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We present a model of two-kinks resulting from an explicit composition of two standards kinks of the $\phi^4$ model based on the procedure of Ref. \cite{uchiyama}. The two-kinks have an additional parameter accounting for the separation of the standard kinks of $\phi^4$ model. We have shown that the two-kinks have two discrete internal modes besides the zeroth mode and the continuous spectrum. This new feature signalizes that the head-on collision a two-kinks/two-antikinks pair exhibits a rich and complex behavior due to the additional channel from which the energy of the system can be stored. We have exhibited the fractal structure associated with the main configurations after the collision. We have inferred the fractality as the imprint of the nonlinear exchange of energy into the two discrete internal modes., Comment: 12 pages, 6 figures

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., Comment: 12 pages, 5 figures

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., Comment: 5 pages, 4 figures. in: 2002 WSEAS International Conference on Wavelet Analysis and Multirate Systems, Vouliagmeni, Greece. arXiv admin note: substantial text overlap with arXiv:1501.07255

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., Comment: 8 pages, 8 figures; Lecture Notes in Computer Science LNCS 7950, pp.380-388, 2013 Springer-Verlag, Heidelberg ISBN: 978-3-642-39093-7

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., Comment: 5 pages, 3 figures

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., Comment: 5 pages, 8 figures, 7 tables

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., Comment: 5 pages, 4 figures: Anais do I Congresso de Inform\'atica da Amaz\^onia, 2001. v.1.pp.285-292

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., Comment: 5 pages, 1 table, Lecture Notes in Computer Science, LNCS 3124, Heidelberg: Springer Verlag, 2004, vol.1, pp.482-487, 2004

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., Comment: 6 pages, 2 tables. In: 10th International Symposium on Communication Theory and Applications 2009, Ambleside, Lake District, UK

This paper introduces the theory and hardware implementation of two new algorithms for computing a single component of the discrete Fourier transform. In terms of multiplicative complexity, both algorithms are more efficient, in general, than the well known Goertzel Algorithm., Comment: 4 pages, 3 figures, 1 table. In: 10th International Symposium on Communication Theory and Applications, Ambleside, UK

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., Comment: 6 pages, 5 figures

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., Comment: 7 pages, 3 figures

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., Comment: 6 pages, 9 figures

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., Comment: 9 pages, 5 figures. In: Coding, Communication and Broadcasting.1 ed.Hertfordshire: Reseach Studies Press (RSP), 2000. ISBN 0-86380-259-1

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., Comment: 6 pages, 6 tables, VI International Telecommunications Symposium (ITS2006), September 3-6, Fortaleza, Brazil

We present an implementation of the Galerkin-Collocation method to determine the initial data for non-rotating distorted three dimensional black holes in the inversion and puncture schemes. The numerical method combines the key features of the Galerkin and Collocation methods which produces accurate initial data. We evaluated the ADM mass of the initial data sets, and we have provided the angular structure of the gravitational wave distribution at the initial hypersurface by evaluating the scalar $\Psi_4$ for asymptotic observers., Comment: 11 pages, 9 figures

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., Comment: 4 pages, 4 figures. IEEE VI Southern Programmable Logic Conference 2010

The k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cask(.) function over GF(q), which in turn leads to a finite field Hartley Transform. The main properties of this new discrete transform are presented and areas for possible applications are mentioned., Comment: 7 pages, IEEE/SBT International Telecommunication Symposium, ITS, 1998, Sao Paulo, Brazil

An approach for approximately calculating the number of genes in a genome is presented, which takes into account the average protein length expected for the species. A number of virus, bacterial and eukaryotic genomes are scrutinized. Genome figures are presented, which support the average protein size of a species as a criterion for assessing life complexity. The human gene distribution in the 23 chromosomes is investigated emphasizing the genomic rate, the mean 'exon' length, and the mean 'exons per gene'. It is shown that storing all genes of a single human definitely requires less than 12 MB., Comment: 6 pages, 1 figure, 5 tables

The human visual color response is driven by specialized cells called cones, which exist in three types, viz. R, G, and B. Software is developed to simulate how color images are displayed for different types of color blindness. Specified the default color deficiency associated with a user, it generates a preview of the rainbow (in the visible range, from red to violet) and shows up, side by side with a colorful image provided as input, the display correspondent colorblind. The idea is to provide an image processing after image acquisition to enable a better perception ofcolors by the color blind. Examples of pseudo-correction are shown for the case of Protanopia (red blindness). The system is adapted into a screen of an i-pad or a cellphone in which the colorblind observe the camera, the image processed with color detail previously imperceptible by his naked eye. As prospecting, wearable computer glasses could be manufactured to provide a corrected image playback. The approach can also provide augmented reality for human vision by adding the UV or IR responses as a new feature of Google Glass., Comment: 4 pages, 6 figures, XXIV Congresso Brasileiro de Engenharia Biomedica, Uberlandia, MG, Brazil, 2014

