Performance of Modified Jacobi Sequences with Good Merit Factor
K. Gurumurty, Legendre Sequences
Abstract
K. Gurumurty, Legendre Sequences
Abstract
With ideal periodic autocorrelation functions the Quadratic residue and twin prime sequences are well known types of binary sequence. Legendre sequences and modified Jacobi sequences are much larger families of sequences. These sequences do not have ideal autocorrelation functions, but they do exhibit out-of- phase autocorrelation values which are independent of their lengths, and so the longer sequences may be useful. In this project work modified Jacobi sequences are generated for the length < 10000 and k ≤ 30. After generation of the modified Jacobi sequences periodic merit factor has been found out and got the good merit factor 7614 for the length 9991.
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With ideal periodic autocorrelation functions the Quadratic residue and twin prime sequences are well known types of binary sequence. Legendre sequences and modified Jacobi sequences are much larger families of sequences. These sequences do not have ideal autocorrelation functions, but they do exhibit out-of- phase autocorrelation values which are independent of their lengths, and so the longer sequences may be useful. In this project work modified Jacobi sequences are generated for the length < 10000 and k ≤ 30. After generation of the modified Jacobi sequences periodic merit factor has been found out and got the good merit factor 7614 for the length 9991.
Key concepts: Autocorrelation, Mathematics, Legendre polynomials, Ideal (ethics), Pseudorandom binary sequence, Sequence (biology), Quadratic equation, Binary number