‐shift orthogonal real sequences are defined from their autocorrelation functions. Then, it is shown that those numerical sequences are odd‐shift orthogonal sequences if they are skew‐symmetrical sequences. Finally, the properties of the generating functions that derive those odd‐shift orthogonal sequences are shown, together with the generation algorithm.