Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

Recent Advances in Variable Digital Filters

Variable digital filters are widely used in a number of applications of signal processing because of their capability of self-tuning frequency characteristics such as the cutoff frequency and the bandwidth. This chapter introduces recent advances on variable digital filters, focusing on the problems of design and realization, and application to adaptive filtering. In the topic on design and realization, we address two major approaches: one is the frequency transformation and the other is the multi-dimensional polynomial approximation of filter coefficients. In the topic on adaptive filtering, we introduce the details of adaptive band-pass/band-stop filtering that include the well-known adaptive notch filtering

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Theory, design and application of gradient adaptive lattice filters

SIGLELD:D48933/84 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

An FPGA architecture design of a high performance adaptive notch filter

The occurrence of narrowband interference near frequencies carrying information is a common problem in modern control and signal processing applications. A very narrow notch filter is required in order to remove the unwanted signal while not compromising the integrity of the carrier signal. In many practical situations, the interference may wander within a frequency band, in which case a wider notch filter would be needed to guarantee its removal, which may also allow for the degradation of information being carried in nearby frequencies. If the interference frequency could be autonomously tracked, a narrow bandwidth notch filter could be successfully implemented for the particular frequency. Adaptive signal processing is a powerful technique that can be used in the tracking and elimination of such a signal. An application where an adaptive notch filter becomes necessary is in biomedical instrumentation, such as the electrocardiogram recorder. The recordings can become useless when in the presence of electromagnetic fields generated by power lines. Research was conducted to fully characterize the interference. Research on notch filter structures and adaptive filter algorithms has been carried out. The lattice form filter structure was chosen for its inherent stability and performance benefits. A new adaptive filter algorithm was developed targeting a hardware implementation. The algorithm used techniques from several other algorithms that were found to be beneficial. This work developed the hardware implementation of a lattice form adaptive notch filter to be used for the removal of power line interference from electrocardiogram signals. The various design tradeo s encountered were documented. The final design was targeted toward multiple field programmable gate arrays using multiple optimization efforts. Those results were then compared. The adaptive notch filter was able to successfully track and remove the interfering signal. The lattice form structure utilized by the proposed filter was verified to exhibit an inherently stable realization. The filter was subjected to various environments that modeled the different power line disturbances that could be present. The final filter design resulted in a 3 dB bandwidth of 15.8908 Hz, and a null depth of 54 dB. For the baseline test case, the algorithm achieved convergence after 270 iterations. The final hardware implementation was successfully verified against the MATLAB simulation results. A speedup of 3.8 was seen between the Xilinx Virtex-5 and Spartan-II device technologies. The final design used a small fraction of the available resources for each of the two devices that were characterized. This would allow the component to be more readily available to be added to existing projects, or further optimized by utilizing additional logic

Adaptive notch filtering for tracking multiple complex sinusoid signals

This thesis is related to the field of digital signal processing; where the aim of this research is to develop features of an infinite impulse response adaptive notch filter capable of tracking multiple complex sinusoid signals. Adaptive notch filters are commonly used in: Radar, Sonar, and Communication systems, and have the ability to track the frequencies of real or complex sinusoid signals; thus removing noise from an estimate, and enhancing the performance of a system. This research programme began by implementing four currently proposed adaptive notch structures. These structures were simulated and compared: for tracking between two and four signals; however, in their current form they are only capable of tracking real sinusoid signals. Next, one of these structures is developed further, to facilitate the ability to track complex sinusoid signals. This original structure gives superior performance over Regalia's comparable structure under certain conditions, which has been proven by simulations and results. Complex adaptive notch filter structures generally contain two parameters: the first tracks a target frequency, then the second controls the adaptive notch filter's bandwidth. This thesis develops the notch filter, so that the bandwidth parameter can be adapted via a method of steepest ascent; and also investigates tracking complex-valued chirp signals. Lastly, stochastic search methods are considered; and particle swarm optimisation has been applied to reinitialise an adaptive notch filter, when tracking two signals; thus more quickly locating an unknown frequency, after the frequency of the complex sinusoid signal jumps

The theory of linear prediction

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vector linear prediction is explained in considerable detail and so is the theory of line spectral processes. This focus and its small size make the book different from many excellent texts which cover the topic, including a few that are actually dedicated to linear prediction. There are several examples and computer-based demonstrations of the theory. Applications are mentioned wherever appropriate, but the focus is not on the detailed development of these applications. The writing style is meant to be suitable for self-study as well as for classroom use at the senior and first-year graduate levels. The text is self-contained for readers with introductory exposure to signal processing, random processes, and the theory of matrices, and a historical perspective and detailed outline are given in the first chapter