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Statistical Analysis and Design of Chaotic Systems
Published in M.P. Kennedy, R. Rovatti, G. Setti, Chaotic Electronics in Telecommunications, 2018
Wolfgang Schwarz, Marco Götz, Kristina Kelber, Andreas Abel, Thomas Falk, Frank Dachselt
Well known cumulants are the mean value κx1, the variance κx2, the covariance κx,y1,1, the skewness κx3 (measuring the asymmetry of a PDF), and the curtosis κx4 (describing the deviation of a PDF from a Gaussian PDF). Cumulants possess a set of special properties, which explain their wide exploitation: Gaussian PDF have cumulants of 1st and 2nd order only, i.e. the PDF is fully described by these cumulants.Joint cumulants of independent variables vanish (e.g. κx1,x2q1,q2=0 for independent x1, x2).the cumulant of a sum of independent variables is the sum of the respective cumulants of the variables (e.g κx+y3=κx3+κy3).
Overview of Statistical Signal Processing
Published in Vijay K. Madisetti, The Digital Signal Processing Handbook, 2017
For most analyses, cumulants are preferred to moments because the cumulants of order 3 and higher for a Gaussian process are identically zero. Thus, signal processing methods based on higher-order cumulants have the advantage of being “blind” to any form of Gaussian noise.
Probability, Random Variables, and Stochastic Processes
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
The various cumulants are related to the moments as follows: () λ1=E{χ}=μχ () λ2=E{(χ−E{χ})2}=σχ2 () λ3=E{(χ−E{χ})3} () λ4=E{χ4}−4E{χ3}E{χ}−3(E{χ2})2+12E{χ2}(E{χ})2−6(E{χ})4
Automatic modulation recognition based on mixed-type features
Published in International Journal of Electronics, 2021
Xin-Rui Jiang, Hui Chen, Yao-Dong Zhao, Wen-Qin Wang
If the modulation signal own high-order statistical characteristics, the high-order cumulant feature is an application of mathematical methods to distinguish signal types in the field of communication (Abdelbar et al., 2018; Xie et al., 2019). The recognition method using high-order cumulants in Wang & Li (2019) can achieve the recognition rate 90% at SNR 10 dB for 2PSK, 8PSK, 4PAM and 16QAM signals. And the recognition method (S. Li et al., 2012) using high-order cumulant feature and support vector machine method can reach the recognition rate 94% of 8 signals as 2ASK, 4ASK, 2FSK, 4FSK, 2PSK, 4PSK, 8PSK and 16QAM at SNR-1 dB. But the high-order cumulant feature for some types of signals is too similar or none, which results in difficulties to distinguish them. Machine learning methods are also used in AMC (S. Li et al., 2012; Shi et al., 2019). A three-layer neural network (Zhu et al., 2016) was also designed to identify seven digital modulation signals using cyclic spectrum characteristics. Note that, most existing works mainly focus on the zero-mean Gaussian noise case; non-Gaussian noise scenario (Liu, 2019) will be considered in the further work.
Signal fingerprint feature extraction and recognition method for communication satellite
Published in Connection Science, 2022
These advantages make higher-order cumulants and their spectra an important tool in signal processing. The spectrum formed by higher-order accumulations is called multispectrum, also known as higher-order spectrum. Among them, when the order k = 3, it is the spectrum with the lowest order, called bispectrum. Because the higher the order of the high-order accumulation amount, the higher the computational complexity will be, which will affect the practicability of the actual scene application. Therefore, the bispectrum estimation method is the most commonly used in the analysis of high-order spectral signals, and it also has good performance in terms of performance. The following focuses on the definition of bispectrum:
Risk preference evaluation – a fourth dimension of the application of the Laplace transform
Published in International Journal of Production Research, 2018
From (10), the first two cumulants will be the mean and the variance . The function will be shown to be closely related to our CME function to be derived in the next section.