Topic
Probability-generating function
About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.
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15 Jul 2001TL;DR: A nonlinear function based on the cost function as a Kullback-Leibler divergence between the joint probability density function of the source vector and its parametric model, is proposed, which is equivalent to maximization of the information transfer between inputs and outputs.
Abstract: Blind source separation (BSS) deals with separating independent signals form their linear mixtures observed at different sensors. In this paper a nonlinear function based on the cost function as a Kullback-Leibler divergence between the joint probability density function of the source vector and its parametric model, is proposed. This cost function is equivalent to maximization of the information transfer between inputs and outputs, and minimization of the mutual information between components of the output vector. Derivation process becomes extremely simple due to a simple approximation. Simulations with communication signals indicate that the proposed algorithm provides better accuracy.
2 citations
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2 citations
27 Oct 1966
TL;DR: A computer program to carry out this method for generating digitally a time series with a given power spectral density function was written for the Control Data Corporation 3200 computer, and the program was tried on some specific example problems.
Abstract: : This paper gives a method for generating digitally a time series with a given power spectral density function. A computer program to carry out this method was written for the Control Data Corporation 3200 computer, and the program was tried on some specific example problems. Then for each of these examples, the power spectral density function of the generated time series was compared with the specified, theoretical power spectral density function.
2 citations
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TL;DR: In this paper, the authors studied random power series of the form f(z) = z xn in which the gap lengths are random while the coefficients are all 1, and they defined the mean function p(z).
Abstract: Power series Ezxn are studied, where {X,) is a strictly increasing integer-valued stochastic process. RANDOM POWER SERIES; NATURAL BOUNDARY The function theoretic properties of random functions are discussed in the monograph of Kahane (1985), and random power series in particular are surveyed by Lukacs (1975), Chapter 5. Walk (1968) drew attention to the parallels between probability 1 properties of random power series and those of certain deterministic lacunary series. Brief references to the properties of fixed lacunary series can be found in, for example Titchmarsh (1939), ?7.4. Arnold (1966) studied series in which the sequence of powers for which the coefficient is non-zero is specified deterministically, but the values of the coefficients are random. This note is about lacunary series of the form f(z) = z xn in which the gap lengths are random while the coefficients are all 1. 0 Corresponding to any random power series we define the mean function p(z) = Ef(z) and the real variance function v(z) = E(f(z) - p(z)), provided the relevant sums converge. The indices occurring in a realisation of f(z) form a catalogue of the states visited by the sample sequence {X,} and p(z) is a generating function for the expected numbers of visits of the process to the states.
2 citations