H. M. de Oliveira

H. M. de Oliveira, R. J. Cintra, R. M. Campello de Souza

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.

H. M. de Oliveira, R. G. F. Távora, R. J. Cintra et al.

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.

H. M. de Oliveira, R. J. Cintra, R. C. de Oliveira

This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an analysis with a filter bank of constant quality factor is revisited on these bases. It is shown that if the wavelet spectral support is limited into the band $[f_m,f_M]$, then an orthogonal analysis is guaranteed provided that $f_M \leq 3f_m$, a quite simple result, but that invokes some parallel with the Nyquist rate. Nevertheless, in cases of orthogonal wavelets whose spectrum does not verify this condition, it is shown how to construct an "equivalent" filter bank with no spectral overlapping.

R. M. Campello de Souza, H. M. de Oliveira, D. Silva

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.

H. M. de Oliveira, F. Chaves

Continuous standard windowing is revisited and a new taper shape is introduced, which is based on the normal circular distribution by von Mises. Continuous-time windows are considered and their spectra obtained. A brief comparison with classical window families is performed in terms of their spectral properties. These windows can be used as an alternative in spectral analysis.

M. M. S. Lira, H. M. de Oliveira, M. A. Carvalho et al.

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).

R. J. Cintra, H. M. de Oliveira, C. O. Cintra

A new multiplication-free transform derived from DHT is introduced: the RHT. Investigations on the properties of the RHT led us to the concept of weak-inversion. Using new constructs, we show that RHT is not involutional like the DHT, but exhibits quasi-involutional property, a new definition derived from the periodicity of matrices. Thus instead of using the actual inverse transform, the RHT is viewed as an involutional transform, allowing the use of direct (multiplication-free) to evaluate the inverse. A fast algorithm to compute RHT is presented. This algorithm show embedded properties. We also extended RHT to the two-dimensional case. This permitted us to perform a preliminary analysis on the effects of RHT on images. Despite of some SNR loss, RHT can be very interesting for applications involving image monitoring associated to decision making, such as military applications or medical imaging.

H. M. de Oliveira, R. C. de Oliveira

It is shown how binary sequences can be associated with automatic composition of monophonic pieces. We are concerned with the composition of e-music from finite field structures. The information at the input may be either random or information from a black-and-white, grayscale or color picture. New e-compositions and music score are made available, including a new piece from the famous Lenna picture: the score of the e-music <<Between Lenna's eyes in C major.>> The corresponding stretch of music score are presented. Some particular structures, including clock arithmetic (mod 12), GF(7), GF(8), GF(13) and GF(17) are addressed. Further, multilevel block-codes are also used in a new approach of e-music composition, engendering a particular style as an e-composer. As an example, Pascal multilevel block codes recently introduced are handled to generate a new style of electronic music over GF(13).

H. M. de Oliveira, R. C. de Oliveira

A short overview demystifying the midi audio format is presented. The goal is to explain the file structure and how the instructions are used to produce a music signal, both in the case of monophonic signals as for polyphonic signals.

H. M. de Oliveira, J. Ranhel, R. B. A. Alves

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.

H. M. de Oliveira

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.

P. Carrion, H. M. de Oliveira, R. M. Campello de Souza

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.

R. J. Cintra, V. S. Dimitrov, H. M. de Oliveira et al.

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.

E. L. F. Da Silva, H. M. de Oliveira

A new algorithm for voice automatic syllabic splitting in the Portuguese language is proposed, which is based on the envelope of the speech signal of the input audio file. A computational implementation in MatlabTM is presented and made available at the URL http://www2.ee.ufpe.br/codec/divisao_silabica.html. Due to its straightforwardness, the proposed method is very attractive for embedded systems (e.g. i-phones). It can also be used as a screen to assist more sophisticated methods. Voice excerpts containing more than one syllable and identified by the same envelope are named as super-syllables and they are subsequently separated. The results indicate which samples corresponds to the beginning and end of each detected syllable. Preliminary tests were performed to fifty words at an identification rate circa 70% (further improvements may be incorporated to treat particular phonemes). This algorithm is also useful in voice command systems, as a tool in the teaching of Portuguese language or even for patients with speech pathology.

M. M. S. Lira, H. M. de Oliveira, R. J. Cintra et al.

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.

R. J. Cintra, H. M. de Oliveira, L. R. Soares

In this paper we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional first and second kind Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality and perfect reconstruction conditions. Chebyshev wavelets have compact support, their filters possess good selectivity, but they are not orthogonal. The convergence of the cascade algorithm of Chebyshev wavelets is proved by using properties of Markov chains. Computational implementation of these wavelets and some clear-cut applications are presented. Proposed wavelets are suitable for signal denoising.