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

Abstract

This paper proposes a real-valued orthogonal periodic sequence of a period N=2^ν derived from a real-valued shift-orthogonal finite-length sequence of length M=2^ν+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=2^ν generated from real-valued shift-orthogonal finite-length sequence of length M=2^ν+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