In the last two decades, the field of time-frequency analysis has evolved into a widely recognized and applied discipline of signal processing. Besides linear time-frequency representations such as the short-time Fourier transform, the Gabor transform, and the wavelet transform, an important contribution to this development has undoubtedly been the Wigner distribution (WD) which holds an exceptional position within the field of bilinear/quadratic time-frequency representations.

The WD was first defined in quantum mechanics as early as 1932 by the later Nobel laureate E. Wigner. In 1948, J. Ville introduced this concept in signal analysis. Based on investigations of its mathematical structure and properties by N.G. de Bruijn in 1967, the WD was brought to the attention of a larger signal processing community in 1980. The WD was soon recognized to be important for two reasons: firstly, it provides a powerful theoretical basis for quadratic time-frequency analysis; secondly, its discrete-time form (supplemented by suitable windowing and smoothing) is an eminently practical signal analysis tool.

The seven chapters of this book cover a wide range of different aspects of the WD and other linear time-frequency distributions: properties such as positivity, spread, and interference term geometry; signal synthesis methods and their application to signal design, time-frequency filtering, and signal separation; WD based analysis of nonstationary random processes; singular value decompositions and their application to WD based detection and classification; and optical applications of the WD. The size of the chapters has been chosen such that an in-depth treatment of the various topics isachieved.

Linear signal spaces are of fundamental importance in signal and system theory, communication theory, and modern signal processing. This book proposes a time-frequency analysis of linear signal spaces that is based on two novel time-frequency representations called the `Wigner distribution of a linear signal space' and the `ambiguity function of a linear signal space'. Besides being a useful display and analysis tool, the Wigner distribution of a linear signal space allows the design of high-resolution time-frequency filtering methods. This book develops such methods and applies them to the enhancement, decomposition, estimation, and detection of noisy deterministic and stochastic signals. Formulation of the filtering (estimation, detection) methods in the time-frequency plane yields a direct interpretation of the effect of adding or deleting information, changing parameters, etc. In a sense, the prior information and the signal processing tasks are brought to life in the time-frequency plane. The ambiguity function of a linear signal space, on the other hand, is closely related to a novel maximum-likelihood multipulse estimator of the range and Doppler shift of a slowly fluctuating point target - an estimation problem that is important in radar and sonar. Specifically, the ambiguity function of a linear signal space is relevant to the problem of optimally designing a set of radar pulses. The concepts and methods presented are amply illustrated by examples and pictures. Time-Frequency Analysis and Synthesis of Linear Signal Spaces: Time-Frequency Filters, Signal Detection and Estimation, and Range-Doppler Estimation is an excellent reference and may be used as a text for advanced courses covering the subject.

Linear signal spaces are of fundamental importance in signal and system theory, communication theory, and modern signal processing. This book proposes a time-frequency analysis of linear signal spaces that is based on two novel time-frequency representations called the Wigner distribution of a linear signal space' and the ambiguity function of a linear signal space'. Besides being a useful display and analysis tool, the Wigner distribution of a linear signal space allows the design of high-resolution time-frequency filtering methods. This book develops such methods and applies them to the enhancement, decomposition, estimation, and detection of noisy deterministic and stochastic signals. Formulation of the filtering (estimation, detection) methods in the time-frequency plane yields a direct interpretation of the effect of adding or deleting information, changing parameters, etc. In a sense, the prior information and the signal processing tasks are brought to life in the time-frequency plane. The ambiguity function of a linear signal space, on the other hand, is closely related to a novel maximum-likelihood multipulse estimator of the range and Doppler shift of a slowly fluctuating point target - an estimation problem that is important in radar and sonar. Specifically, the ambiguity function of a linear signal space is relevant to the problem of optimally designing a set of radar pulses. The concepts and methods presented are amply illustrated by examples and pictures. Time-Frequency Analysis and Synthesis of Linear Signal Spaces: Time-Frequency Filters, Signal Detection and Estimation, and Range-Doppler Estimation is an excellent reference and may be used as a text for advanced courses covering the subject.

As a result of higher frequencies and increased user mobility, researchers and systems designers are shifting their focus from time-invariant models to channels that vary within a block. Wireless Communications Over Rapidly Time-Varying Channels explains the latest theoretical advances and practical methods to give an understanding of rapidly time varying channels, together with performance trade-offs and potential performance gains, providing the expertise to develop future wireless systems technology. As well as an overview of the issues of developing wireless systems using time-varying channels, the book gives extensive coverage to methods for estimating and equalizing rapidly time-varying channels, including a discussion of training data optimization, as well as providing models and transceiver methods for time-varying ultra-wideband channels.

Dieses Buch bietet eine Einfuhrung in die Theorie der statistischen Signalbeschreibung mit spezieller Betonung der digitalen Nachrichtenubertragungstechnik. Im ersten Kapitel wird der Begriff eines nachrichtentechnischen Signals und seine Beschreibungsmoeglichkeiten kurz erlautert. Das zweite Kapitel geht speziell auf den Aspekt der Zufalligkeit und Unbestimmtheit von Signalen ein. Dabei wird die praktische Anwendung der Wahrscheinlichkeitstheorie auf die fundamentalen Probleme der Nachrichtenubertragung dargestellt. Der Begriff der Information und seine Anwendung auf Quellencodierung und Kanalkapazitat werden anhand einfacher Beispiele erklart. Das dritte Kapitel fuhrt den Begriff der Zufallsvariablen und ihrer Beschreibung durch Verteilungsfunktion, Wahrscheinlichkeitsdichte und Erwartungswerte ein. Anschliessend werden die Grundgedanken der Schatzung von Parametern von Verteilungsfunktionen und charakteristische Eigenschaften wie Varianz und Bias erklart. Weitere Kapitel befassen sich mit der Modellierung von Nutzsignalen und Stoerungen, wichtigen Beschreibungsmoeglichkeiten wie AKF und Leistungsdichtespektrum sowie speziellen stochastischen Prozessen und deren mathematischer Beschreibung. Abschliessend werden noch binare Pseudozufallsfolgen sowie die Anwendung des Konzepts stochastischer Prozesse auf den Entwurf von Systemen zur Signalverarbeitung diskutiert. Bei der Aufbereitung des Stoffes wurde auf groesstmoegliche Anschaulichkeit und Lesbarkeit Wert gelegt. Die Beschreibung der angesprochenen Sachverhalte wurde soweit formalisiert, dass dem Leser ein tieferes Endringen in weiterfuhrende Litertur ohne Probleme moeglich sein wird.