A real-valued periodic orthogonal sequence derived from a real-valued shift-orthogonal finite-length sequence and its fast periodic correlation algorithm

This paper proposes a real-valued orthogonal periodic sequence of a period N=2ν derived from a real-valued shift-orthogonal finite-length sequence of length M=2ν+1. This paper also explains the principle of a fast correlation algorithm that efficiently executes periodic correlation processing for this real-valued orthogonal periodic sequence. The sidelobe of an aperiodic autocorrelation function for a real-valued shift-orthogonal finite-length sequence (length of M) is 0 except for the right and left ends of the shift. If the subsequent sequence of first values repeatedly overlap the final values of this sequence, a real-valued orthogonal periodic sequence of a period N=M−1 can be obtained. A real-valued orthogonal periodic sequence of a period N=2ν generated from real-valued shift-orthogonal finite-length sequence of length M=2ν+1 is obtained by convoluting partial sequences and based on that controls the number of multiplications and the number of additions to increment on the order of Nlog2N without using fast Fourier transformation. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(10): 18–28, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20294