A study on the empirical distribution of the scaled Hankel matrix eigenvalues
نویسندگان
چکیده
The empirical distribution of the eigenvalues of the matrix XX(T) divided by its trace is evaluated, where X is a random Hankel matrix. The distribution of eigenvalues for symmetric and nonsymmetric distributions is assessed with various criteria. This yields several important properties with broad application, particularly for noise reduction and filtering in signal processing and time series analysis.
منابع مشابه
A Unique Approach of Noise Elimination from Electroencephalography Signals between Normal and Meditation State
In this paper, unique approach is presented for the electroencephalography (EEG) signals analysis. This is based on Eigen values distribution of a matrix which is called as scaled Hankel matrix. This gives us a way to find out the number of Eigen values essential for noise reduction and extraction of signal in singular spectrum analysis. This paper gives us an approach to classify the EEG signa...
متن کاملEigenvalues-based LSB steganalysis
So far, various components of image characteristics have been used for steganalysis, including the histogram characteristic function, adjacent colors distribution, and sample pair analysis. However, some certain steganography methods have been proposed that can thwart some analysis approaches through managing the embedding patterns. In this regard, the present paper is intended to introduce a n...
متن کاملOn the numerical condition of a generalized Hankel eigenvalue problem
The generalized eigenvalue problem ̃ Hy= λHy with H a Hankel matrix and ̃ H the corresponding shifted Hankel matrix occurs in number of applications such as the reconstruction of the shape of a polygon from its moments, the determination of abscissa of quadrature formulas, of poles of Padé approximants, or of the unknown powers of a sparse black box polynomial in computer algebra. In many of th...
متن کاملCalculation of One-dimensional Forward Modelling of Helicopter-borne Electromagnetic Data and a Sensitivity Matrix Using Fast Hankel Transforms
The helicopter-borne electromagnetic (HEM) frequency-domain exploration method is an airborne electromagnetic (AEM) technique that is widely used for vast and rough areas for resistivity imaging. The vast amount of digitized data flowing from the HEM method requires an efficient and accurate inversion algorithm. Generally, the inverse modelling of HEM data in the first step requires a precise a...
متن کاملBalanced Random Toeplitz and Hankel Matrices
Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property–the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is sca...
متن کامل