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
Kertas kerja ini mempertimbangkan reka bentuk penapis FIR menggunakan teknik pengekodan ramalan linear, yang mana pekalinya tergolong dalam set integer yang kecil, supaya pekali mempunyai panjang perkataan yang kecil. Sebelum ini, pengaturcaraan integer digunakan untuk mencari pekali penapis tersebut. Walau bagaimanapun, kaedah reka bentuk menggunakan pengaturcaraan integer mengalami kos pengiraan yang tinggi apabila panjang penapis meningkat. Pengiraan dengan cepat boleh menjadi larangan. Dalam makalah ini, kami mencadangkan dua reka bentuk penapis FIR berkod ramalan berdasarkan algoritma pengaturcaraan linear Karmarkar yang diubah suai, yang diketahui lebih sesuai untuk menyelesaikan masalah besar. Pertama, kami merumuskan masalah itu sebagai masalah ralat minimax berwajaran dan menyusunnya dalam bentuk yang algoritma Karmarkar yang diubah suai boleh digunakan. Algoritma reka bentuk mempunyai kerumitan (rendah) yang sama seperti kaedah kuasa dua berwajaran, tetapi ia boleh menyelesaikan masalah dengan beberapa kekangan, manakala kaedah kuasa dua berwajaran tidak boleh. Walau bagaimanapun, algoritma mengalami kesukaran kerana keadaan sakit yang disebabkan oleh penyongsangan matriks apabila susunan penapis ramalan adalah tinggi. Untuk mengelakkan kesukaran ini, kami merumuskan reka bentuk sebagai masalah ralat mutlak paling kurang wajaran. Dengan menggunakan algoritma kedua yang dicadangkan ini, penapis dengan pekali panjang perkataan yang lebih pendek boleh didapati menggunakan penapis peramal peringkat lebih tinggi dengan mengorbankan lebih banyak kos pengiraan. Untuk mengurangkan lagi panjang perkataan pekali, tindak balas impuls penapis dipisahkan kepada dua bahagian yang mempunyai julat nilai pekali yang berbeza. Setiap bahagian menggunakan faktor penskalaan yang berbeza untuk menskalakan nilai pekali. Dengan pekali panjang kata yang kecil, penapis boleh direalisasikan tanpa pengganda perkakasan menggunakan perwakilan nombor bertanda-radix rendah. Setiap pekali diedarkan dalam ruang sebagai 2-3 ternary {0,
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Salinan
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
Salinan
@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},}
Salinan
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 -