Filtering Random Graph Processes Over Random Time-Varying Graphs

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochastic- ity in both the graph topology as well as the signal itself. To bridge this gap, we examine the statistical behavior of the two key filter types, finite impulse response (FIR) and autoregressive moving average (ARMA) graph filters, when operating on random time- varying graph signals (or random graph processes) over random time-varying graphs. Our analysis shows that (i) in expectation, the filters behave as the same deterministic filters operating on a deterministic graph, being the expected graph, having as input signal a deterministic signal, being the expected signal, and (ii) there are meaningful upper bounds for the variance of the filter output. We conclude the paper by proposing two novel ways of exploiting randomness to improve (joint graph-time) noise cancellation, as well as to reduce the computational complexity of graph filtering. As demonstrated by numerical results, these methods outperform the disjoint average and denoise algorithm, and yield a (up to) four times complexity redution, with very little difference from the optimal solution

Learning algorithms for adaptive digital filtering

In this thesis, we consider the problem of parameter optimisation in adaptive digital filtering. Adaptive digital filtering can be accomplished using both Finite Impulse Response (FIR) filters and Infinite Impulse Response Filters (IIR) filters. Adaptive FIR filtering algorithms are well established. However, the potential computational advantages of IIR filters has led to an increase in research on adaptive IIR filtering algorithms. These algorithms are studied in detail in this thesis and the limitations of current adaptive IIR filtering algorithms are identified. New approaches to adaptive IIR filtering using intelligent learning algorithms are proposed. These include Stochastic Learning Automata, Evolutionary Algorithms and Annealing Algorithms. Each of these techniques are used for the filtering problem and simulation results are presented showing the performance of the algorithms for adaptive IIR filtering. The relative merits and demerits of the different schemes are discussed. Two practical applications of adaptive IIR filtering are simulated and results of using the new adaptive strategies are presented. Other than the new approaches used, two new hybrid schemes are proposed based on concepts from genetic algorithms and annealing. It is shown with the help of simulation studies, that these hybrid schemes provide a superior performance to the exclusive use of any one scheme

A study on adaptive filtering for noise and echo cancellation.

The objective of this thesis is to investigate the adaptive filtering technique on the application of noise and echo cancellation. As a relatively new area in Digital Signal Processing (DSP), adaptive filters have gained a lot of popularity in the past several decades due to the advantages that they can deal with time-varying digital system and they do not require a priori knowledge of the statistics of the information to be processed. Adaptive filters have been successfully applied in a great many areas such as communications, speech processing, image processing, and noise/echo cancellation. Since Bernard Widrow and his colleagues introduced adaptive filter in the 1960s, many researchers have been working on noise/echo cancellation by using adaptive filters with different algorithms. Among these algorithms, normalized least mean square (NLMS) provides an efficient and robust approach, in which the model parameters are obtained on the base of mean square error (MSE). The choice of a structure for the adaptive filters also plays an important role on the performance of the algorithm as a whole. For this purpose, two different filter structures: finite impulse response (FIR) filter and infinite impulse response (IIR) filter have been studied. The adaptive processes with two kinds of filter structures and the aforementioned algorithm have been implemented and simulated using Matlab.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .J53. Source: Masters Abstracts International, Volume: 44-01, page: 0472. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Volterra and general polynomial related filtering

Journal ArticleThis paper presents a review of polynomial filtering and, in particular, of tlie truncated Volterra filters. Following the introduction of the general properties of such filters, issues such as eficieiit realizations, design, adaptive algoritlims and stability are discussed

The application of genetic algorithms to the adaptation of IIR filters

The adaptation of an IIR filter is a very difficult problem due to its non-quadratic performance surface and potential instability. Conventional adaptive IIR algorithms suffer from potential instability problems and a high cost for stability monitoring. Therefore, there is much interest in adaptive IIR filters based on alternative algorithms. Genetic algorithms are a family of search algorithms based on natural selection and genetics. They have been successfully used in many different areas. Genetic algorithms applied to the adaptation of IIR filtering problems are studied in this thesis, and show that the genetic algorithm approach has a number of advantages over conventional gradient algorithms, particularly, for the adaptation of high order adaptive IIR filters, IIR filters with poles close to the unit circle and IIR filters with multi-modal error surfaces. The conventional gradient algorithms have difficulty solving these problems. Coefficient results are presented for various orders of IIR filters in this thesis. In the computer simulations presented in this thesis, the direct, cascade, parallel and lattice form IIR filter structures have been used and compared. The lattice form IIR filter structure shows its superiority over the cascade and parallel form IIR filter structures in terms of its mean square error convergence performance

Single-ensemble-based eigen-processing methods for color flow imaging-Part I. the Hankel-SVD filter

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slow- time ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen- space dimension estimated from a frequency-based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: (1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter- to-blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter- downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving- tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi-ensemble- based eigen-filter (which showed a 2 to 3 dB separation). © 2006 IEEE.published_or_final_versio

Output-error LMS bilinear filters with stability monitoring

Journal ArticleABSTRACT This paper introduces output-error LMS bilinear filters with stability monitoring. Bilinear filters are recursive nonlinear systems that belong to the class of polynomial systems. Because of the feedback structure, such models are able to represent many nonlinear systems efficiently. However, the usefulness of adaptive bilinear filters is greatly restricted unless they are guaranteed to perform in a stable manner. A stability monitoring scheme is proposed to overcome the stability problem. The paper concludes with simulation results that demonstrate the usefulness of oiir technique

Acoustic Echo Cancellation and their Application in ADF

In this paper, we present an overview of the principal, structure and the application of the echo cancellation and kind of application to improve the performance of the systems. Echo is a process in which a delayed and distorted version o the original sound or voice signal is reflected back to the source. For the acoustic echo canceller much and more study are required to make the good tracking speed fast and reduce the computational complexity. Due to the increasing the processing requirement, widespread implementation had to wait for advances in LSI, VLSI echo canceller appeared. DOI: 10.17762/ijritcc2321-8169.150513