12,526 research outputs found
Adaptive signal processing algorithms for noncircular complex data
The complex domain provides a natural processing framework for a large class of signals
encountered in communications, radar, biomedical engineering and renewable
energy. Statistical signal processing in C has traditionally been viewed as a straightforward
extension of the corresponding algorithms in the real domain R, however,
recent developments in augmented complex statistics show that, in general, this leads
to under-modelling. This direct treatment of complex-valued signals has led to advances
in so called widely linear modelling and the introduction of a generalised
framework for the differentiability of both analytic and non-analytic complex and
quaternion functions. In this thesis, supervised and blind complex adaptive algorithms
capable of processing the generality of complex and quaternion signals (both
circular and noncircular) in both noise-free and noisy environments are developed;
their usefulness in real-world applications is demonstrated through case studies.
The focus of this thesis is on the use of augmented statistics and widely linear modelling.
The standard complex least mean square (CLMS) algorithm is extended to
perform optimally for the generality of complex-valued signals, and is shown to outperform
the CLMS algorithm. Next, extraction of latent complex-valued signals from
large mixtures is addressed. This is achieved by developing several classes of complex
blind source extraction algorithms based on fundamental signal properties such
as smoothness, predictability and degree of Gaussianity, with the analysis of the existence
and uniqueness of the solutions also provided. These algorithms are shown
to facilitate real-time applications, such as those in brain computer interfacing (BCI).
Due to their modified cost functions and the widely linear mixing model, this class of
algorithms perform well in both noise-free and noisy environments. Next, based on a
widely linear quaternion model, the FastICA algorithm is extended to the quaternion
domain to provide separation of the generality of quaternion signals. The enhanced
performances of the widely linear algorithms are illustrated in renewable energy and
biomedical applications, in particular, for the prediction of wind profiles and extraction
of artifacts from EEG recordings
Predictable Feature Analysis
Every organism in an environment, whether biological, robotic or virtual,
must be able to predict certain aspects of its environment in order to survive
or perform whatever task is intended. It needs a model that is capable of
estimating the consequences of possible actions, so that planning, control, and
decision-making become feasible. For scientific purposes, such models are
usually created in a problem specific manner using differential equations and
other techniques from control- and system-theory. In contrast to that, we aim
for an unsupervised approach that builds up the desired model in a
self-organized fashion. Inspired by Slow Feature Analysis (SFA), our approach
is to extract sub-signals from the input, that behave as predictable as
possible. These "predictable features" are highly relevant for modeling,
because predictability is a desired property of the needed
consequence-estimating model by definition. In our approach, we measure
predictability with respect to a certain prediction model. We focus here on the
solution of the arising optimization problem and present a tractable algorithm
based on algebraic methods which we call Predictable Feature Analysis (PFA). We
prove that the algorithm finds the globally optimal signal, if this signal can
be predicted with low error. To deal with cases where the optimal signal has a
significant prediction error, we provide a robust, heuristically motivated
variant of the algorithm and verify it empirically. Additionally, we give
formal criteria a prediction-model must meet to be suitable for measuring
predictability in the PFA setting and also provide a suitable default-model
along with a formal proof that it meets these criteria
Communication Theoretic Data Analytics
Widespread use of the Internet and social networks invokes the generation of
big data, which is proving to be useful in a number of applications. To deal
with explosively growing amounts of data, data analytics has emerged as a
critical technology related to computing, signal processing, and information
networking. In this paper, a formalism is considered in which data is modeled
as a generalized social network and communication theory and information theory
are thereby extended to data analytics. First, the creation of an equalizer to
optimize information transfer between two data variables is considered, and
financial data is used to demonstrate the advantages. Then, an information
coupling approach based on information geometry is applied for dimensionality
reduction, with a pattern recognition example to illustrate the effectiveness.
These initial trials suggest the potential of communication theoretic data
analytics for a wide range of applications.Comment: Published in IEEE Journal on Selected Areas in Communications, Jan.
201
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