75 research outputs found
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
Sampling from a system-theoretic viewpoint: Part I - Concepts and tools
This paper is first in a series of papers studying 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. In this paper we present the paradigm and revise underlying technical tools, such as the lifting technique and some topics of the operator theory. This material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems, recovering many hitherto considered different solutions and leading to new results. Some of these applications are discussed in the second part
Recent Advances in Theory and Methods for Nonstationary Signal Analysis
Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing
time series, it should be remembered that nature can
be amazingly complex and that many of the theoretical
constructs used in stochastic process theory, for example,
linearity, ergodicity, normality, and particularly stationarity,
are mathematical fairy tales. There are no stationary time
series in the strict mathematical sense; at the very least, everything
has a beginning and an end. Thus, while it is necessary
to know the theory of stationary processes, one should not
adhere to it dogmatically when analyzing data from physical
sources, particularly when the observations span an extended
period. Nonstationary signals are appropriate models for
signals arising in several fields of applications including
communications, speech and audio, mechanics, geophysics,
climatology, solar and space physics, optics, and biomedical
engineering. Nonstationary models account for possible time
variations of statistical functions and/or spectral characteristics
of signals. Thus, they provide analysis tools more general
than the classical Fourier transform for finite-energy signals
or the power spectrum for finite-power stationary signals.
Nonstationarity, being a “nonproperty” has been analyzed
from several different points of view. Several approaches
that generalize the traditional concepts of Fourier analysis
have been considered, including time-frequency, time-scale,
and wavelet analysis, and fractional Fourier and linear
canonical transforms
Recent Advances in Theory and Methods for Nonstationary Signal Analysis
Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing
time series, it should be remembered that nature can
be amazingly complex and that many of the theoretical
constructs used in stochastic process theory, for example,
linearity, ergodicity, normality, and particularly stationarity,
are mathematical fairy tales. There are no stationary time
series in the strict mathematical sense; at the very least, everything
has a beginning and an end. Thus, while it is necessary
to know the theory of stationary processes, one should not
adhere to it dogmatically when analyzing data from physical
sources, particularly when the observations span an extended
period. Nonstationary signals are appropriate models for
signals arising in several fields of applications including
communications, speech and audio, mechanics, geophysics,
climatology, solar and space physics, optics, and biomedical
engineering. Nonstationary models account for possible time
variations of statistical functions and/or spectral characteristics
of signals. Thus, they provide analysis tools more general
than the classical Fourier transform for finite-energy signals
or the power spectrum for finite-power stationary signals.
Nonstationarity, being a “nonproperty” has been analyzed
from several different points of view. Several approaches
that generalize the traditional concepts of Fourier analysis
have been considered, including time-frequency, time-scale,
and wavelet analysis, and fractional Fourier and linear
canonical transforms
Extended GFDM Framework: OTFS and GFDM Comparison
Orthogonal time frequency space modulation (OTFS) has been recently proposed
to achieve time and frequency diversity, especially in linear time-variant
(LTV) channels with large Doppler frequencies. The idea is based on the
precoding of the data symbols using symplectic finite Fourier transform (SFFT)
then transmitting them by mean of orthogonal frequency division multiplexing
(OFDM) waveform. Consequently, the demodulator and channel equalization can be
coupled in one processing step. As a distinguished feature, the demodulated
data symbols have roughly equal gain independent of the channel selectivity. On
the other hand, generalized frequency division multiplexing (GFDM) modulation
also employs the spreading over the time and frequency domains using circular
filtering. Accordingly, the data symbols are implicitly precoded in a similar
way as applying SFFT in OTFS. In this paper, we present an extended
representation of GFDM which shows that OTFS can be processed as a GFDM signal
with simple permutation. Nevertheless, this permutation is the key factor
behind the outstanding performance of OTFS in LTV channels, as demonstrated in
this work. Furthermore, the representation of OTFS in the GFDM framework
provides an efficient implementation, that has been intensively investigated
for GFDM, and facilitates the understanding of the OTFS distinct features.Comment: Accepted in IEEE Global Communications Conference 9-13 December 2018
Abu Dhabi, UA
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