Ideal Sequence Design in Time-Frequency Space

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti? c communities with signi? cant devel- ments in harmonic analysis, ranging from abstract harmonic analysis to basic app- cations. The title of the series re? ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation - pend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ? ourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship - tween harmonic analysis and ? elds such as signal processing, partial differential equations (PDEs), and image processing is re? ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

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. - #x002A; -Permutations. - Permutation Sequences. - Modulation. - Sequence Sets. - Echo Analysis. - Sequence Shaping. - Problems.