Digital Filtering Problems Research Articles

Evaluation of spline functions for digital filtering problems

Methods for the evaluation of spline functions for digital filtering in data processing systems are developed. Basis polynomials of general form and basis discrete orthogonal polynomials are considered. Computations are organized by solving constrained optimization problems. Recurrences for the system of normalized discrete orthogonal polynomials and their derivatives are obtained. The proposed spline functions on discrete orthogonal polynomials reduce the computational cost and approximation errors compared with the case of general polynomials. The results of the statistical simulation of the application of spline functions based on discrete orthogonal polynomials in digital filtering problems are presented.

Noise Reduction Algorithms in a Generalized Transform Domain

Noise reduction for speech applications is often formulated as a digital filtering problem, where the clean speech estimate is obtained by passing the noisy speech through a linear filter/transform. With such a formulation, the core issue of noise reduction becomes how to design an optimal filter (based on the statistics of the speech and noise signals) that can significantly suppress noise without introducing perceptually noticeable speech distortion. The optimal filters can be designed either in the time or in a transform domain. The advantage of working in a transform space is that, if the transform is selected properly, the speech and noise signals may be better separated in that space, thereby enabling better filter estimation and noise reduction performance. Although many different transforms exist, most efforts in the field of noise reduction have been focused only on the Fourier and Karhunen-Loeve transforms. Even with these two, no formal study has been carried out to investigate which transform can outperform the other. In this paper, we reformulate the noise reduction problem into a more generalized transform domain. We will show some of the advantages of working in this generalized domain, such as 1) different transforms can be used to replace each other without any requirement to change the algorithm (optimal filter) formulation, and 2) it is easier to fairly compare different transforms for their noise reduction performance. We will also address how to design different optimal and suboptimal filters in such a generalized transform domain.

Construction of optimal algorithms for mass computations in digital filtering problems

Theoretical results are reviewed that are concerned with the construction of speed-optimal parallel-pipeline algorithms for mass calculations in solving filtering problems. The optimality is proved in the corresponding classes of algorithms equivalent in terms of information graphs. The effectiveness of using the developed algorithmic constructions for filtering problems is investigated.

Signal analysis and identification for induction motor sensorless control

This paper presents signal analysis and identification methods for achieving sensorless vector control of induction motors. The sensorless scheme is based on high frequency signal injection for operating at low and zero speed. The identification is done using least square algorithm and sliding discrete Fourier transform. Analog and digital filtering problems are also discussed. Simulation and experimental results are presented to confirm theoretical studies.

Time-domain simulation of two electrons in a quantum dot

A time-domain simulation method is presented that utilizes the Hartree–Fock formulation to characterize two particles in a quantum dot. The basis of the simulation is the finite-difference time-domain method. The computation is made tractable by formulating the Coulomb and exchange terms as digital filtering problems, and utilizing two-dimensional fast Fourier transforms. Two-electron wave packet dynamics are calculated.

Algorithms with Limited Parallelism for Solving One Digital Filtering Problem

Algorithms with Limited Parallelism for Solving One Digital Filtering Problem

On Optimal in One Class Algorithm for Solving Three-Dimensional Digital Filtering Problem

On Optimal in One Class Algorithm for Solving Three-Dimensional Digital Filtering Problem

Digital filtering techniques for use with the FDTD method

In recent years, the finite-difference time-domain (FDTD) method has been used to simulate a wide range of frequency dependent media. The accuracy of these simulations often depends on how accurately the complex dielectric constant is simulated in the sampled time domain used by FDTD. This paper describes the process of modelling the complex dielectric constant as a digital filtering problem and uses Z transforms to convert the frequency domain expression to a sampled time domain expression. Copyright © 1999 John Wiley & Sons, Ltd.

Digital filtering techniques for use with the FDTD method

In recent years, the finite-difference time-domain (FDTD) method has been used to simulate a wide range of frequency dependent media. The accuracy of these simulations often depends on how accurately the complex dielectric constant is simulated in the sampled time domain used by FDTD. This paper describes the process of modelling the complex dielectric constant as a digital filtering problem and uses Z transforms to convert the frequency domain expression to a sampled time domain expression. Copyright © 1999 John Wiley & Sons, Ltd.

Z-transform theory and the FDTD method

In implementing the finite-difference time-domain (FDTD) method on materials which are dispersive or nonlinear, the relationship between the flux density and the electric field can be the most complicated part of the problem. Because the FDTD method is a sampled time-domain method, this relationship can be can be looked upon as a digital filtering problem. The Z transform is typically used in digital filtering and signal processing problems. The paper illustrates the use of the Z transform in implementing the FDTD method where complicated dispersive or nonlinear materials are involved.

A note on the evaluation of complex integrals using filtering interpretations

The evaluation of complex integrals of the form r_{k} = \frac{1}{2\pij}\oint H(z) H(z^{-1}) z^{k}\frac{dz}{z} for all k is frequently required in control, communications, and digital filtering problems. The major drawback of all existing methods is that the evaluation of the integral has to be preceded or followed by a check of the stability of the transfer function H(z) to ensure that {r_{k}}\min{-\infin}\max{+\infin} is a true correlation sequence. In this correspondence we modify the method proposed in [1] to yield a simple linear algorithm that does not require a separate cheek for the stability of H(z) . The filtering interpretations proposed in [1] are extended to the evaluation of more general complex integrals with integrands of the form H(z) G(z^{-1}) . Finally, an algorithm using the Levinson recursions is presented as a fast method to generate correlation sequences in the ARMA case.

Randomly sampled digital filters

The concept of a randomly sampled digital filter is introduced and formulated in this paper. An equivalent problem, which is of utmost importance in digital filtering, is also considered, namely, the problem of digital filtering with faulty samplers. Error analysis is carried out in two different approaches: 1) frequency response method, and 2) worst-case analysis. With the confirmation of experimental verification, very simple formulas are derived that are applicable under different realistic assumptions, and are most appealing to practical design purposes.