1,317 research outputs found
The degeneracy of the genetic code and Hadamard matrices
The matrix form of the presentation of the genetic code is described as the
cognitive form to analyze structures of the genetic code. A similar matrix form
is utilized in the theory of signal processing. The Kronecker family of the
genetic matrices is investigated, which is based on the genetic matrix [C A; U
G], where C, A, U, G are the letters of the genetic alphabet. This matrix in
the third Kronecker power is the (8*8)-matrix, which contains 64 triplets.
Peculiarities of the degeneracy of the vertebrate mitochondria genetic code are
reflected in the symmetrical black-and-white mosaic of this genetic
(8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard
matrices unexpectedly, which are famous in the theory of signal processing,
spectral analysis, quantum mechanics and quantum computers. A special
decomposition of numeric genetic matrices reveals their close relations with a
family of 8-dimensional hypercomplex numbers (not Cayley's octonions). Some
hypothesis and thoughts are formulated on the basis of these phenomenological
facts.Comment: 26 pages; 21 figures; added materials and reference
XFT: An Extension of the Discrete Fractional Fourier Transform
In recent years there has been a growing interest in the fractional Fourier
transform driven by its large number of applications. The literature in this
field follows two main routes. On the one hand, the areas where the ordinary
Fourier transform has been applied are being revisited to use this intermediate
time-frequency representation of signals, and on the other hand, fast
algorithms for numerical computation of the fractional Fourier transform are
devised. In this paper we derive a Gaussian-like quadrature of the continuous
fractional Fourier transform. This quadrature is given in terms of the Hermite
polynomials and their zeros. By using some asymptotic formulas, we rewrite the
quadrature as a chirp-fft-chirp transformation, yielding a fast discretization
of the fractional Fourier transform and its inverse in closed form. We extend
the range of the fractional Fourier transform by considering arbitrary complex
values inside the unitary circle and not only at the boundary. We find that,
the chirp-fft-chirp transformation evaluated at z=i, becomes a more accurate
version of the fft which can be used for non-periodic functions.Comment: New examples are give
Signal Flow Graph Approach to Efficient DST I-IV Algorithms
In this paper, fast and efficient discrete sine transformation (DST)
algorithms are presented based on the factorization of sparse, scaled
orthogonal, rotation, rotation-reflection, and butterfly matrices. These
algorithms are completely recursive and solely based on DST I-IV. The presented
algorithms have low arithmetic cost compared to the known fast DST algorithms.
Furthermore, the language of signal flow graph representation of digital
structures is used to describe these efficient and recursive DST algorithms
having points signal flow graph for DST-I and points signal flow
graphs for DST II-IV
Multiplier-less discrete sinusoidal and lapped transforms using sum-of-powers-of-two (SOPOT) coefficients
This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [10] is used to parameterize all the DCTs and DSTs in terms of certain (2×2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with the same set of SOPOT coefficients. A random search algorithm is also proposed to search for these SOPOT coefficients. Experimental results show that the (2×2) basic matrix can be implemented, on the average, in 6 to 12 additions. The proposed algorithms therefore require only O(N log2N) additions, which is very attractive for VLSI implementation. Using these SOPOT DCTs/DSTs, a family of SOPOT Lapped Transforms (LT) is also developed. They have similar coding gains but much lower complexity than their real-valued counterparts.published_or_final_versio
Wavelet transforms versus Fourier transforms
This note is a very basic introduction to wavelets. It starts with an
orthogonal basis of piecewise constant functions, constructed by dilation and
translation. The ``wavelet transform'' maps each to its coefficients
with respect to this basis. The mathematics is simple and the transform is fast
(faster than the Fast Fourier Transform, which we briefly explain), but
approximation by piecewise constants is poor. To improve this first wavelet, we
are led to dilation equations and their unusual solutions. Higher-order
wavelets are constructed, and it is surprisingly quick to compute with them ---
always indirectly and recursively. We comment informally on the contest between
these transforms in signal processing, especially for video and image
compression (including high-definition television). So far the Fourier
Transform --- or its 8 by 8 windowed version, the Discrete Cosine Transform ---
is often chosen. But wavelets are already competitive, and they are ahead for
fingerprints. We present a sample of this developing theory.Comment: 18 page
Removing interference components in time frequency representations using morphological operators
