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H. M. de Oliveira

Publications and source records attributed to H. M. de Oliveira.

At least 37 records · Page 2Linked to original sources
arXiv2015

Wavelets for Elliptical Waveguide Problems

New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is related to the solution of a Mathieu equation of odd characteristic exponent. The number of notches of these analysing filters can be easily designed. Wavelets derived by this method have potential application in the fields of optics, microwaves and electromagnetism.

math.CA↗
arXiv2015

A Short Survey on Arithmetic Transforms and the Arithmetic Hartley Transform

Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced: the Arithmetic Hartley transform. The interpolation process is shown to be the key element of the arithmetic transform theory.

math.CA↗
arXiv2015

Application of Enhanced-2D-CWT in Topographic Images for Mapping Landslide Risk Areas

There has been lately a number of catastrophic events of landslides and mudslides in the mountainous region of Rio de Janeiro, Brazil. Those were caused by intense rain in localities where there was unplanned occupation of slopes of hills and mountains. Thus, it became imperative creating an inventory of landslide risk areas in densely populated cities. This work presents a way of demarcating risk areas by using the bidimensional Continuous Wavelet Transform (2D-CWT) applied to high resolution topographic images of the mountainous region of Rio de Janeiro.

cs.CV↗
arXiv2015

Shannon and Renyi Entropy of Wavelets

This paper reports a new reading for wavelets, which is based on the classical 'De Broglie' principle. The wave-particle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved that any wavelet of the same family has the same Shannon entropy of its mother wavelet. Finally, the Shannon entropy for a few standard wavelet families is determined.

cs.IT↗
arXiv2015

Quantum Decoding with Venn Diagrams

The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to engineers. An illustrative example is presented of a naive perfect quantum code (Hamming-like code) with five-qubits for transmitting a single qubit of information. Also the (9,1)-Shor codes is addressed.

cs.IT↗
arXiv2015

Huygens Wave Equations in the Field of 2D-CWT

In this paper it is shown the performing of an optical transform to state the scalar diffraction in the formulation of the wavelet transform and the 'wave equations'. From there, a bridge is build between equations of spherical waves presented in 1678 by Huygens and the continuous wavelet transform. For such a purpose, wavelets are introduced that meet the principles of waves and the properties of wavelets. The following equations are applied in solution to show a correspondence between the Huygens-Fresnel diffraction and the wavelet transform.

math.AP↗
arXiv2015

Radix-2 Fast Hartley Transform Revisited

A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast DHT algorithms and a multiplication-free fast algorithm for the Hadamard Transform.

cs.DM↗
arXiv2015

The Discrete Cosine Transform over Prime Finite Fields

This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced. The FFDCT pair in GF(p) is defined, having blocklengths that are divisors of (p+1)/2. A special case is the Mersenne FFDCT, defined when p is a Mersenne prime. In this instance blocklengths that are powers of two are possible and radix-2 fast algorithms can be used to compute the transform.

cs.DM↗
arXiv2015

Fourier Codes

A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform. A decoding technique for such codes is proposed.

cs.IT↗
arXiv2015

Genomic Imaging Based on Codongrams and a^2grams

This paper introduces new tools for genomic signal processing, which can assist for genomic attribute extracting or describing biologically meaningful features embedded in a DNA. The codongrams and a2grams are offered as an alternative to spectrograms and scalograms. Twenty different a^2grams are defined for a genome, one for each amino acid (valgram is an a^2gram for valine; alagram is an a^2gram for alanine and so on). They provide information about the distribution and occurrence of the investigated amino acid. In particular, the metgram can be used to find out potential start position of genes within a genome. This approach can help implementing a new diagnosis test for genetic diseases by providing a type of DNA-medical imaging.

q-bio.OT↗
arXiv2015

Converting ECG and other paper legated biomedical maps into digital signals

This paper presents a digital signal processing tool developed using MatlabTM, which provides a very low-cost and effective strategy for analog-to-digital conversion of legated paper biomedical maps without requiring dedicated hardware. This software-based approach is particularly helpful for digitalizing biomedical signals acquired from analogical devices equipped with a plottingter. Albeit signals used in biomedical diagnosis are the primary concern, this imaging processing tool is suitable to modernize facilities in a non-expensive way. Legated paper ECG and EEG charts can be fast and efficiently digitalized in order to be added in existing up-to-date medical data banks, improving the follow-up of patients.

cs.OH↗
arXiv2015

The Genetic Code revisited: Inner-to-outer map, 2D-Gray map, and World-map Genetic Representations

How to represent the genetic code? Despite the fact that it is extensively known, the DNA mapping into proteins remains as one of the relevant discoveries of genetics. However, modern genomic signal processing usually requires converting symbolic-DNA strings into complex-valued signals in order to take full advantage of a broad variety of digital processing techniques. The genetic code is revisited in this paper, addressing alternative representations for it, which can be worthy for genomic signal processing. Three original representations are discussed. The inner-to-outer map builds on the unbalanced role of nucleotides of a 'codon' and it seems to be suitable for handling information-theory-based matter. The two-dimensional-Gray map representation is offered as a mathematically structured map that can help interpreting spectrograms or scalograms. Finally, the world-map representation for the genetic code is investigated, which can particularly be valuable for educational purposes -besides furnishing plenty of room for application of distance-based algorithms.

q-bio.OT↗
arXiv2015

A Family of Wavelets and a new Orthogonal Multiresolution Analysis Based on the Nyquist Criterion

A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic Interference (ISI) elimination. An orthogonal Multiresolution Analysis (MRA) is presented, showing that the roll-off parameter should be kept below 1/3. The pass-band behaviour of the Wavelet Fourier spectrum is examined. The left and right roll-off regions are asymmetric; nevertheless the Q-constant analysis philosophy is maintained. Finally, a generalisation of the (square root) raised cosine wavelets is proposed.

math.CA↗
arXiv2015

Orthogonal Multilevel Spreading Sequence Design

Finite field transforms are offered as a new tool of spreading sequence design. This approach exploits orthogonality properties of synchronous non-binary sequences defined over a complex finite field. It is promising for channels supporting a high signal-to-noise ratio. New digital multiplex schemes based on such sequences have also been introduced, which are multilevel Code Division Multiplex. These schemes termed Galois-field Division Multiplex (GDM) are based on transforms for which there exists fast algorithms. They are also convenient from the hardware viewpoint since they can be implemented by a Digital Signal Processor. A new Efficient-bandwidth code-division-multiple-access (CDMA) is introduced, which is based on multilevel spread spectrum sequences over a Galois field. The primary advantage of such schemes regarding classical multiple access digital schemes is their better spectral efficiency. Galois-Fourier transforms contain some redundancy and only cyclotomic coefficients are needed to be transmitted yielding compact spectrum requirements.

cs.IT↗
arXiv2015

Wavelet Analysis as an Information Processing Technique

A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.

cs.IT↗
arXiv2015

A Flexible Implementation of a Matrix Laurent Series-Based 16-Point Fast Fourier and Hartley Transforms

This paper describes a flexible architecture for implementing a new fast computation of the discrete Fourier and Hartley transforms, which is based on a matrix Laurent series. The device calculates the transforms based on a single bit selection operator. The hardware structure and synthesis are presented, which handled a 16-point fast transform in 65 nsec, with a Xilinx SPARTAN 3E device.

math.NA↗
arXiv2015

Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets

Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.

math.CA↗