Just as one uses the power spectrum of the Fourier transform of data given as a function of a one-dimensional variable to find periodicities in the translation of the variable, one may use the power spectrum of the Mellin transform to find periodicities in the magnification. The relation of the Fourier transform to the Mellin transform is discussed, and a theorem of the Wiener-Khinchine type is presented. The use of the Mellin transform, offers a new method of extracting meaningful features from data, particularly when the data is noisy.
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.
This book treats the various aspects of noise from magnetic recording media and the impact on system performance. Several authors present discussions of: materials and processes used to fabricate media for computer data storage, theoretical aspects of noise and micromagnetic behavior, experimental methods and characterization, and system analysis. In the past decade thin film recording media have largely displaced particlate media in rigid disk recording systems. During the same period of time the field has evolved from the prevalent belief that thin film media were virtually noiseless to a detailed understanding of the origin and the manifestation of noise in these new media. This understanding has lead to the ability to make the very low noise media needed in present applications. The present state of understanding of both particulate and thin film media is summarized.
Nature provides many examples of physical systems that are described by deterministic equations of motion, but that nevertheless exhibit nonpredictable behavior. The detailed description of turbulent motions remains perhaps the outstanding unsolved problem of classical physics. In recent years, however, a new theory has been formulated that succeeds in making quantitative predictions describing certain transitions to turbulence. Its significance lies in its possible application to large classes (often very dissimilar) of nonlinear systems. Since the publication of Universality in Chaos in 1984, progress has continued to be made in our understanding of nonlinear dynamical systems and chaos. This second edition extends the collection of articles to cover recent developments in the field, including the use of statistical mechanics techniques in the study of strange sets arising in dynamics. It concentrates on the universal aspects of chaotic motions, the qualitative and quantitative predictions that apply to large classes of physical systems. Much like the previous edition, this book will be an indispensable reference for researchers and graduate students interested in chaotic dynamics in the physical, biological, and mathematical sciences as well as engineering.
