The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Este artigo considera o projeto de filtros FIR usando a técnica de codificação preditiva linear, para a qual os coeficientes pertencem a um pequeno conjunto de inteiros, de modo que os coeficientes tenham comprimentos de palavras pequenos. Anteriormente, a programação inteira era usada para encontrar os coeficientes de tais filtros. Entretanto, o método de projeto que utiliza programação inteira sofre de alto custo computacional à medida que o comprimento do filtro aumenta. A computação pode rapidamente se tornar uma proibição. Neste artigo, propomos dois projetos de filtros FIR com codificação preditiva baseados em um algoritmo de programação linear de Karmarkar modificado, que é conhecido por ser mais adequado para resolver grandes problemas. Primeiro, formulamos o problema como um problema de erro minimax ponderado e o organizamos de uma forma que o algoritmo de Karmarkar modificado possa ser aplicado. O algoritmo de projeto tem a mesma (baixa) complexidade do método dos mínimos quadrados ponderados, mas pode resolver problemas com algumas restrições, enquanto o método dos mínimos quadrados ponderados não pode. Porém, o algoritmo apresenta uma dificuldade devido a um problema causado pela inversão da matriz quando a ordem do filtro preditivo é alta. Para evitar esta dificuldade, formulamos o projeto como um problema de erro mínimo absoluto ponderado. Ao usar este segundo algoritmo proposto, um filtro com comprimento de palavra de coeficiente mais curto pode ser encontrado usando um filtro preditor de ordem superior às custas de mais custo computacional. Para reduzir ainda mais o comprimento da palavra do coeficiente, a resposta ao impulso do filtro é separada em duas seções com diferentes faixas de valores de coeficiente. Cada seção usa um fator de escala diferente para escalar os valores dos coeficientes. Com comprimento de palavra de coeficiente pequeno, o filtro pode ser realizado sem multiplicadores de hardware usando uma representação numérica de dígitos assinados de raiz baixa. Cada coeficiente é distribuído no espaço como 2-3 ternário {0,
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copiar
Phakphoom BOONYANANT, Sawasd TANTARATANA, "Design and Multiplier-Free Realization of Predictive-Encoded FIR Filters Using Karmarkar's LP Algorithm" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 1, pp. 198-209, January 2002, doi: .
Abstract: This paper considers FIR filter design using linear predictive coding technique, for which the coefficients belong to a small set of integers, so that the coefficients have small wordlengths. Previously, integer programming was used to find the coefficients of such filters. However, the design method using integer programming suffers from high computational cost as the filter length increases. The computation can quickly become prohibition. In this paper, we propose two designs of predictive encoded FIR filters based on a modified Karmarkar's linear programming algorithm, which is known to be more suitable for solving large problems. First, we formulate the problem as a weighted minimax error problem and arrange it in a form that the modified Karmarkar algorithm can be applied. The design algorithm has the same (low) complexity as that of the weighted least-square method, but it can solve problems with some constraints, whereas the weighted least-square method cannot. However, the algorithm has a difficulty due to an ill condition caused by matrix inversion when the predictive filter order is high. To avoid this difficulty, we formulate the design as a weighted least absolute error problem. By using this second proposed algorithm, a filter with shorter coefficient wordlength can be found using a higher-order predictor filter at the expense of more computational cost. To further reduce the coefficient wordlength, the filter impulse response is separated into two sections having different ranges of coefficient values. Each section uses a different scaling factor to scale the coefficient values. With small coefficient wordlength, the filter can be realized without hardware multipliers using a low-radix signed-digit number representation. Each coefficient is distributed in space as 2-3 ternary {0,
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_1_198/_p
Copiar
@ARTICLE{e85-a_1_198,
author={Phakphoom BOONYANANT, Sawasd TANTARATANA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Design and Multiplier-Free Realization of Predictive-Encoded FIR Filters Using Karmarkar's LP Algorithm},
year={2002},
volume={E85-A},
number={1},
pages={198-209},
abstract={This paper considers FIR filter design using linear predictive coding technique, for which the coefficients belong to a small set of integers, so that the coefficients have small wordlengths. Previously, integer programming was used to find the coefficients of such filters. However, the design method using integer programming suffers from high computational cost as the filter length increases. The computation can quickly become prohibition. In this paper, we propose two designs of predictive encoded FIR filters based on a modified Karmarkar's linear programming algorithm, which is known to be more suitable for solving large problems. First, we formulate the problem as a weighted minimax error problem and arrange it in a form that the modified Karmarkar algorithm can be applied. The design algorithm has the same (low) complexity as that of the weighted least-square method, but it can solve problems with some constraints, whereas the weighted least-square method cannot. However, the algorithm has a difficulty due to an ill condition caused by matrix inversion when the predictive filter order is high. To avoid this difficulty, we formulate the design as a weighted least absolute error problem. By using this second proposed algorithm, a filter with shorter coefficient wordlength can be found using a higher-order predictor filter at the expense of more computational cost. To further reduce the coefficient wordlength, the filter impulse response is separated into two sections having different ranges of coefficient values. Each section uses a different scaling factor to scale the coefficient values. With small coefficient wordlength, the filter can be realized without hardware multipliers using a low-radix signed-digit number representation. Each coefficient is distributed in space as 2-3 ternary {0,
keywords={},
doi={},
ISSN={},
month={January},}
Copiar
TY - JOUR
TI - Design and Multiplier-Free Realization of Predictive-Encoded FIR Filters Using Karmarkar's LP Algorithm
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 198
EP - 209
AU - Phakphoom BOONYANANT
AU - Sawasd TANTARATANA
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2002
AB - This paper considers FIR filter design using linear predictive coding technique, for which the coefficients belong to a small set of integers, so that the coefficients have small wordlengths. Previously, integer programming was used to find the coefficients of such filters. However, the design method using integer programming suffers from high computational cost as the filter length increases. The computation can quickly become prohibition. In this paper, we propose two designs of predictive encoded FIR filters based on a modified Karmarkar's linear programming algorithm, which is known to be more suitable for solving large problems. First, we formulate the problem as a weighted minimax error problem and arrange it in a form that the modified Karmarkar algorithm can be applied. The design algorithm has the same (low) complexity as that of the weighted least-square method, but it can solve problems with some constraints, whereas the weighted least-square method cannot. However, the algorithm has a difficulty due to an ill condition caused by matrix inversion when the predictive filter order is high. To avoid this difficulty, we formulate the design as a weighted least absolute error problem. By using this second proposed algorithm, a filter with shorter coefficient wordlength can be found using a higher-order predictor filter at the expense of more computational cost. To further reduce the coefficient wordlength, the filter impulse response is separated into two sections having different ranges of coefficient values. Each section uses a different scaling factor to scale the coefficient values. With small coefficient wordlength, the filter can be realized without hardware multipliers using a low-radix signed-digit number representation. Each coefficient is distributed in space as 2-3 ternary {0,
ER -