Sharif Digital Repository

Employing array of antennas in amny signal processing application has received considerable attention in recent years due to major advances in design and implementation of large dimentional antennas. In many applications we deal with such large dimentional antennas which challenge the traditional signal processing algorithms. Since most of traditional signal processing algorithms assume that the number of samples is much more than the number of array elements while it is not possible to collect so many samples due to hardware and time constraints.
In this thesis we exploit new results in random matrix theory to charachterize and describe the properties of Sample Covariance Matrices... 

Let G be a graph of order n. The signless Laplacian matrix or Q-matrix of G is Q(G)=D(G)+A(G), where A(G) is the adjacency matrix of G and D(G) is diagonal degree matrix of G. The signless Laplacian characteristic polynomial or Q-polinomial of G is QG(x)=det(xI-Q(G)) and its roots are called signless Laplacian eigenvalues or Q-eigenvalues of G. If R is vertex-degree incidence matrix of G, then Q(G)=RRt. So Q(G) is a positive semi-definite matrix, i.e. its eigenvalues are none-negative. Let q1(G)≥q2(G)≥…≥qn(G) denote the signless Laplacian eigenvalues of G. A theory in which graphs are studied by means of eigenvalues of Q(G) is called signless Laplaciian theory or Q-theory.In this research,... 

Let G be a simple graph. An eigenvalue of G, is a main eigenvalue if the corresponding eigenspace has a non-orthogonal eigenvector to the all-one vector j. A signed graph is a graph with a sign to each edge. If in the adjacency matrix of background graph change elements that corresponded by -1, set -1 and in the other elements don’t make any change, then we reach the sign matrix of a signed graph. By an eigenvalue of a signed graph, we mean an eigenvalue of its sign matrix. In this research, we study main eigenvalues of graphs and signed graphs. At first, we present the necessary and sufficient conditions for any graph which has exactly m main eigenvalues. Then, by introducing and creating... 

The spectrum of a graph is related to many important combinatorial parameters. Let (G), ′(G) be the maximum number of edge-disjoint spanning trees and edge-connectivity of a graph G,respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of (G), we use eigenvalue interlacing for quotient matrix associated to graph to get the relationship between eigenvalues of a graph and bounds of (G) and ′(G). We also study the relationship between eigenvalues and bounds of (G) and ′(G) in a multigraph G. In the first chapter we prove eigenvalue interlacing and give several applications of it for obtaining bounds for characteristic numbers of... 

In this thesis, we study the treewidth of social networks. The importance of studding treewidth is for two reasons. The first is that for the graph with bounded treewidth, many optimization problems that are NP-hard in general, can be solved in polynomial or even linear time. The second is that the high value of treewidth in a graph, reflects some high degree of connectivity and robustness, which is an essential factor in designing many networks. But the problem is that determining the value of treewidth in a graph is NP-complete so, computing the treewidth of real complex networks is not feasible. We first review the related works and mention the weakness of the past works, then introduce a... 

Let G be a graph with adjacency matrix A and Δ be a diagonal matrix whose diagonal entries are the degree sequence of G. Then the matrices L = Δ− A and Q = Δ+A are called Laplacian matrix and signless Laplacian matrix of G, respectively. The eigenvalues of A, L, and Q are arranged decreasingly and denoted by λ1 ≥ · · · ≥ λn, μ1 ≥ · · · ≥ μn ≥ 0, and q1 ≥ · · · ≥ qn ≥ 0, respectively. The energy of a graph G is defined as E(G) :=
n
i=1
|λi|.
Furthermore, the incidence energy, the signed incidence energy, and the H¨uckel energy of G are
defined as
IE(G) :=
n
i=1
√
qi, LE(G) :=
n
i=1
√
μi, HE(G) :=

2
r
i=1 λi, n=... 

