Orthogonal Residue Sequences

This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences have autocorrelation function that is zero everywhere excepting at the origin. These sequences may be used as keys in communication applications in a manner that is analogous to the use of PN sequences in spread spectrum systems.

[1]  S. Kak.  The discrete Hilbert transform , 1970 .

[2]  A. Viterbi.  CDMA: Principles of Spread Spectrum Communication , 1995 .

[3]  I. Roy,et al.  On robust estimation of discrete Hilbert transform of noisy data , 2013 .

[4]  Xianbin Wang,et al.  Transmitter identification using embedded pseudo random sequences , 2004, IEEE Transactions on Broadcasting.

[5]  Alexander Katsevich,et al.  Spectral Analysis of the Truncated Hilbert Transform with Overlap , 2013, SIAM J. Math. Anal..

[6]  L. Javier García-Villalba,et al.  An efficient algorithm to generate binary sequences for cryptographic purposes , 2001, Theor. Comput. Sci..

[7]  Subhash Kak,et al.  Hilbert transformation for discrete data , 1973 .

[8]  M R Arnison,et al.  Using the Hilbert transform for 3D visualization of differential interference contrast microscope images , 2000, Journal of microscopy.

[9]  Vamsi Sashank Kotagiri.  New Results on the Number Theoretic Hilbert Transform , 2013, ArXiv.

[10]  Subhash C. Kak,et al.  A two-layered mesh array for matrix multiplication , 1988, Parallel Comput..

[11]  Renuka Kandregula.  The Basic Discrete Hilbert Transform with an Information Hiding Application , 2009, ArXiv.

[12]  S. K. Padala,et al.  Systolic arrays for the discrete Hilbert transform , 1997 .

[13]  Subhash C. Kak,et al.  Multilayered array computing , 1988, Inf. Sci..

[14]  S. Kak,et al.  On speech encryption using waveform scrambling , 1977, Bell Labs technical journal.

[15]  I. Noda,et al.  Determination of Two-Dimensional Correlation Spectra Using the Hilbert Transform , 2000 .

[16]  Subhash C. Kak,et al.  The Number Theoretic Hilbert Transform , 2013, Circuits, Systems, and Signal Processing.