R M Campello de Souza | Universidade Federal de Pernambuco (original) (raw)

Papers by R M Campello de Souza

Research paper thumbnail of Transformadas Numéricas de Hartley

Anais do XVIII Simpósio Brasileiro de Telecomunicações

Transformadas discretas desempenham um importante papel em Engenharia e suas aplicações devem-se ... more Transformadas discretas desempenham um importante papel em Engenharia e suas aplicações devem-se principalmente à existência das chamadas transformadas rápidas. Especificamente, transformadas discretas definidas sobre corpos finitos são atraentes ...

Research paper thumbnail of Fourier Codes

A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-chec... more 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.

Research paper thumbnail of On a Density for Sets of Integers

Cornell University - arXiv, Feb 9, 2015

A relationship between the Riemann zeta function and a density on integer sets is explored. Sever... more A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.

Research paper thumbnail of A Low-throughput Wavelet-based Steganography Audio Scheme

arXiv: Multimedia, Feb 5, 2015

Research paper thumbnail of Multiuser Communication Based on the DFT Eigenstructure

Cornell University - arXiv, Feb 6, 2017

The eigenstructure of the discrete Fourier transform (DFT) is examined and new systematic procedu... more The eigenstructure of the discrete Fourier transform (DFT) is examined and new systematic procedures to generate eigenvectors of the unitary DFT are proposed. DFT eigenvectors are suggested as user signatures for data communication over the real adder channel (RAC). The proposed multiuser communication system over the 2-user RAC is detailed.

Research paper thumbnail of Implementação de um Detector DTMF utilizando o algoritmo JCO

Anais do XXVII Simpósio Brasileiro de Telecomunicações, 2009

Resumo-Este artigo apresenta uma implementação eficiente para um detector DTMF, no sentido de red... more Resumo-Este artigo apresenta uma implementação eficiente para um detector DTMF, no sentido de reduzir a complexidade aritmética do procedimento, em relaçãoàs técnicas conhecidas. Para isso, a implementação utiliza o novo algoritmo JCO e o algoritmo de Goertzel. Resultados de simulações são apresentados.

Research paper thumbnail of The Hamming and Golay Number-Theoretic Transforms

Anais de XXXVI Simpósio Brasileiro de Telecomunicações e Processamento de Sinais, 2018

New number-theoretic transforms are derived from known linear block codes over finite fields. In ... more New number-theoretic transforms are derived from known linear block codes over finite fields. In particular, two new such transforms are built from perfect codes, namely the Hamming number-theoretic transform and the Golay numbertheoretic transform. A few properties of these new transforms are presented.

Research paper thumbnail of Processamento Digital para Computação da Função Ambiguidade Cruzada Banda Larga

Anais de XXXVI Simpósio Brasileiro de Telecomunicações e Processamento de Sinais, 2018

Resumo-Este artigo apresenta duas novas técnicas de processamento digital para computar valores d... more Resumo-Este artigo apresenta duas novas técnicas de processamento digital para computar valores da função ambiguidade banda larga, queé usada em sistemas de radar e sonar para estimar a posição e velocidade de alvos. Um projeto de sonar na faixa deáudioé apresentado e simulações são realizadas para avaliar o desempenho das técnicas. Palavras-Chave-função ambiguidade, radar, sonar, processamento digital de sinais, filtro casado. Abstract-Two new digital processing techniques are introduced for computing the broadband ambiguity function, which can be used in radar and sonar systems to estimate a peak of speed and range of targets. A sonar project in the audio range and simulation was carried out to assess the performance of these techniques.

Research paper thumbnail of A Transformada Numérica de Pascal

Anais de XXXIII Simpósio Brasileiro de Telecomunicações, 2015

Resumo-Uma nova transformada linear sobre corpos finitos é introduzida, a transformada numérica d... more Resumo-Uma nova transformada linear sobre corpos finitos é introduzida, a transformada numérica de Pascal (TNP). A matriz de transformação da TNP é obtida do triângulo de Pascal, com elementos considerados sobre GF(p). Algumas propriedades da TNP são apresentadas e potenciais aplicações da mesma são sugeridas.

