Combinatorics

Discrete mathematics

Physics

Synchronizing

Topology (electrical circuits)

Mathematics

Algorithm

Set (abstract data type)

Programming language

Code (set theory)

Pulse (music)

Computer science

Phase (matter)

Quantum mechanics

Telecommunications

Detector

IEEE Transactions on Information Theory

A method of generating phase shift pulse codes of arbitrarily long length with zero periodic correlation except for the peak for zero shift is presented. The codes are of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p^2</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> is any prime number, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> different phase shifts corresponding to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> th roots of unity are necessary to generate them. Since <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> different phase shifts are required, these codes are not as easy to generate and process as the binary codes, but this does not seem to be a serious limitation to their usefulness. Application of these codes can be made as interpulse phase modulation for range resolution in pulse Doppler radars or for a method of synchronizing a pulse code communication system.

Phase shift pulse codes with good periodic correlation properties