Cariolaro G. Unified Signal Theory

Springer, 2011. — 946 p. — ISBN10: 0857294636, ISBN13: 978-0857294630.The increasing application of information technology in a variety of fields has led to a high degree of diversification, to the extent that it is difficult to clearly delimit the scope of this discipline and to establish its distinctive characteristics. Nevertheless, it is well recognized that signals are salient features of this discipline and have a paramount influence on all the related fields, such as physics, astronomy, biology, medicine, oceanography and meteorology, among others, that take advantage of the electronic and the digital revolutions. The fact that signals are the greatest protagonists of this evolution was clear from the beginning of the electronic era. In fact, recalling the definition of electronics as the production, transmission and use of information (Everett, 1948) and considering that signals are the physical carriers of information, we arrive at the conclusion that signals play a fundamental role in every field related to information technology. As a natural consequence, it follows that the enormous growth of information technology, and its diversification, are regularly transferred to the discipline that specifically deals with signals, that is, Signal Theory.
The idea of a Unified Signal Theory (UST) stems from the requirement that the large variety of signals (continuous-time, discrete-time, aperiodic, periodic, one-dimensional, two-dimensional, etc.) proposed over the last few decades can be treated efficiently and with conceptual economy. The target of the UST is a unified introduction and development of signal operations, such as convolution, filtering, Fourier transformation, as well as system formulation and analysis. This approach is rather atypical, with respect to standard signal theories, where different definitions and separate developments are provided for each specific class of signals.Part I Classic Theory.
Classical Signal Theory.
Part II Unified Signal Theory.
Unified Theory: Fundamentals.
Unified Theory: Signal Domain Analysis.
Unified Theory: Frequency Domain Analysis.
Unified Theory: Signal Transformations.
Unified Theory: Multirate Transformations.
Unified Theory: Sampling and Interpolation.
Part III Specific Classes of Signals and Applications.
Signals Defined on R.
Signals on R/Z(T_p).
Signals on Z(T).
Signals on Z(T)/Z(T_p).
Signal Analysis via Digital Signal Processing.
Signal Expansions, Filter Banks, and Subband Decomposition.
Multiresolution and Wavelets.
Advanced Topics on Multidimensional Signals.
Study of Images.