An Introduction to Statistical Signal Processing

The theory of random processes is a branch of probability theory and probability theory is a special case of the branch of mathematics known as measure theory. 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 nd volume by integrating a constant over the set. From physics we can nd 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.

Từ khóa: lý thuyết xác suất, xử lý tín hiệu, công nghệ tín hiệu, Statistical Signal Processing, probability theory, measure theory