Abstruct-The discrete wavelet decomposition of second-order harmonizable random processes is considered. The deterministic wavelet decomposition of a complex exponential is examined, where its pointwise and bounded convergence to the function is proved. This result is then used for establishing the stochastic wavelet decomposition of harmonizable processes. The similarities and differences betw...

In our recent work we have introduced a framework for extracting features from solid of mechanical artifacts in polyhedral representation based on scale-space feature decomposition [1]. Our approach used recent developments in efficient hierarchical decomposition of metric data using its spectral properties. In that work, through spectral decomposition, we were able to reduce the problem of mat...

Category decomposition method for un-mixing of mixels (Mixed Pixels) which is acquired with spaceborne based visible to near infrared radiometers by means of Maximum Entropy Method (MEM) with parameter estimation based on Simulated Annealing: SA is proposed. Through simulation studies with spectral characteristics of the ground cover targets which are derived from spectral library and actual re...

Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation’s effectivity properties on the sound formal basis of computable analysi...

Given an undamped gyroscopic system GðλÞ 1⁄4 Mλ þ CλþK with M , K symmetric and C skew-symmetric, this paper presents a real-valued spectral decomposition of GðλÞ by a real standard pair ðX;TÞ and a skew-symmetric parameter matrix S . When T is assumed to be a block diagonal matrix, the parameter matrix S has a special structure. This spectral decomposition is applied to solve the quadratic inv...

Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging leads to a time-series decomposition. In this algorithm, a single free parameter, window length K, is involved which is the FIR filter length for the time series. There are no generally accepted criter...

The Leverrier-Faddeev algorithm, as modified by Gower (1980), is little-known but is useful for deriving the algebraic, rather than numerical, spectral structure of matrices occurring in statistical methodology. An example is given of deriving explicit forms for the singular value decomposition of any block-circulant matrix and the spectral decomposition of any symmetric block-circulant matrix....

In this paper we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are una...

Finite type subshifts with finite number of symbols are important sort of discrete dynamical systems (often called symbolic dynamics) and are intensively studied [2, 3, 4, 5, 6]. Mañé proved a theorem (for finite type subshifts generated by 0, 1-square matrices), stating that topological transitivity and topological mixing can be reduced to algebraic properties of associated matrices [5]. In th...