By Gray R.M., Davisson L.D.

This quantity describes the fundamental instruments and strategies of statistical sign processing. At each degree, theoretical rules are associated with particular functions in communications and sign processing. The ebook starts with an outline of uncomplicated chance, random items, expectation, and second-order second idea, by way of a wide selection of examples of the most well-liked random method types and their easy makes use of and houses. particular purposes to the research of random signs and platforms for speaking, estimating, detecting, modulating, and different processing of signs are interspersed through the textual content.

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Extra resources for An Introduction to Statistical Signal Processing

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Such a sequence of sets is said to be nested and increasing. For example, the sequence Fn = [1, 2 − 1/n) of subsets of the real line is increasing. The sequence (−n, a) is also increasing. Intuitively, the first example increases to a limit of [1, 2) in the sense that every point in the set [1, 2) is eventually included in one of the F n . Similarly, the sequence in the second example increases to (−∞, a). 3 Probability Spaces 39 in the sequence: lim Fn = n→∞ ∞ Fn . (a) illustrates such a sequence in a Venn diagram.

Observe that from elementary calculus we can find volume by integrating a constant over the set. From physics we can find mass by integrating a mass density or summing point masses over a set. In both cases the set is a region of three-dimensional space. In a similar manner, probabilities will be computed by integrals of densities of probability or sums of “point masses” of probability. Both probability theory and measure theory consider only nonnegative real-valued set functions. The value assigned by the function to a set is called the probability or the measure of the set, respectively.

Probability theory and measure theory both concentrate on functions that assign real numbers to certain sets in an abstract space according to certain rules. These set functions can be viewed as measures of the size or weight of the sets. For example, the precise notion of area in two-dimensional Euclidean space and volume in three-dimensional space are both examples of measures on sets. Other measures on sets in three dimensions are mass and weight. Observe that from elementary calculus we can find volume by integrating a constant over the set.

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