Multirate Statistical Signal Processing by Omid S. Jahromi

By Omid S. Jahromi

The skill to approach indications at a number of sampling charges can assist lessen expenditures and enhance functionality in lots of DSP purposes starting from sign compression to instant communications, client leisure items and sensor networks. the idea of multirate sign processing has witnessed loads of growth because the e-book of the 1st textbook by means of Ronald E. Crochiere and Lawrence R. Rabiner in 1983. besides the fact that, this growth has been almost always within the zone of deterministic platforms with emphasis on perfect-reconstruction filter out banks, orthogonal filter out banks, platforms with a similar sampling cost throughout all channels and tree-structured platforms.

Multirate Statistical sign Processing introduces a statistical conception for extracting info from a number of similar signs that experience diversified sampling premiums. This new conception generalizes the traditional (deterministic) concept of multirate platforms past a lot of its constraints. in addition, it makes it possible for the formula and answer of numerous new difficulties akin to spectrum estimation, time-delay estimation and sensor fusion within the realm of multirate sign processing.

The writer offers history fabric, key ideas, power purposes and modern learn whereas awesome the fitting stability among readability and brevity. The publication is self-contained and offers a worthy source for sign processing researchers, graduate scholars and working towards engineers.

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These are the points which are not majorized by Y nor do they majorize it. This observation has important algebraic interpretations as discussed in the next subsection. 3 Algebraic properties of majorization In this subsection we review properties of the binary relation as an ordering relation on sets. 2 Measuring inequality 25 terminology. See Rosenfeld (1968) or Mac Lane and Birkhoff (1967) for a wellwritten introduction to the theory of ordered sets. Let ξ, η and ν be any three elements of Ω.

Wu (1997), randomness is usually quantified using Shannon’s entropy. Recall from Chapter 2 that the notion of entropy of a scalar random variable translates to the notion of entropy rate for WSS random signals. Recall also that when x(n) is Gaussian, the entropy rate is given by H(Px ) = 1 1 1 ln 2π + + 2 2 4π π −π ln Px (ejω )dω. 3 The Maximum Entropy principle 49 Let Γ = {ρi (k) : i = 0, . . , M − 1, k = 0, 1, . . , L − 1} denote the set of known autocorrelation coefficients obtained from the available low-rate signals vi (n).

2. A vector X is majorized by Y ∈ RM + if and only if X lies in the convex hull of the orbit of Y under the group of permutation matrices. An immediate result of the above theorem is that for a fixed Y the set {X : X Y } is convex. It is, however, not true for {X : Y X} as illustrated in the following example. 4. Consider a point Y ∈ R3+ as our reference point. Let c = 1 yi . Define ∆ = {X ∈ R3+ : x1 + x2 + x3 = c}. Obviously, ∆ is a plane triangle that also includes Y . The sets {X : X ∈ ∆, X Y } and {X : X ∈ ∆, Y X} are denoted by gray color in Fig.

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