Quantum-Mechanical Signal Processing and Spectral Analysis: (Series in Atomic Molecular Physics)

The book presents a treatment of the use of quantum mechanical methods in spectral analysis. This is achieved through the use of an algorithm known as the fast Pade transform (FPT), which offers significant advantages over the more conventionally used fast Fourier transform (FFT), including markedly enhanced resolution and signal-to-noise ratios and more comprehensive analysis of individual spectral peaks. The use of the FPT is then extended to generic signal processing problems, demonstrating that time signals and data sets can be analysed in the same fashion. The advantages of using these quantum mechanical methods over conventional analytical techniques are illustrated through application to (a) ion cyclotron resonance mass spectroscopy, (b) nuclear magnetic resonance (NMR) and magnetic resonance spectrocopy (MRS) and (c) theoretically generated autocorrelation functions for molecular systems. The methods presented in the book will allow researchers involved in spectral analysis and signal processing to evaluate data with an accuracy not possible with the most numerically rigorous conventional methods.

Table of Contents:
Preface, General Introduction, Direct Link of Spectral Analysis with Eigenvalue Problems in Quantum Physics, Ubiquitous Padé Approximant across Quantum Physics and Signal processing, Versatile Lanczos Methods for Nearest Neighbour Interactions, Synergistic Combination of the Padé and Lanczos Methodologies, First Exact analytical Padé Method and continued Fractions, Algorithmic Strengths of Methods of Moments in Physics and Mathematics, Proof-of-Principle Illustrations of Quantum-mechanical Signal Processing, General Conclusions,Outlook for Quantum-mechanical Processing of generic time signals, Appendices, References

Review :
"The special importance of this book, in my opinion, is that it links different investigations from various branches of science: physics, mathematics, chemistry, medicine, and numerical analysis. Moreover, the book also addresses similar problems from engineering. It is clearly shown that a number of phenomena that seemed not to be directly connected, actually are, and this realization is expected to spur progress in many areas. Most importantly, the applicability and superiority of the presented spectral methods are demonstrated. The book is superbly written, and it is self-contained, so that it can be treated as a fundamental source of information for researchers and students in a wide range of fields. Therefore, I strongly recommend this book to colleagues and students." -Professor Ivan Mancev "The present book concerns one of the most beautiful and useful developments in mathematics. It takes the reader from the classical moment problem of Stieltjes via Pade's rational representations, using Hankel determinants and Frobenius normal forms, through the Krylov-Lanczos development to modern algorithmic techniques and codes. The deeper algebraic connections between signal processing and quantum mechanics are implicit and leaven important concrete applications typical of the interdisciplinary faculties of physics and medicine." -Professor Erkki Brandas