scholarly journals A Version of the FastICA Algorithm Based on the Secant Method Combined with Simple Iterations Method

2008 ◽  
pp. 312-320 ◽  
Author(s):  
Doru Constantin ◽  
Luminita State
Keyword(s):  
Secant Method ◽  
Fastica Algorithm

A novel FastICA algorithm based on improved secant method for Intelligent drive

2021 ◽  
Vol 40 (1) ◽  
pp. 165-178
Author(s):  
Hongzhe Liu ◽  
Qikun Zhang ◽  
Cheng Xu ◽  
Zhao Ye
Keyword(s):  
Signal Processing ◽  
Statistical Signal Processing ◽  
Descent Method ◽  
Secant Method ◽  
Gradient Descent Method ◽  
Speech Separation ◽  
Initial Value ◽  
Signal Processing Technique ◽  
Fixed Point Algorithm ◽  
Fastica Algorithm

Blind Source Separation(BSS) is one of the research hotspots in the field of signal processing. In order to improve the accuracy of speech recognition in driving environment, the driver’s speech signal must be enhanced to improve its signal to noise ratio(SNR). Independent component analysis (ICA) algorithm is the most classical and efficient blind statistical signal processing technique. Compared with other improved ICA algorithms, fixed-point algorithm (FastICA) is well known for its fast convergence speed and good robustness. However, the convergence of FastICA algorithm is comparatively susceptible to the initial value selection of the original demixing matrix and the calculation of the iterative process is relatively large. In this paper, the gradient descent method is used to reduce the effect of initial value. What’s more, the improved secant method is proposed to speed up the convergence rate and reduce the amount of computation. As the results of mixed speech separation experiment turn out, the improved algorithm is of better performance relative to the standard FastICA algorithm. Experimental results show that the proposed algorithm improves the speech quality of the target driver. It is suitable for speech separation in driving environment with low SNR.

scholarly journals Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 169
Author(s):  
Avram Sidi
Keyword(s):  
Nonlinear Equations ◽  
Local Convergence ◽  
Real Root ◽  
Numerical Procedure ◽  
Secant Method ◽  
Convergence Theory ◽  
Simple Complex ◽  
Real Roots ◽  
Complex Roots ◽  
Appl Math

The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1<sk<2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1<s2<s3<⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.

A Research on Complex FastICA Algorithm Based UNB Signal Detection

2011 ◽  
Vol 219-220 ◽  
pp. 1584-1588
Author(s):  
Shi Kai Zhang
Keyword(s):  
Computer Simulation ◽  
Signal Detection ◽  
Cost Function ◽  
Communication Technology ◽  
Modulation Method ◽  
First Principle ◽  
Modulation Format ◽  
High Efficient ◽  
Fastica Algorithm ◽  
Potential Use

Spectrum is limited, in order to develop high efficient modem, Complex FastICA algorithm is studied about its potential use in UNB signal detection. First, principle of Complex FastICA is presented, kurtosis and cost function are analyzed, and realization of Complex FastICA is given; then, M-EBPSK modulation method is supposed as a kind of UNB modulation format, UNB-ICA model for UNB received signal with interference and noise is presented by analyzing the characteristics of M-EBPSK modulation; finally, computer simulation is done by using nosy UNB-ICA model based on Complex FastICA Algorithm, the experimental results show that Complex FastICA Algorithm can suppress the interference and improve detection BER in contrast to the traditional methods, it is hopeful that the method can be used in UNB communication technology.

scholarly journals PEMAHAMAN METODE NUMERIK MENGGUNAKAN PEMPROGRMAN MATLAB (Studi Kasus : Metode Secant)

2017 ◽  
Vol 1 (1) ◽  
pp. 89
Author(s):  
Melda Panjaitan
Keyword(s):  
Approximate Solution ◽  
Problem Solving ◽  
Numerical Methods ◽  
Numerical Method ◽  
Mathematical Problem ◽  
Secant Method ◽  
Mathematical Problem Solving ◽  
Real Solution ◽  
True Solution ◽  
Solution Approach

Abstract - The numerical method is a powerful mathematical problem solving tool. With numerical methods, we get a solution that approaches or approaches a true solution so that a numerical solution is also called an approximate solution or solution approach, but almost the solution can be made as accurately as we want. The solution almost certainly isn't exactly the same as the real solution, so there is a difference between the two. This difference is called an error. the solution using numerical methods is always in the form of numbers. The secant method requires two initial estimates that must enclose the roots of the equation. Keywords - Numerical Method, Secant Method

A Method for Extracting Signals with Specific Normalized Kurtosis Range

2013 ◽  
Vol 756-759 ◽  
pp. 3845-3848
Author(s):  
Yong Jian Zhao ◽  
Mei Xia Qu ◽  
Hai Ning Jiang
Keyword(s):  
A Priori ◽  
Signal Separation ◽  
Blind Signal Separation ◽  
Validity And Reliability ◽  
Original Source ◽  
Blind Source Extraction ◽  
Blind Signal ◽  
Extraction Algorithm ◽  
Fastica Algorithm ◽  
Source Extraction

The famous FastICA algorithm has been widely used for blind signal separation. For every process, it only converges to an original source which has the maximum negentropy of the underlying signals. To ensure the first output is the desired signal, we incorporate a priori knowledge as a constraint into the FastICA algorithm to construct a robust blind source extraction algorithm. One can extract the desired signal if its normalized kurtosis is known to lie in a specific range, whereas other unwanted signals do not belong to this range. Experimental results on biomedical signals illustrate the validity and reliability of the proposed method.

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