By Robert M. Gray

ISBN-10: 0521838606

ISBN-13: 9780521838603

This quantity describes the fundamental instruments and methods of statistical sign processing. At each degree, theoretical principles are associated with particular purposes in communications and sign processing. The booklet starts off with an summary of simple chance, random items, expectation, and second-order second concept, through a wide selection of examples of the most well-liked random approach versions and their easy makes use of and homes. particular purposes to the research of random signs and platforms for speaking, estimating, detecting, modulating, and different processing of indications are interspersed in the course of the textual content.

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**Extra resources for An Introduction to Statistical Signal Processing**

**Sample text**

Other examples are the space of all rational numbers, the space of all even integers, and the space of all periodic sequences of integers. 3] are called discrete spaces. Spaces with finite or countably infinite numbers of elements are called discrete spaces. 4] An interval of the real line ℜ, for example, Ω = (a, b). We might consider an open interval (a, b), a closed interval [a, b], a half-open interval [a, b) or (a, b], or even the entire real line ℜ itself. 4] that are not discrete are said to be continuous.

We know that this event space contains all one-dimensional events by construction. We next consider what other events must be in F I by virtue of its being an event space. After the one-dimensional events that pin down the value of a single coordinate of the vector or sequence or waveform, the next most general kinds of events are finite-dimensional sets that separately pin down the values at a finite number of coordinates. Let K be a finite collection of members of I and hence K ⊂ I. Say that K has K members, which we shall denote as {ki ; i = 0, 1, .

As particular examples, {0, 1}2 = {00, 01, 10, 11} and {0, 1}3 = {000, 001, 010, 011, 100, 101, 110, 111}, [0, 1]2 is the unit square in the plane, and [0, 1]3 is the unit cube in three-dimensional Euclidean space. Alternative notations for a Cartesian product space are k−1 Ai , Ai = i∈Zk i=0 where again the Ai are all replicas or copies of A, that is, where Ai = A, all i. Other notations for such a finite-dimensional Cartesian product are k ×i∈Zk Ai = ×k−1 i=0 Ai = A . This and other product spaces will prove to be useful ways of describing abstract spaces which model sequences of elements from another abstract space.

### An Introduction to Statistical Signal Processing by Robert M. Gray

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