By Robert M. Gray

ISBN-10: 0521131820

ISBN-13: 9780521131827

This quantity describes the basic instruments and strategies of statistical sign processing. At each degree, theoretical principles are associated with particular purposes in communications and sign processing. The publication starts with an outline of uncomplicated chance, random gadgets, expectation, and second-order second concept, by way of a wide selection of examples of the preferred random procedure types and their uncomplicated makes use of and homes. particular purposes to the research of random indications and structures for speaking, estimating, detecting, modulating, and different processing of signs are interspersed during the textual content.

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Let I be an index set such as a finite set of integers Zk , the set of all integers Z, the set of all nonnegative integers Z+ , the real line , or the nonnegative reals [0, ∞). Given a family of spaces {At ; t ∈ I}, define the product space AI = Ai = { all {at ; t ∈ I}; at ∈ At , all t} . t∈I The notation ×t∈I At is also used for the same thing. 3. PROBABILITY SPACES 31 are drawn from some fixed space. This leads to two notations for the space of all k−dimensional vectors with coordinates in A : Ak and AZk .

11). 4]. Form a new abstract space consisting of all waveforms or functions of time with values in A, for example, all real-valued time functions or continuous time signals. This space is also modeled as a product space. For example, the infinite two-sided space for a given A is At = { all waveforms {x(t); t ∈ (−∞, ∞)}; x(t) ∈ A, all t}, t∈ with a similar definition for one-sided spaces and for time functions on a finite time interval. Note that we indexed sequences (discrete time signals) using subscripts, as in xn , and we indexed waveforms (continuous time signals) using parentheses, as in x(t).

It enters at a fundamental level if one realizes that each individual point ω ∈ Ω produced in an experiment can be viewed as a signal , it might be a single voltage conveying the value of a measurement, a vector of values, a sequence of values, or a waveform, any one of which can be interpreted as a signal measured in the environment or received from a remote transmitter or extracted from a physical medium that was previously recorded. Signal processing in general is the performing of some operation on the signal.

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An Introduction to Statistical Signal Processing by Robert M. Gray

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