Research paper thumbnail of Constructing Fast Algorithms by Expanding a Set of Matrices into Rank-1 Matrices

Circuits, Systems, and Signal Processing, 2019

This paper introduces the notion of numerical basis for a numerical space and uses it to establis... more This paper introduces the notion of numerical basis for a numerical space and uses it to establish a relation between a fast algorithm for computing a discrete linear transform and the problem of expanding a given finite set of matrices as a linear combination of rank-1 matrices. It is shown that the number of multiplications of the algorithm is given by the number of rank-1 matrices in the expansion. Applying this approach, an algorithm for computing three components of the nine-point discrete Fourier transform (DFT) and an algorithm to compute the seven-point DFT with the least possible number of multiplications are shown.

Research paper thumbnail of Transformações Lineares para Correção de Surtos Bidimensionais

Journal of Communication and Information Systems, 1998

Resumo •Neste trabalho, uma tecmca para corre£ao deerros em surtos bidimensionais e apresentada. ... more Resumo •Neste trabalho, uma tecmca para corre£ao deerros em surtos bidimensionais e apresentada. 0 procedimento faz uso de transforma£6es lineares que mapeiam tais surtos em urna serie de configura£6es de erros aleat6rios corrigiveis.

Research paper thumbnail of The eigenstructure and Jordan form of the Fourier transform over fields of characteristic 2 and a generalized Vandermonde-type formula

Linear Algebra and its Applications, 2016

Research paper thumbnail of Trigonometry in finite fields and a new Hartley transform

Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252)

Absrrucr-A trigonometry for finite fields is introduced. In particular, the k-trigonometric funct... more Absrrucr-A trigonometry for finite fields is introduced. In particular, the k-trigonometric functions over the Galois Field GF(q) are defined and their main properties derived. This leads to the definition of the cq(.) function over GF(q), which in turn leads to a finite field Hartley Transform ...

Research paper thumbnail of Novas Ferramentas para Processamento de Sinais em Corpos Finitos

Research paper thumbnail of Expansões Polinomiais de Exponenciais em Corpos Finitos GF(p)

Uma das mais poderosas teorias em Matemática é a Análise Real. Este trabalho introduz novas ferra... more Uma das mais poderosas teorias em Matemática é a Análise Real. Este trabalho introduz novas ferramentas para corpos finitos, similares àquelas da Análise clássica, visando a concepção de uma Análise para corpos finitos. Esta teoria vem sendo usada em Engenharia Elétrica, é a base de códigos algébricos, e está relacionada, de várias formas, a campos de investigação tais como criptografia, espalhamento espectral e análise de sinais através das transformadas de corpo finito.

Research paper thumbnail of Hartley number theoretic transforms

Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)

The Hartley number theoretic transform (HNTT) is introduced, in particular, the Mersenne HNTT is ... more The Hartley number theoretic transform (HNTT) is introduced, in particular, the Mersenne HNTT is defined and some multiplication free transforms are given

Research paper thumbnail of Fragile watermarking using finite field trigonometrical transforms

Signal Processing: Image Communication, 2009

Fragile digital watermarking has been applied for authentication and alteration detection in imag... more 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.

Research paper thumbnail of Fractional cosine and sine transforms over finite fields

Linear Algebra and its Applications, 2013

In this paper, we introduce fractional cosine and sine transforms over finite fields. The basis f... more In this paper, we introduce fractional cosine and sine transforms over finite fields. The basis for the definition of such transforms, which are respectively referred by the acronyms GFrCT and GFrST, is the recently proposed fractional Fourier transform over finite fields (GFrFT) [1]. More specifically, we use the eigenvectors of the finite field Fourier transform to construct eigenvectors of the finite field cosine and sine transforms. Such eigenvectors are then used in spectral expansions that allow to compute fractional powers of the finite field cosine and sine transform matrices.

Research paper thumbnail of Design method for two-channel cyclic filter banks over fields of characteristic two

Electronics Letters, 2009

A new perfect reconstruction condition for two-channel biorthogonal cyclic filter banks over fiel... more A new perfect reconstruction condition for two-channel biorthogonal cyclic filter banks over fields of characteristic two is introduced, from which a technique for designing such filter banks is described. The result is based on a new transform, the cyclic Z-transform over a finite field.

Research paper thumbnail of A Transformada Discreta do Seno em um Corpo Finito

Anais do XXVIII …, 2005

Transformadas discretas definidas sobre estruturas finitas ou infinitas tem muitas aplicaç˜oes em... more Transformadas discretas definidas sobre estruturas finitas ou infinitas tem muitas aplicaç˜oes em En-genharia. Dentre as várias transformadas discretas definidas sobre os reais ou complexos, a transfor-mada discreta de Fourier (TDF) e as transforma-das discretas do ...

