||A central goal in signal analysis is to extract information from signals that are related to real-world phenomena. Examples are the analysis of speech, images, and signals in medical or geophysical applications. One reason for analyzing such signals is to achieve better understanding of the underlying physical phenomena. Another is to find compact representations of signals which allow compact storage or efficient transmission of signals through real-world environments. The methods of analyzing signals are wide spread and range from classical Fourier analysis to various types of linear time-frequency transforms and model-based and non-linear approaches. This book concentrates on transforms, but also gives a brief introduction to linear estimation theory and related signal analysis methods. The text is self-contained for readers with some background in system theory and digital signal processing, as typically gained in undergraduate courses in electrical and computer engineering.
The first five chapters of this book cover the classical concepts of signal representation, including integral and discrete transforms. Chapter 1 contains an introduction to signals and signal spaces. It explains the basic tools for classifying signals and describing their properties. Chapter 2 gives an introduction to integral signal representation. Examples are the Fourier, Hartley and Hilbert transforms. Chapter 3 discusses the concepts and tools for discrete signal representation. Examples of discrete transforms are given in Chapter 4. Some of the latter are studied comprehensively, while others are only briefly introduced, to a level required in the later chapters. Chapter 5 is dedicated to the processing of stochastic processes using discrete transforms and model-based approaches. It explains the Karhunen-Loeve transform and the whitening transform, gives an introduction to linear estimation theory and optimal filtering, and discusses methods of estimating autocorrelation sequences and power spectra.
The final four chapters of this book are dedicated to transforms that provide time-frequency signal representations. In Chapter 6, multirate filter banks are considered. They form the discrete-time variant of time-frequency transforms. The chapter gives an introduction to the field and provides an overview of filter design methods. The classical method of time-frequency analysis is the short-time Fourier transform, which is discussed in Chapter 7. This transform was introduced by Gabor in 1946 and is used in many applications, especially in the form of spectrograms. The most prominent example of linear transforms with time-frequency localization is the wavelet transform.