Titlebook: Unified Signal Theory; Gianfranco Cariolaro Textbook 2011 Springer-Verlag London Limited 2011

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Unified Theory: Signal Transformationsconcept of .. The development is mainly confined to . transformations, but . transformations are also briefly considered. Linear transformations will be further developed in the next two chapters with multirate transformations and with sampling and interpolation, which are important examples of transformations between different domains.

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Unified Theory: Sampling and Interpolationge. With the Unified Signal Theory, it is possible to formulate a ., which includes a variety of results as corollaries. Band-limitation is formulated in terms of a cell of the frequency domain, which must contain the support of the Fourier transform, and the interpolator too must be defined in terms of this cell.

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Introductionsidering the variety of signals encountered in applications (continuous-time, discrete-time, one-dimensional, two-dimensional, etc.), the model of deterministic signals is applied, with the conclusion that a first unified model has the form .(.), .∈., where . is a complex function defined on an appr

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Classical Signal Theoryy” means that, for each class, definitions and development are presented independently. For convenience, we call this approach the . Signal Theory in contrast to the approach of this book, the . Signal Theory. The classes of signals we will consider are: . These classes are introduced to give reader

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Unified Theory: Signal Domain Analysisorms). This chapter deals with the Haar integral of signals specified on LCA groups, which represents the fundamental functional of the Unified Signal Theory. Using the Haar integral, the classes of signals are formulated in a Hilbert space, where also a theory of symmetries is developed. The convol

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Unified Theory: Signal Transformations. It represents a very general concept that can be used to describe operations, however complicated, although it is often convenient to decompose a complicated operation into a sequence of simpler ones. The Unified Signal Theory gives a very general definition, which includes the case where the outp

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Unified Theory: Sampling and Interpolationith the consequent loss of signal values. . goes in the opposite direction, with the creation of new signal values, starting from the surviving samples. In this context, the basic problem is the recovery of the original signal from its samples. The structure of the recovery tf is potentially given b