2023/11/02 by David Gregoratti, Gregoratti, David, Xavier Arteaga +3 · 3 citations
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #Signal Processing (eess.SP) #electronic engineering #graph theory and CDMA systems #information engineering
paper · pdf · doi:10.48550/arxiv.2311.01035
openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a compilation of well-known results about Zadoff-Chu sequences, including all proofs with a consistent mathematical notation, for easy reference. Moreover, for a Zadoff-Chu sequence xu[n] of prime length NZC and root index u, a formula is derived that allows computing the first term (frequency zero) of its discrete Fourier transform, Xu[0], with constant complexity independent of the sequence length, as opposed to accumulating all its NZC terms. The formula stems from a famous result in analytic number theory and is an interesting complement to the fact that the discrete Fourier transform of a Zadoff-Chu sequence is itself a Zadoff-Chu sequence whose terms are scaled by Xu[0]. Finally, the paper concludes with a brief analysis of time-continuous signals derived from Zadoff-Chu sequences, especially those obtained by OFDM-modulating a Zadoff-Chu sequence.