scholarly journals Some properties and algorithms for fourth order spectral analysis of complex signals

2002 ◽  
Author(s):  
C. Huet ◽  
J. Le Roux
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Complex Signals

scholarly journals On Singular Dissipative Fourth-Order Differential Operator in Lim-4 Case

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ekin Uğurlu ◽  
Elgiz Bairamov
Keyword(s):  
Spectral Analysis ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Inverse Operator ◽  
Order Differential Operator ◽  
Associated Functions ◽  
Fourth Order Differential Operator

A singular dissipative fourth-order differential operator in lim-4 case is considered. To investigate the spectral analysis of this operator, it is passed to the inverse operator with the help of Everitt's method. Finally, using Lidskiĭ's theorem, it is proved that the system of all eigen- and associated functions of this operator (also the boundary value problem) is complete.

Higher-order spectral analysis of complex signals

2006 ◽  
Vol 86 (11) ◽  
pp. 3321-3333 ◽  
Author(s):  
Peter J. Schreier ◽  
Louis L. Scharf
Keyword(s):  
Spectral Analysis ◽  
Higher Order ◽  
Complex Signals

scholarly journals Dynamic Behaviors of Soliton Solutions for a Three-Coupled Lakshmanan-Porsezian-Daniel Model

2021 ◽  
Author(s):  
Beibei Hu ◽  
Ji Lin ◽  
Ling Zhang
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Nonlinear Dynamical ◽  
Jump Matrix ◽  
Dynamical Behaviors ◽  
Helical Protein ◽  
Order Dispersion ◽  
Dispersion Term

Abstract In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4×4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

scholarly journals Periodogram estimating the spectral power density based upon signals’ binary-sign stochastic quantization using window functions

2021 ◽  
Vol 20 (2) ◽  
pp. 341-370
Author(s):  
Vladimir Yakimov
Keyword(s):  
Spectral Analysis ◽  
Discrete Event ◽  
Frequency Resolution ◽  
Dominant Factor ◽  
Stochastic Quantization ◽  
Digital Form ◽  
Complex Signals ◽  
Multiplicative Complexity ◽  
Event Modeling ◽  
Window Functions

Spectral analysis of signals is used as one of the main methods for studying systems and objects of various physical natures. Under conditions of a priori statistical uncertainty, the signals are subject to random changes and noise. Spectral analysis of such signals involves the estimation of the power spectral density (PSD). One of the classical methods for estimating PSD is the periodogram method. The algorithms that implement this method in digital form are based on the discrete Fourier transform. Digital multiplication operations are mass operations in these algorithms. The use of window functions leads to an increase in the number of these operations. Multiplication operations are among the most time consuming operations. They are the dominant factor in determining the computational capabilities of an algorithm and determine its multiplicative complexity. The paper deals with the problem of reducing the multiplicative complexity of calculating the periodogram estimate of the PSD using window functions. The problem is solved based on the use of binary-sign stochastic quantization for converting a signal into digital form. This two-level signal quantization is carried out without systematic error. Based on the theory of discrete-event modeling, the result of a binary-sign stochastic quantization in time is considered as a chronological sequence of significant events determined by the change in its values. The use of a discrete-event model for the result of binary-sign stochastic quantization provided an analytical calculation of integration operations during the transition from the analog form of the periodogram estimation of the SPM to the mathematical procedures for calculating it in discrete form. These procedures became the basis for the development of a digital algorithm. The main computational operations of the algorithm are addition and subtraction arithmetic operations. Reducing the number of multiplication operations decreases the overall computational complexity of the PSD estimation. Numerical experiments were carried out to study the algorithm operation. They were carried out on the basis of simulation modeling of the discrete-event procedure of binary-sign stochastic quantization. The results of calculating the PSD estimates are presented using a number of the most famous window functions as an example. The results obtained indicate that the use of the developed algorithm allows calculating periodogram estimates of PSD with high accuracy and frequency resolution in the presence of additive white noise at a low signal-to-noise ratio. The practical implementation of the algorithm is carried out in the form of a functionally independent software module. This module can be used as a part of complex metrologically significant software for operational analysis of the frequency composition of complex signals.

Spectral analysis of a fourth-order differential pencil on the whole real line

2012 ◽  
Vol 85 (1) ◽  
pp. 57-59
Author(s):  
S. S. Mirzoev ◽  
E. G. Orudzhev ◽  
A. R. Aliev
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Real Line
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