Because of the growing interest in real-time stability monitoring, there is a need for online methods that can detect off-nominal behavior in control systems. Therefore, we present a real-time frequency domain method for detecting oscillations in control systems. The method uses recursive Fourier transform for representing the measured time domain signal in frequency domain. Oscillations are th...

We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor iX_i floor$ where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random variables, with support in [0,...

Aggregation-based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model twodimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysis ...

We describe a fast solver for the inhomogeneous heat equation in free space, following the time evolution of the solution in the Fourier domain. It relies on a recently developed spectral approximation of the free-space heat kernel coupled with the non-uniform fast Fourier transform. Unlike finite difference and finite element techniques, there is no need for artificial boundary conditions on a...

In this paper a module consisting of a Fast Least Mean Square (FLMS) filter is modeled and verified to eliminate acoustic echo, which is a problem for hands free communication. However the acoustic echo cancellation (AEC) is modeled using digital signal processing technique especially Simulink Blocksets. The needed algorithm code is generated in Matlab Simulink programming. At the simulation le...

Aggregation–based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model two– dimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysi...

This paper presents a general approach for obtaining optimal filters as well as filter sequences. A filter is termed optimal when it minimizes a chosen distance measure with respect to an ideal filter. The method allows specification of the metric via simultaneous weighting functions in multiple domains, e.g. the spatio-temporal space and the Fourier space. It is shown how convolution kernels f...

A parallel algorithm for solving the Poisson equation with either Dirichlet or Neumann conditions is presented. The solver follows some of the principles introduced in a previous fast algorithm for evaluating singular integral transforms by Daripa et. al. [8, 2]. Here we present recursive relations in Fourier space together with fast Fourier transforms which lead to a fast and accurate algorith...

We derive two new algorithms for reconstructing a discretetime 1-D signal from the phase of its discrete-time Fourier transform (DTFT) at irregular frequencies. Previous algorithms for this problem have either required the computation of a matrix nullspace, requiring O(N) computations, or have been iterative in nature; for the latter, the irregularity of the frequency samples precludes use of t...

we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...