The Bounded Real Characteristic Function and Nehari Extensions

1994 ◽  
pp. 264-315
Author(s):  
P. A. Fuhrmann
Keyword(s):  
Characteristic Function ◽  
Real Characteristic

The characteristic functions of functions

1968 ◽  
Vol 307 (1490) ◽  
pp. 317-334 ◽  
Keyword(s):  
Multivariate Analysis ◽  
Characteristic Function ◽  
Gaussian Model ◽  
Random Variable ◽  
Stable Distributions ◽  
Characteristic Functions ◽  
Real Characteristic ◽  
Vector Random Variable

The characteristic functions of various functions of a real or vector random variable are expressed in terms of the characteristic function of that variable. In the examples there is special emphasis on the stable distributions that have real characteristic functions. Some of the results suggest the practicability of generalizing traditional multivariate analysis beyond the multi-Gaussian model.

scholarly journals Computing the Sound of the Sea in a Seashell

2021 ◽  
Author(s):  
Jonathan Ben-Artzi ◽  
Marco Marletta ◽  
Frank Rösler
Keyword(s):  
Characteristic Function ◽  
Helmholtz Resonator ◽  
Positive Answer ◽  
Approximation Procedure ◽  
Universal Algorithm

AbstractThe question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to assume is that the resonator chamber is bounded and that its boundary is $${{\mathcal {C}}}^2$$ C 2 . The proof is constructive, providing a universal algorithm which only needs to access the values of the characteristic function of the chamber at any requested point.

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

scholarly journals Three State Estimation Fusion Methods Based on the Characteristic Function Filtering

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1440
Author(s):  
Yiran Yuan ◽  
Chenglin Wen ◽  
Yiting Qiu ◽  
Xiaohui Sun
Keyword(s):  
Characteristic Function ◽  
State Estimation ◽  
Packet Loss ◽  
Estimation Accuracy ◽  
Measurement Systems ◽  
Fusion Methods ◽  
Estimation Fusion ◽  
Parallel Filter ◽  
Sequential Filter ◽  
Better Than

There are three state estimation fusion methods for a class of strong nonlinear measurement systems, based on the characteristic function filter, namely the centralized filter, parallel filter, and sequential filter. Under ideal communication conditions, the centralized filter can obtain the best state estimation accuracy, and the parallel filter can simplify centralized calculation complexity and improve feasibility; in addition, the performance of the sequential filter is very close to that of the centralized filter and far better than that of the parallel filter. However, the sequential filter can tolerate non-ideal conditions, such as delay and packet loss, and the first two filters cannot operate normally online for delay and will be invalid for packet loss. The performance of the three designed fusion filters is illustrated by three typical cases, which are all better than that of the most popular Extended Kalman Filter (EKF) performance.

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