Ideal Sequence Design in Time-Frequency Space [electronic resource] : Applications to Radar, Sonar, and Communication Systems / by Richard Tolimieri, Andrzej K. Brodzik, Myoung An.

Review of Algebra -- Permutations and Permutation Matrices -- Finite Fourier Transform -- Convolution and Correlation -- Discrete Chirps -- Zak Transform -- Zak Space Correlation Formula -- Zak Space Representation of Chirps -- *-Permutations -- Permutation Sequences -- Modulation -- Sequence Sets -- Echo Analysis -- Sequence Shaping -- Problems.

This self-contained book develops theory and algorithms leading to systematic sequence design in time-frequency space. The primary tool used is the Zak transform, which provides sparse representation for the Fourier transform, convolution, and correlation. Using this multi-dimensional representation, the authors construct a large class of sequence sets satisfying pairwise ideal correlation. The complex algebraic analysis of sequences is replaced by an elegant and efficient geometric analysis of images, whose advantage is realized as an N to N! increase in the number of ideal sequence sets. Topics and features: * Mathematical development of the theory is illustrated with many examples. * Standard communication theory and Zak space methods are numerically compared. * Application areas covered include pulse radar and sonar, multi-beam radar and sonar imaging systems, remote identification of dielectrics, and code division multiple-access communication. * Background is provided in two introductory chapters on matrix algebra, tensor products, and permutation groups. * A list of open problems is presented and directions for further research are discussed. Ideal Sequence Design in Time-Frequency Space is an excellent reference text for graduate students, researchers, and engineers interested in radar, sonar, and communication systems. The work may also be used as a supplementary textbook for a graduate course or seminar on sequence design in time-frequency space.