Filter Bank Fusion Frames

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of noise and erasures. However, up to this point, few implementable constructions of such frames were known; we show how to construct them using oversampled filter banks. In this work, we first provide polyphase domain characterizations of filter bank fusion frames. We then use these characterizations to construct filter bank fusion frame versions of discrete wavelet and Gabor transforms, emphasizing those specific finite impulse response filters whose frequency responses are well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas

Analysis and design of multirate-multivariable sampled data systems

Imperial Users onl

On optimal design and applications of linear transforms

Linear transforms are encountered in many fields of applied science and engineering. In the past, conventional block transforms provided acceptable answers to different practical problems. But now, under increasing competitive pressures, with the growing reservoir of theory and a corresponding development of computing facilities, a real demand has been created for methods that systematically improve performance. As a result the past two decades have seen the explosive growth of a class of linear transform theory known as multiresolution signal decomposition. The goal of this work is to design and apply these advanced signal processing techniques to several different problems. The optimal design of subband filter banks is considered first. Several design examples are presented for M-band filter banks. Conventional design approaches are found to present problems when the number of constraints increases. A novel optimization method is proposed using a step-by-step design of a hierarchical subband tree. This method is shown to possess performance improvements in applications such as subband image coding. The subband tree structuring is then discussed and generalized algorithms are presented. Next, the attention is focused on the interference excision problem in direct sequence spread spectrum (DSSS) communications. The analytical and experimental performance of the DSSS receiver employing excision are presented. Different excision techniques are evaluated and ranked along with the proposed adaptive subband transform-based excises. The robustness of the considered methods is investigated for either time-localized or frequency-localized interferers. A domain switchable excision algorithm is also presented. Finally, sonic of the ideas associated with the interference excision problem are utilized in the spectral shaping of a particular biological signal, namely heart rate variability. The improvements for the spectral shaping process are shown for time-frequency analysis. In general, this dissertation demonstrates the proliferation of new tools for digital signal processing

Covariance-Based Estimation for Clustered Sensor Networks Subject to Random Deception Attacks

In this paper, a cluster-based approach is used to address the distributed fusion estimation problem (filtering and fixed-point smoothing) for discrete-time stochastic signals in the presence of random deception attacks. At each sampling time, measured outputs of the signal are provided by a networked system, whose sensors are grouped into clusters. Each cluster is connected to a local processor which gathers the measured outputs of its sensors and, in turn, the local processors of all clusters are connected with a global fusion center. The proposed cluster-based fusion estimation structure involves two stages. First, every single sensor in a cluster transmits its observations to the corresponding local processor, where least-squares local estimators are designed by an innovation approach. During this transmission, deception attacks to the sensor measurements may be randomly launched by an adversary, with known probabilities of success that may be different at each sensor. In the second stage, the local estimators are sent to the fusion center, where they are combined to generate the proposed fusion estimators. The covariance-based design of the distributed fusion filtering and fixed-point smoothing algorithms does not require full knowledge of the signal evolution model, but only the first and second order moments of the processes involved in the observation model. Simulations are provided to illustrate the theoretical results and analyze the effect of the attack success probability on the estimation performance.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)

Digital flight control systems

The design of stable feedback control laws for sampled-data systems with variable rate sampling was investigated. These types of sampled-data systems arise naturally in digital flight control systems which use digital actuators where it is desirable to decrease the number of control computer output commands in order to save wear and tear of the associated equipment. The design of aircraft control systems which are optimally tolerant of sensor and actuator failures was also studied. Detection of the failed sensor or actuator must be resolved and if the estimate of the state is used in the control law, then it is also desirable to have an estimator which will give the optimal state estimate even under the failed conditions

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

Sampling from a system-theoretic viewpoint

This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. \ud \ud The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the $L^2$-norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is $l$-causal for a given $l\geq 0,$ i.e., that its impulse response is zero in the time interval $(-\infty,-l h),$ where $h$ is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function

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

Compressive Spectrum Sensing in Cognitive IoT

PhDWith the rising of new paradigms in wireless communications such as Internet of things (IoT), current static frequency allocation policy faces a primary challenge of spectrum scarcity, and thus encourages the IoT devices to have cognitive capabilities to access the underutilised spectrum in the temporal and spatial dimensions. Wideband spectrum sensing is one of the key functions to enable dynamic spectrum access, but entails a major implementation challenge in terms of sampling rate and computation cost since the sampling rate of analog-to-digital converters (ADCs) should be higher than twice of the spectrum bandwidth based on the Nyquist-Shannon sampling theorem. By exploiting the sparse nature of wideband spectrum, sub-Nyquist sampling and sparse signal recovery have shown potential capabilities in handling these problems, which are directly related to compressive sensing (CS) from the viewpoint of its origin. To invoke sub-Nyquist wideband spectrum sensing in IoT, blind signal acquisition with low-complexity sparse recovery is desirable on compact IoT devices. Moreover, with cooperation among distributed IoT devices, the complexity of sampling and reconstruc- tion can be further reduced with performance guarantee. Specifically, an adaptively- regularized iterative reweighted least squares (AR-IRLS) reconstruction algorithm is proposed to speed up the convergence of reconstruction with less number of iterations. Furthermore, a low-complexity compressive spectrum sensing algorithm is proposed to reduce computation complexity in each iteration of IRLS-based reconstruction algorithm, from cubic time to linear time. Besides, to transfer computation burden from the IoT devices to the core network, a joint iterative reweighted sparse recovery scheme with geo-location database is proposed to adopt the occupied channel information from geo- location database to reduce the complexity in the signal reconstruction. Since numerous IoT devices access or release the spectrum randomly, the sparsity levels of wideband spec-trum signals are varying and unknown. A blind CS-based sensing algorithm is proposed to enable the local secondary users (SUs) to adaptively adjust the sensing time or sam- pling rate without knowledge of spectral sparsity. Apart from the signal reconstruction at the back-end, a distributed sub-Nyquist sensing scheme is proposed by utilizing the surrounding IoT devices to jointly sample the spectrum based on the multi-coset sam- pling theory, in which only the minimum number of low-rate ADCs on the IoT devices are required to form coset samplers without the prior knowledge of the number of occu- pied channels and signal-to-noise ratios. The models of the proposed algorithms are derived and verified by numerical analyses and tested on both real-world and simulated TV white space signals