32,267 research outputs found
Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform
The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT
Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms
The Heisenberg uncertainty principle of harmonic analysis plays an important role in modern applied mathematical applications, signal processing and physics community. The generalizations and extensions of the classical uncertainty principle to the novel transforms are becoming one of the most hottest research topics recently. In this paper, we firstly obtain the uncertainty principle for Wigner-Ville distribution and ambiguity function associate with the linear canonical transform, and then the -dimensional cases are investigated in detail based on the proposed Heisenberg uncertainty principle of the -dimensional linear canonical transform
Immirzi Ambiguity in the Kinematics of Quantum General Relativity
The Immirzi ambiguity arises in loop quantum gravity when geometric operators
are represented in terms of different connections that are related by means of
an extended Wick transform. We analyze the action of this transform in gravity
coupled with matter fields and discuss its analogy with the Wick rotation on
which the Thiemann transform between Euclidean and Lorentzian gravity is based.
In addition, we prove that the effect of this extended Wick transform is
equivalent to a constant scale transformation as far as the symplectic
structure and kinematical constraints are concerned. This equivalence is broken
in the dynamical evolution. Our results are applied to the discussion of the
black hole entropy in the limit of large horizon areas. We first argue that,
since the entropy calculation is performed for horizons of fixed constant area,
one might in principle choose an Immirzi parameter that depends on this
quantity. This would spoil the linearity with the area in the entropy formula.
We then show that the Immirzi parameter appears as a constant scaling in all
the steps where dynamical information plays a relevant role in the entropy
calculation. This fact, together with the kinematical equivalence of the
Immirzi ambiguity with a change of scale, is used to preclude the potential
non-linearity of the entropy on physical grounds.Comment: very minor stylistic changes, version published in Phys. Rev.
Basic Filters for Convolutional Neural Networks Applied to Music: Training or Design?
When convolutional neural networks are used to tackle learning problems based
on music or, more generally, time series data, raw one-dimensional data are
commonly pre-processed to obtain spectrogram or mel-spectrogram coefficients,
which are then used as input to the actual neural network. In this
contribution, we investigate, both theoretically and experimentally, the
influence of this pre-processing step on the network's performance and pose the
question, whether replacing it by applying adaptive or learned filters directly
to the raw data, can improve learning success. The theoretical results show
that approximately reproducing mel-spectrogram coefficients by applying
adaptive filters and subsequent time-averaging is in principle possible. We
also conducted extensive experimental work on the task of singing voice
detection in music. The results of these experiments show that for
classification based on Convolutional Neural Networks the features obtained
from adaptive filter banks followed by time-averaging perform better than the
canonical Fourier-transform-based mel-spectrogram coefficients. Alternative
adaptive approaches with center frequencies or time-averaging lengths learned
from training data perform equally well.Comment: Completely revised version; 21 pages, 4 figure
A survey of uncertainty principles and some signal processing applications
The goal of this paper is to review the main trends in the domain of
uncertainty principles and localization, emphasize their mutual connections and
investigate practical consequences. The discussion is strongly oriented
towards, and motivated by signal processing problems, from which significant
advances have been made recently. Relations with sparse approximation and
coding problems are emphasized
- …