Time-frequency representations have been of great interest in the analysis and classification of non-stationary signals. The use of highly selective transformation techniques is a valuable tool for obtaining accurate information for studies of this type. The Wigner-Ville distribution has high time and frequency selectivity in addition to meeting some interesting mathematical properties. However, due to the bi-linearity of the transform, interference terms emerge when the transform is applied over multi-component signals. In this paper, we propose a technique to remove cross-components from the Wigner-Ville transform using image processing algorithms. The proposed method exploits the advantages of non-linear morphological filters, using a spectrogram to obtain an adequate marker for the morphological processing of the Wigner-Ville transform. Unlike traditional smoothing techniques, this algorithm provides cross-term attenuations while preserving time-frequency resolutions. Moreover, it could also be applied to distributions with different interference geometries. The method has been applied to a set of different time-frequency transforms, with promising results. © 2011 Elsevier Inc. All rights reserved.This work was supported by the National R&D Program under Grant TEC2008-02975 (Spain), FEDER programme and Generalitat Valenciana CMAP 340.Gómez García, S.; Naranjo Ornedo, V.; Miralles Ricós, R. (2011). Removing interference components in time frequency representations using morphological operators. Journal of Visual Communication and Image Representation. 22(1):401-410. doi:10.1016/j.jvcir.2011.03.007S40141022
The DLMT. An alternative to the DCT
In the last recent years, with the popularity of image compression techniques, many architectures have been proposed. Those have been generally based on the Forward and Inverse Discrete Cosine Transform (FDCT, IDCT). Alternatively, compression schemes based on discrete “wavelets” transform (DWT), used, both, in JPEG2000 coding standard and in the next H264-SVC (Scalable Video Coding), do not need to divide the image into non-overlapping blocks or macroblocks. This paper discusses the DLMT (Discrete Lopez-Moreno Transform). It proposes a new scheme intermediate between the DCT and the DWT (Discrete Wavelet Transform). The DLMT is computationally very similar to the DCT and uses quasi-sinusoidal functions, so the emergence of artifact blocks and their effects have a relative low importance. The use of quasi-sinusoidal functions has allowed achieving a multiresolution control quite close to that obtained by a DWT, but without increasing the computational complexity of the transformation. The DLMT can also be applied over a whole image, but this does not involve increasing computational complexity. Simulation results in MATLAB show that the proposed DLMT has significant performance benefits and improvements comparing with the DC
Implications of invariance of the Hamiltonian under canonical transformations in phase space
We observe that, within the effective generating function formalism for the
implementation of canonical transformations within wave mechanics, non-trivial
canonical transformations which leave invariant the form of the Hamilton
function of the classical analogue of a quantum system manifest themselves in
an integral equation for its stationary state eigenfunctions. We restrict
ourselves to that subclass of these dynamical symmetries for which the
corresponding effective generating functions are necessaarily free of quantum
corrections. We demonstrate that infinite families of such transformations
exist for a variety of familiar conservative systems of one degree of freedom.
We show how the geometry of the canonical transformations and the symmetry of
the effective generating function can be exploited to pin down the precise form
of the integral equations for stationary state eigenfunctions. We recover
several integral equations found in the literature on standard special
functions of mathematical physics. We end with a brief discussion (relevant to
string theory) of the generalization to scalar field theories in 1+1
dimensions.Comment: REVTeX v3.1, 13 page
Single-photon two-qubit SWAP gate for entanglement manipulation
A SWAP operation between different types of qubits of single photons is
essential for manipulating hyperentangled photons for a variety of
applications. We have implemented an efficient SWAP gate for the momentum and
polarization degrees of freedom of single photons. The SWAP gate was utilized
in a single-photon two-qubit quantum logic circuit to deterministically
transfer momentum entanglement between a pair of down-converted photons to
polarization entanglement. The polarization entanglement thus obtained violates
Bell's inequality by more than 150 standard deviations.Comment: Changes in the body of the paper, one reference added, typos
correcte
Rigid-Motion Scattering for Texture Classification
A rigid-motion scattering computes adaptive invariants along translations and
rotations, with a deep convolutional network. Convolutions are calculated on
the rigid-motion group, with wavelets defined on the translation and rotation
variables. It preserves joint rotation and translation information, while
providing global invariants at any desired scale. Texture classification is
studied, through the characterization of stationary processes from a single
realization. State-of-the-art results are obtained on multiple texture data
bases, with important rotation and scaling variabilities.Comment: 19 pages, submitted to International Journal of Computer Visio
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