A new approach to multiple access based on finite field transforms is investigated. These schemes, termed Galois-Division Multiple Access (GDMA), offer compact bandwidth requirements. A new digital transform, the Finite Field Hartley Transform (FFHT) requires to deal with fields of characteristic p, p \neq 2. A binary-to-p-ary (p \neq 2) mapping based on the opportunistic secondary channel is introduced. This allows the use of GDMA in conjunction with available digital systems. The performance of GDMA is also evaluated., Comment: 6 pages, 4 figures. In: XIX Simposio Brasileiro de Telecomunicacoes, 2001, Fortaleza, CE, Brazil

An original multiplex scheme is introduced, which is based on Mallat's multiresolution formulation of wavelet systems. This system is adaptable and its implementation is well matched to digital signal processors and computers. The approach termed multiresolution division multiplex (MRDM) is intensive in signal processing (SP) tools, extremely flexible and can combine a variety of tributaries at different bit rates. A broad variety of orthogonal wavelet systems can endow with MRDM and the channel waveforms, and consequently the spectral shape and system performance depend upon the selected wavelets. Demultiplex can be done efficiently, since the number of floating multiplications and additions increase only linearly with the length of signals. A Haar-based MRDM scheme is presented to illustrate the versatility of this new multiplex approach., Comment: 5 pages, 8 figures, ITS International Telecomm. Symposium, Brazil, 2006

This paper exploits the multiresolution analysis in the fault analysis on transmission lines. Faults were simulated using the ATP (Alternative Transient Program), considering signals at 128/cycle. A nonorthogonal multiresolution analysis was provided by Gegenbauer scaling and wavelet filters. In the cases where the signal reconstruction is not required, orthogonality may be immaterial. Gegenbauer filter banks are thereby offered in this paper as a tool for analyzing fault signals on transmission lines. Results are compared to those ones derived from a 4-coefficient Daubechies filter. The main advantages in favor of Gegenbauer filters are their smaller computational effort and their constant group delay, as they are symmetric filters., Comment: 6 pages, 12 figures. In: Transmission and Distribution IEEE/PES/T&D Latin America, Sao Paulo, Brazil, 2004

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., Comment: 8 pages, 14 figures

Spread-spectrum systems are presented, which are based on Finite Field Fourier Transforms. Orthogonal spreading sequences defined over a finite field are derived. New digital multiplex schemes based on such spread-spectrum systems are also introduced, which are multilevel Coding Division Multiplex. These schemes termed Galois-field Division Multiplex (GDM) offer compact bandwidth requirements because only leaders of cyclotomic cosets are needed to be transmitted., Comment: 6 pages, 7 figures. Int. Conf. on System Engineering, Comm. and. Info. Technol., Punta Arenas, Chile, 2001

We have investigated the head-on collision of a two-kink and a two-antikink pair that arises as a generalization of the $\phi^4$ model. We have evolved numerically the Klein-Gordon equation with a new spectral algorithm whose accuracy and convergence were attested by the numerical tests. As a general result, the two-kink pair is annihilated radiating away most of the scalar field. It is possible the production of oscillons-like configurations after the collision that bounce and coalesce to form a small amplitude oscillon at the origin. The new feature is the formation of a sequence of quasi-stationary structures that we have identified as lump-like solutions of non-topological nature. The amount of time these structures survives depends on the fine-tuning of the impact velocity., Comment: 14 pages, 9 figures

Shape-invariant signals under the Discrete Fourier Transform are investigated, leading to a class of eigenfunctions for the unitary discrete Fourier operator. Such invariant sequences (eigensequences) are suggested as user signatures over the real adder channel (t-RAC) and a multiuser communication system over the t-RAC is presented., Comment: 6 pages, 1 figure, 1 table. VI International Telecommunications Symposium (ITS2006)

This paper presents the foundations of a computer oriented approach for preparing a list of random treatment assignments to be adopted in randomised controlled trials. Software is presented which can be applied in the earliest stage of clinical trials and bioequivalence assays. This allocation of patients to treatment in clinical trials ensures exactly equal treatment numbers. The investigation of the randomness properties of an assignment leads to the concept of a 'strong randomised list'. The new approach introduced in this note is based on thresholds and produces a strong randomised list of treatment assignments., Comment: 8 pages. XIV Reuniao Anual da Federacao de Sociedades de Biologia Experimental FeSBE, Caxamb\'u, Brazil, 1999

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., Comment: 6 pages, XX Simp\'osio Bras. de Telecomunica\c{c}\~oes, Rio de Janeiro, Brazil, 2003. Fixed typos

Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented., Comment: 6 pages, 5 figures, Proc. IEEE/SBrT Int. Telecomm. Symp., 2002. pp.362-367

This paper presents a new approach for a vocoder design based on full frequency masking by octaves in addition to a technique for spectral filling via beta probability distribution. Some psycho-acoustic characteristics of human hearing - inaudibility masking in frequency and phase - are used as a basis for the proposed algorithm. The results confirm that this technique may be useful to save bandwidth in applications requiring intelligibility. It is recommended for the legal eavesdropping of long voice conversations., Comment: 7 pages, 3 figures, 3 tables, XXXV Cong. Nac. de Matematica Aplicada e Computacional, Natal, RN, Brazil 2014

A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived., Comment: 7 pages, 5 figures; VII Encontro Regional de Matem\'atica Aplicada e Computacional, 2007, Recife

In this paper a variant of the classical hierarchical cluster analysis is reported. This agglomerative (bottom-up) cluster technique is referred to as the Adaptive Mean-Linkage Algorithm. It can be interpreted as a linkage algorithm where the value of the threshold is conveniently up-dated at each interaction. The superiority of the adaptive clustering with respect to the average-linkage algorithm follows because it achieves a good compromise on threshold values: Thresholds based on the cut-off distance are sufficiently small to assure the homogeneity and also large enough to guarantee at least a pair of merging sets. This approach is applied to a set of possible substituents in a chemical series., Comment: 4 pages, 2 figures, 2 tables. Congresso Brasileiro de Automatica CBA, Natal, RN, Brazil, 2002

Real-valued block codes are introduced, which are derived from Discrete Fourier Transforms (DFT) and Discrete Hartley Transforms (DHT). These algebraic structures are built from the eigensequences of the transforms. Generator and parity check matrices were computed for codes up to block length N=24. They can be viewed as lattices codes so the main parameters (dimension, minimal norm, area of the Voronoi region, density, and centre density) are computed. Particularly, Hamming-Hartley and Golay-Hartley block codes are presented. These codes may possibly help an efficient computation of a DHT/DFT., Comment: 5 pages, 4 tables, 1 appedix. conference: XXV Simposio Brasileiro de Telecomunicacoes, SBrT'07, Recife, PE, Brazil, 2007

Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the so-called fast transforms. In this paper some fast algorithms are derived which meet the lower bound on the multiplicative complexity of the DFT/DHT. The approach is based on a decomposition of the DHT into layers of Walsh-Hadamard transforms. In particular, fast algorithms for short block lengths such as $N \in \{4, 8, 12, 24\}$ are presented., Comment: Fixed several typos. 7 pages, 5 figures, XVIII Simp\'osio Brasileiro de Telecomunica\c{c}\~oes, 2000, Gramado, RS, Brazil

New continuous wavelets of compact support are introduced, which are related to the beta distribution. They can be built from probability distributions using 'blur'derivatives. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a soft variety of Haar wavelets whose shape is fine-tuned by two parameters a and b. Close expressions for beta wavelets and scale functions as well as their spectra are derived. Their importance is due to the Central Limit Theorem applied for compactly supported signals., Comment: 7 pages, 4 figures. Journal of Communication and Information Systems, former Journal of the Brazilian Telecommunications Society, ISSN 1980-6604 pp.105-111

In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet functions and is named as the Fourier-Like and Hartley-Like wavelet analysis. A Hilbert transform analysis on the wavelet theory is also included., Comment: 7 pages, 10 figures, Anais do XXII Simp\'osio Brasileiro de Telecomunica\c{c}\~oes, Campinas, 2005

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., Comment: 6 pages, 1 figure

This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FF-Wavelets) including FF-Haar and FF-Daubechies are derived. Non-orthogonal FF-wavelets such as B-spline over GF(p) are also considered. A few examples of multiresolution analysis over Finite fields are presented showing how to perform Laplacian pyramid filtering of finite block lengths sequences. An application of FF-wavelets to design spread-spectrum sequences is presented., Comment: 4 pages, 1 figure. conference: XIX Simposio Brasileiro de Telecomunicacoes, 2001, Fortaleza, CE, Brazil

This paper presents a novel approach for deciding on the appropriateness or not of an acquired fingerprint image into a given database. The process begins with the assembly of a training base in an image space constructed by combining Principal Component Analysis (PCA) and edge detection. Then, the parameter H, a new feature that helps in the decision making about the relevance of a fingerprint image in databases, is derived from a relationship between Euclidean and Mahalanobian distances. This procedure ends with the lifting of the curve of the Receiver Operating Characteristic (ROC), where the thresholds defined on the parameter H are chosen according to the acceptable rates of false positives and false negatives., Comment: 5 pages, 9 figures. SBrT/IEEE International Telecommunication Symposium, ITS 2010, Manaus, AM, Brazil

The Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard Amplitude Modulation Systems (e.g. A3E, H3E, J3E, C3F). A cornucopia of algebraic curves is then derived assuming a single tone or a double tone modulation signal. The ratio of the frequency of the tone modulator (fm) and carrier frequency (fc) is considered in two distinct cases, namely: fm/fc<1 and fm/fc>=1. The geometric figures are some sort of Lissajours figures. Different shapes appear looking like epicycloids (including cardioids), rhodonea curves, Lemniscates, folium of Descartes or Lam\'e curves. The role played by the modulation index is elucidated in each case., Comment: 10 pages, 15 figures. ISSN 2320-9364

Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representations for signals called derivagrams are introduced, which are similar to spectrograms. This approach corroborates the impact of wavelets in modern signal analysis., Comment: 6 pages, 4 figures. conference: XXII Simposio Brasileiro de Telecomunicacoes, SBrT'05, 2005, Campinas, SP, Brazil

General guidelines for a new fast computation of blocklength 8m+4 DFTs are presented, which is based on a Laurent series involving matrices. Results of non-trivial real multiplicative complexity are presented for blocklengths N=64, achieving lower multiplication counts than previously published FFTs. A detailed description for the cases m=1 and m=2 is presented., Comment: 6 pages, 2 figures, 2 tables. Conference: XXVII Simposio Brasileiro de Telecomunicacoes - SBrT'09, 2009, Blumenau, SC, Brazil

This paper presents the preliminary of a novel scheme of steganography, and introduces the idea of combining two secret keys in the operation. The first secret key encrypts the text using a standard cryptographic scheme (e.g. IDEA, SAFER+, etc.) prior to the wavelet audio decomposition. The way in which the cipher text is embedded in the file requires another key, namely a stego-key, which is associated with features of the audio wavelet analysis., Comment: 2 pages, 1 figure, conference: 8th Brazilian Symposium on Information and Computer System Security, 2008, Gramado, RS, Brazil

This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and their spectra are introduced here. The frequency detection properties of daublets are investigated through scalograms derived from these new analytical expressions. These near-daublets have been implemented on the Matlab wavelet toolbox and a few scalograms presented. This approach can be valuable for wavelet synthesis from hardware or for application involving continuous wavelet-based systems, such as wavelet OFDM., Comment: 6 pages, 6 figures, 3 tables. Conference: International Telecommunication Symposium, ITS 2010, Manaus, AM , Brazil

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated with Legendre multiresolution analysis is a linear phase finite impulse response filter (FIR)., Comment: 6 pages, 6 figures, 1 table In: Computational Methods in Circuits and Systems Applications, WSEAS press, pp.211-215, 2003. ISBN: 960-8052-88-2

Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient fast transforms. In this paper some fast algorithms are derived. The theoretical lower bound on the multiplicative complexity for the DFT/DHT are achieved. The approach is based on the factorization of DHT matrices. Algorithms for short blocklengths such as $N \in \{3, 5, 6, 12, 24 \}$ are presented., Comment: 10 pages, 4 figures, 2 tables, International Conference on System Engineering, Communications and Information Technologies, 2001, Punta Arenas. ICSECIT 2001 Proceedings. Punta Arenas: Universidad de Magallanes, 2001

Fragile digital watermarking has been applied for authentication and alteration detection in images. Utilizing the cosine and Hartley transforms over finite fields, a new transform domain fragile watermarking scheme is introduced. A watermark is embedded into a host image via a blockwise application of two-dimensional finite field cosine or Hartley transforms. Additionally, the considered finite field transforms are adjusted to be number theoretic transforms, appropriate for error-free calculation. The employed technique can provide invisible fragile watermarking for authentication systems with tamper location capability. It is shown that the choice of the finite field characteristic is pivotal to obtain perceptually invisible watermarked images. It is also shown that the generated watermarked images can be used as publicly available signature data for authentication purposes., Comment: 9 pages, 7 figures, 2 tables

A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were proposed. The FFHT exhibits interesting symmetries, which are exploited to derive tailored fast transform algorithms. The proposed fast algorithms are based on successive decompositions of the FFHT by means of Hadamard-Walsh transforms (HWT). The introduced decompositions meet the lower bound on the multiplicative complexity for all the cases investigated. The complexity of the new algorithms is compared with that of traditional algorithms., Comment: 6 pages, 3 tables, fixed typos, submitted to the Sixth International Symposium on Communication Theory and Applications (ISCTA'01), 2001

Many continuous wavelets are defined in the frequency domain and do not have analytical expressions in the time domain. Meyer wavelet is ordinarily defined in this way. In this note, we derive new straightforward analytical expressions for both the wavelet and scale function for the Meyer basis. The validity of these expressions is corroborated by numerical computations, yielding no approximation error., Comment: 5 pages, 7 figures