The Fourier modal method is one of the most important methods in the analysis of flat periodic structures (gratings). Using this method, the problem of wave propagation in the periodic medium leads to an eigenproblem, in which eigenvalues represent the propagation constants and eigenvector or eigenfunctions determine the filed distribution of the modes. On the other side, considering all the generalizations and modifications reported so far, the Fourier modal method still faces two fundamental problems. First, for problems involving large dielectric constants or high contrasts, the matrix form of the eigenproblem (the modal matrix) can be large, dense, and require a high computational cost.... 

LSB embedding in spatial domain with very low rate can be easily performed and its detection in spite of many researches is very hard, while BOSS competition has been held to break an adaptive embedding algorithm with low rate. Thus, proposing powerful steganalyzer of very low rate in spatial domain is highly requested. In this thesis it has been tried to present some algorithms to detect secret message with very low rate in spatial domain using eigenvalues analysis and relative auto-correlation of image.First approach is based on the analysis of the eigenvalues of the cover correlation matrix that we used for the first time. Image partitioning, correlation function computation,... 

Graph signals are sets of values residing on sets of nodes that are connected via edges. Graph Neural Networks (GNNs) are a type of machine learning model for working with graph-structured data, such as graph signals. GNNs have applications in graph classification, node classification, and link prediction. They can be thought of as learnable filters. In this thesis, our focus is on graph filters and enhancing the performance of GNNs. In the first part, we aim to reduce computational costs in graph signal processing, particularly in graph filters. We explore methods to transform signals to the frequency domain with lower computational cost. In the latter part, we examine regulations in... 

Blind image steganalysis is a technique used for detecting the existence of the data hidden in an image, where no information about the stenographic algorithm is available or usable. In this way, an important problem is to find sensitive features which make noticeable statistical distinction between cover and stego images. New steganalysis methods based on multi-resolution transform, specifically the wavelet and the contourlet transforms, have been proposed in this thesis in order to enhance the detection accuracy of system especially at low embedding rates. In fact, multi-resolution transforms are powerful space-frequency analysis tools that have been found quite successful in detection of... 

Blind image steganalysis is a technique used to, which require no prior information about the steganographic method applied to the stego im- age, determine whether the image contains an embedded message or not. The basic idea of blind steganalysis is to extract some features sensitive to information hiding, and then exploit classifiers for judging whether a given test image contains a secret message.The main focus of this research is to design an choose features sen-sitive to the embedding changes. In fact, we use high order moments in different domains, such as spatial, DCT and multi-resolution do-main, in order to improve the performance of existing steganalyzers.Accordingly, First, we... 

MIMO radar is a next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern, is mapped into a waveform correlation matrix (R) design in the narrowband case. Therefore, waveform design in MIMO radar for beamforming could be broken into two steps, namely correlation matrix design and waveform synthesis for achieving given R. As of now, given a desired beampattern or estimated location information of targets, calculating R has been modeled as an optimization problem like SDP. Also, in some special cases like rectangular beampattern, close form solutions for... 

Nowadays, by proliferation the basis of the phasor-based synchronous wide area measurement system (WAMS), its application for improving electromechanical oscillations damping has been considered by researchers. In interconnected power systems, inter-area modes are usually critical modes. There are two approaches for damping these modes by utilizing WAMS: 1) the traditional approach of using power system stabilizers with wide area signals; and 2) discrete corrective actions by changing the operating conditions. The first approach requires a thorough study at the design stage, installation and testing. Besides, the controller is designed for a specific operating point. Nevertheless, in the... 

Hard disk drives are the main component of computers for permanent data storage. The security of the stored data is related closely to the air gap between the read-write head and the surface of disk. This gap which is created by the aerodynamic force between head and the disk is altered continually by lateral oscillations of disk. In the extreme condition of zero gap and contact between the protective coating layer and subsequently the magnetic material of the disk with the head, the disk will be scratched and damaged. Therefore, the active or passive control of these vibrations has a particular importance in the technology of manufacturing of hard disks. The first step in active control...