Abstract: A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.
Abstract: The relationship between eigenstructure (eigenvalues
and eigenvectors) and latent structure (latent roots and latent vectors)
is established. In control theory eigenstructure is associated with
the state space description of a dynamic multi-variable system and
a latent structure is associated with its matrix fraction description.
Beginning with block controller and block observer state space forms
and moving on to any general state space form, we develop the
identities that relate eigenvectors and latent vectors in either direction.
Numerical examples illustrate this result. A brief discussion of the
potential of these identities in linear control system design follows.
Additionally, we present a consequent result: a quick and easy
method to solve the polynomial eigenvalue problem for regular matrix
polynomials.
Abstract: In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.
Abstract: Each year many people are reported missing in most of the countries in the world owing to various reasons. Arrangements have to be made to find these people after some time. So the investigating agencies are compelled to make out these people by using manpower. But in many cases, the investigations carried out to find out an absconding for a long time may not be successful. At a time like that it may be difficult to identify these people by examining their old photographs, because their facial appearance might have changed mainly due to the natural aging process. On some occasions in forensic medicine if a dead body is found, investigations should be held to make sure that this corpse belongs to the same person disappeared some time ago. With the passage of time the face of the person might have changed and there should be a mechanism to reveal the person-s identity. In order to make this process easy, we must guess and decide as to how he will look like by now. To address this problem this paper presents a way of synthesizing a facial image with the aging effects.
Abstract: Fractional Fourier Transform, which is a
generalization of the classical Fourier Transform, is a powerful tool
for the analysis of transient signals. The discrete Fractional Fourier
Transform Hamiltonians have been proposed in the past with varying
degrees of correlation between their eigenvectors and Hermite
Gaussian functions. In this paper, we propose a new Hamiltonian for
the discrete Fractional Fourier Transform and show that the
eigenvectors of the proposed matrix has a higher degree of
correlation with the Hermite Gaussian functions. Also, the proposed
matrix is shown to give better Fractional Fourier responses with
various transform orders for different signals.
Abstract: Small signal stability causes small perturbations in the
generator that can cause instability in the power network. It is
generally known that small signal stability are directly related to the
generator and load properties. This paper examines the effects of
generator input variations on power system oscillations for a small
signal stability study. Eigenvaules and eigenvectors are used to
examine the stability of the power system. The dynamic power
system's mathematical model is constructed and thus calculated using
load flow and small signal stability toolbox on MATLAB. The power
system model is based on a 3-machine 9-bus system that was
modified to suit this study. In this paper, Participation Factors are a
means to gauge the effects of variation in generation with other
parameters on the network are also incorporated.
Abstract: Principal Component Analysis (PCA) has many
different important applications especially in pattern detection
such as face detection / recognition. Therefore, for real time
applications, the response time is required to be as small as
possible. In this paper, new implementation of PCA for fast
face detection is presented. Such new implementation is
designed based on cross correlation in the frequency domain
between the input image and eigenvectors (weights).
Simulation results show that the proposed implementation of
PCA is faster than conventional one.
Abstract: In this paper we introduce an efficient solution
method for the Eigen-decomposition of bisymmetric and per
symmetric matrices of symmetric structures. Here we decompose
adjacency and Laplacian matrices of symmetric structures to submatrices
with low dimension for fast and easy calculation of
eigenvalues and eigenvectors. Examples are included to show the
efficiency of the method.
Abstract: Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.