Research paper thumbnail of Transformadas Numéricas de Hartley

Anais do XVIII Simpósio Brasileiro de Telecomunicações

Transformadas discretas desempenham um importante papel em Engenharia e suas aplicações devem-se ... more Transformadas discretas desempenham um importante papel em Engenharia e suas aplicações devem-se principalmente à existência das chamadas transformadas rápidas. Especificamente, transformadas discretas definidas sobre corpos finitos são atraentes ...

Research paper thumbnail of Fourier Codes

A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-chec... more 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.

Research paper thumbnail of On a Density for Sets of Integers

Cornell University - arXiv, Feb 9, 2015

A relationship between the Riemann zeta function and a density on integer sets is explored. Sever... more A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.

Research paper thumbnail of A Low-throughput Wavelet-based Steganography Audio Scheme

arXiv: Multimedia, Feb 5, 2015

Research paper thumbnail of Multiuser Communication Based on the DFT Eigenstructure

Cornell University - arXiv, Feb 6, 2017

The eigenstructure of the discrete Fourier transform (DFT) is examined and new systematic procedu... more The eigenstructure of the discrete Fourier transform (DFT) is examined and new systematic procedures to generate eigenvectors of the unitary DFT are proposed. DFT eigenvectors are suggested as user signatures for data communication over the real adder channel (RAC). The proposed multiuser communication system over the 2-user RAC is detailed.

Research paper thumbnail of Implementação de um Detector DTMF utilizando o algoritmo JCO

Anais do XXVII Simpósio Brasileiro de Telecomunicações, 2009

Resumo-Este artigo apresenta uma implementação eficiente para um detector DTMF, no sentido de red... more Resumo-Este artigo apresenta uma implementação eficiente para um detector DTMF, no sentido de reduzir a complexidade aritmética do procedimento, em relaçãoàs técnicas conhecidas. Para isso, a implementação utiliza o novo algoritmo JCO e o algoritmo de Goertzel. Resultados de simulações são apresentados.

Research paper thumbnail of The Hamming and Golay Number-Theoretic Transforms

Anais de XXXVI Simpósio Brasileiro de Telecomunicações e Processamento de Sinais, 2018

New number-theoretic transforms are derived from known linear block codes over finite fields. In ... more New number-theoretic transforms are derived from known linear block codes over finite fields. In particular, two new such transforms are built from perfect codes, namely the Hamming number-theoretic transform and the Golay numbertheoretic transform. A few properties of these new transforms are presented.

Research paper thumbnail of Processamento Digital para Computação da Função Ambiguidade Cruzada Banda Larga

Anais de XXXVI Simpósio Brasileiro de Telecomunicações e Processamento de Sinais, 2018

Resumo-Este artigo apresenta duas novas técnicas de processamento digital para computar valores d... more Resumo-Este artigo apresenta duas novas técnicas de processamento digital para computar valores da função ambiguidade banda larga, queé usada em sistemas de radar e sonar para estimar a posição e velocidade de alvos. Um projeto de sonar na faixa deáudioé apresentado e simulações são realizadas para avaliar o desempenho das técnicas. Palavras-Chave-função ambiguidade, radar, sonar, processamento digital de sinais, filtro casado. Abstract-Two new digital processing techniques are introduced for computing the broadband ambiguity function, which can be used in radar and sonar systems to estimate a peak of speed and range of targets. A sonar project in the audio range and simulation was carried out to assess the performance of these techniques.

Research paper thumbnail of A Transformada Numérica de Pascal

Anais de XXXIII Simpósio Brasileiro de Telecomunicações, 2015

Resumo-Uma nova transformada linear sobre corpos finitos é introduzida, a transformada numérica d... more Resumo-Uma nova transformada linear sobre corpos finitos é introduzida, a transformada numérica de Pascal (TNP). A matriz de transformação da TNP é obtida do triângulo de Pascal, com elementos considerados sobre GF(p). Algumas propriedades da TNP são apresentadas e potenciais aplicações da mesma são sugeridas.

