Bücher von Robert M. Gray

The Fourier transform is one of the most important mathematical tools in a wide variety of fields in science and engineering. In the abstract it can be viewed as the transformation of a signal in one domain (typically time or space) into another domain, the frequency domain. Applications of Fourier transforms, often called Fourier analysis or harmonic analysis, provide useful decompositions of signals into fundamental or "e;primitive"e; components, provide shortcuts to the computation of complicated sums and integrals, and often reveal hidden structure in data. Fourier analysis lies at the base of many theories of science and plays a fundamental role in practical engineering design. The origins of Fourier analysis in science can be found in Ptolemy's decomposing celestial orbits into cycles and epicycles and Pythagorus' de- composing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J. Fourier in his 1822 Theorie analytique de la Chaleur [16] (still available as a Dover reprint) was the first to claim that arbitrary periodic functions could be expanded in a trigonometric (later called a Fourier) series, a claim that was eventually shown to be incorrect, although not too far from the truth. It is an amusing historical sidelight that this work won a prize from the French Academy, in spite of serious concerns expressed by the judges (Laplace, Lagrange, and Legendre) re- garding Fourier's lack of rigor.

This fully updated new edition of the classic work on information theory presents a detailed analysis of Shannon-source and channel-coding theorems, before moving on to address sources, channels, codes and the properties of information and distortion measures.

In this new edition of this classic text, much of the material has been rearranged and revised for pedagogical reasons. Many classic inequalities and proofs are now incorporated into the text, and many citations have been added.

This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.

This two-part work is both a tutorial on and a historical survey of linear predictive coding and the internet protocol.

Derives in a tutorial manner the fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight.

Stochastic Image Processing provides the first thorough treatment of Markov and hidden Markov random fields and their application to image processing.

Source coding theory has as its goal the characterization of the optimal performance achievable in idealized communication systems which must code an information source for transmission over a digital communication or storage channel for transmission to a user.

Conventional block-based segmentation algorithms classify each block separately, assuming independence of feature vectors. Image Segmentation and Compression Using Hidden Markov Models presents a new algorithm that models the statistical dependence among image blocks by two dimensional hidden Markov models (HMMs).

, data compression applied to signals such as speech, audio, images, and video signals (excluding other data types such as financial data or general purpose computer data).

, data compression applied to signals such as speech, audio, images, and video signals (excluding other data types such as financial data or general purpose computer data).

Conventional block-based segmentation algorithms classify each block separately, assuming independence of feature vectors. Image Segmentation and Compression Using Hidden Markov Models presents a new algorithm that models the statistical dependence among image blocks by two dimensional hidden Markov models (HMMs).