Fast Periodic Auto and Cross Correlation Algorithms for an Orthogonal Set of Real-Valued Perfect Sequences from the Huffman Sequence
نویسندگان
چکیده
A perfect sequence has the optimal periodic autocorrelation function where all out-of-phase values are zero, and an orthogonal set has orthogonality that the periodic correlation function for any pair of distinct sequences in the set takes zero at the zero shift. The real-valued perfect sequences of period N = 2 are derived from a real-valued Huffman sequence of length 2 + 1 with ν ≥ n whose out-of-phase aperiodic autocorrelation function takes zero except at the left and right shift-ends. This paper proposes fast periodic autoand cross-correlation algorithms for an orthogonal set of real-valued perfect sequences of period 2. As a result, the number of multiplications and additions can be suppressed on the order N log2 N . Keywords—Finite-length sequence, Perfect sequence, Huffman sequence, Orthogonal set, Fast correlation algorithm.
منابع مشابه
gpALIGNER: A Fast Algorithm for Global Pairwise Alignment of DNA Sequences
Bioinformatics, through the sequencing of the full genomes for many species, is increasingly relying on efficient global alignment tools exhibiting both high sensitivity and specificity. Many computational algorithms have been applied for solving the sequence alignment problem. Dynamic programming, statistical methods, approximation and heuristic algorithms are the most common methods appli...
متن کاملInfrared Wireless Communications using Complementary Sequence
The performance of an infrared wireless system using direct sequence spread spectrum techniques in multipath channels depends very much on the partial correlation properties of the spreading sequences used. Ideally, a spreading sequence should have zero sidelobes in its periodic and aperiodic auto-correlation functions in order to eliminate multipath dispersion. Unfortunately, no such ideal seq...
متن کاملZ-Complementary Sets Based on Sequences with Periodic and Aperiodic Zero Correlation Zone
Methods of constructing Z-complementary sequence sets are described. Different from those constructions using complementary sequences as a kernel, the proposed constructions are based on sequences with periodic and aperiodic zero-correlation zone (PAZCZ). These PAZCZ sequences are unitary sequences, not complementary sequences. By means of interleaving iteration and orthogonal matrix expansion ...
متن کاملAn Integrated Sequence Construction of Binary Zero-Correlation Zone Sequences
The present paper introduces an integrated construction of binary sequences having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed method enables more flexible design of the binary zerocorrelation zone sequence set with respect to it...
متن کاملDesign of Almost Perfect Complementary Sequence Pairs
Sequences with very low out-of-phase auto-correlation and cross-correlation function are widely used for synchronization in mobile communication and multimedia systems where reliable data transmissions are required. For optimum detection, synchronization sequences usually have out-of-phase correlation values that are very low or zero. However sequences with ideal correlation function are very r...
متن کامل