Research paper thumbnail of Constructing Fast Algorithms by Expanding a Set of Matrices into Rank-1 Matrices

Circuits, Systems, and Signal Processing, 2019

This paper introduces the notion of numerical basis for a numerical space and uses it to establis... more This paper introduces the notion of numerical basis for a numerical space and uses it to establish a relation between a fast algorithm for computing a discrete linear transform and the problem of expanding a given finite set of matrices as a linear combination of rank-1 matrices. It is shown that the number of multiplications of the algorithm is given by the number of rank-1 matrices in the expansion. Applying this approach, an algorithm for computing three components of the nine-point discrete Fourier transform (DFT) and an algorithm to compute the seven-point DFT with the least possible number of multiplications are shown.

Research paper thumbnail of Transformações Lineares para Correção de Surtos Bidimensionais

Journal of Communication and Information Systems, 1998

Resumo •Neste trabalho, uma tecmca para corre£ao deerros em surtos bidimensionais e apresentada. ... more Resumo •Neste trabalho, uma tecmca para corre£ao deerros em surtos bidimensionais e apresentada. 0 procedimento faz uso de transforma£6es lineares que mapeiam tais surtos em urna serie de configura£6es de erros aleat6rios corrigiveis.

Research paper thumbnail of The eigenstructure and Jordan form of the Fourier transform over fields of characteristic 2 and a generalized Vandermonde-type formula

Linear Algebra and its Applications, 2016

Research paper thumbnail of Trigonometry in finite fields and a new Hartley transform

Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252)

Absrrucr-A trigonometry for finite fields is introduced. In particular, the k-trigonometric funct... more Absrrucr-A trigonometry for finite fields is introduced. In particular, the k-trigonometric functions over the Galois Field GF(q) are defined and their main properties derived. This leads to the definition of the cq(.) function over GF(q), which in turn leads to a finite field Hartley Transform ...

Research paper thumbnail of Novas Ferramentas para Processamento de Sinais em Corpos Finitos

Research paper thumbnail of Expansões Polinomiais de Exponenciais em Corpos Finitos GF(p)

Uma das mais poderosas teorias em Matemática é a Análise Real. Este trabalho introduz novas ferra... more Uma das mais poderosas teorias em Matemática é a Análise Real. Este trabalho introduz novas ferramentas para corpos finitos, similares àquelas da Análise clássica, visando a concepção de uma Análise para corpos finitos. Esta teoria vem sendo usada em Engenharia Elétrica, é a base de códigos algébricos, e está relacionada, de várias formas, a campos de investigação tais como criptografia, espalhamento espectral e análise de sinais através das transformadas de corpo finito.

Research paper thumbnail of Hartley number theoretic transforms

Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)

The Hartley number theoretic transform (HNTT) is introduced, in particular, the Mersenne HNTT is ... more The Hartley number theoretic transform (HNTT) is introduced, in particular, the Mersenne HNTT is defined and some multiplication free transforms are given

Research paper thumbnail of Fragile watermarking using finite field trigonometrical transforms

Signal Processing: Image Communication, 2009

Fragile digital watermarking has been applied for authentication and alteration detection in imag... more 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.

Research paper thumbnail of Fractional cosine and sine transforms over finite fields

Linear Algebra and its Applications, 2013

In this paper, we introduce fractional cosine and sine transforms over finite fields. The basis f... more In this paper, we introduce fractional cosine and sine transforms over finite fields. The basis for the definition of such transforms, which are respectively referred by the acronyms GFrCT and GFrST, is the recently proposed fractional Fourier transform over finite fields (GFrFT) [1]. More specifically, we use the eigenvectors of the finite field Fourier transform to construct eigenvectors of the finite field cosine and sine transforms. Such eigenvectors are then used in spectral expansions that allow to compute fractional powers of the finite field cosine and sine transform matrices.

Research paper thumbnail of Design method for two-channel cyclic filter banks over fields of characteristic two

Electronics Letters, 2009

A new perfect reconstruction condition for two-channel biorthogonal cyclic filter banks over fiel... more A new perfect reconstruction condition for two-channel biorthogonal cyclic filter banks over fields of characteristic two is introduced, from which a technique for designing such filter banks is described. The result is based on a new transform, the cyclic Z-transform over a finite field.

Research paper thumbnail of A Transformada Discreta do Seno em um Corpo Finito

Anais do XXVIII …, 2005

Transformadas discretas definidas sobre estruturas finitas ou infinitas tem muitas aplicaç˜oes em... more Transformadas discretas definidas sobre estruturas finitas ou infinitas tem muitas aplicaç˜oes em En-genharia. Dentre as várias transformadas discretas definidas sobre os reais ou complexos, a transfor-mada discreta de Fourier (TDF) e as transforma-das discretas do ...