Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order
A digital filter is a digital system used to filter a discrete signal. It can be implemented either by software or by specialized equipment.The use of hypercomplex numbers for building digital filter structures can provide significant benefits. Digital filters with hypercomplex parameters have highe...
Gespeichert in:
| Datum: | 2019 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Ukrainian |
| Veröffentlicht: |
Інститут проблем реєстрації інформації НАН України
2019
|
| Schlagworte: | |
| Online Zugang: | http://drsp.ipri.kiev.ua/article/view/183470 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Data Recording, Storage & Processing |
Institution
Data Recording, Storage & Processing| id |
drspiprikievua-article-183470 |
|---|---|
| record_format |
ojs |
| spelling |
drspiprikievua-article-1834702019-12-10T13:03:03Z Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order Метод генерації гіперкомплексних числових систем для моделювання цифрових реверсивних фільтрів 4-го порядку Kalinovsky, Ya. A. Boyarinova, Yu. E. Khitsko, Ya. V. гіперкомплексна числова система лінійна згортка ізоморфізм множення бікомплексні числа квадриплексні числа система комп’ютерної алгебри hypercomplex numerical system linear convolution isomorphism multiplication bicomplex numbers quadriplex numbers computer algebra system A digital filter is a digital system used to filter a discrete signal. It can be implemented either by software or by specialized equipment.The use of hypercomplex numbers for building digital filter structures can provide significant benefits. Digital filters with hypercomplex parameters have higher speed and better performance in terms of total parametric sensitivity.Although in previous works software filter of 3th order structure synthesis algorithms were proposed, in this paper only software filter of 4th order structure synthesis algorithms are considered.Studies have shown that the expression analysis method for the transfer function denominator norms of the hypercomplex filter allows you to effectively select the hypercomplex number system, which has all the necessary properties.It is shown that only quadriplex number system K and hypercomplex number system obtained by auto doubling of a double-number system W are suitable for the structures synthesis of fourth-order hypercomplex digital filters. These hypercomplex number systems allow to get a complete set of filter transfer function shift operator steps. On the other hand, they have isomorphic weakly filled hypercomplex number systems. Transition to such systems can significantly reduce the number of real operations during the filter operation time.In the work, all transformations and calculations in the hypercomplex domain were performed using the software module for hypercomplex calculations in the Maple computer algebra framework. This fact confirms the efficiency of this software module. Tabl.: 2. Refs: 17 titles. Представлено метод вибору гіперкомплексних числових систем (ГЧС) для моделювання цифрових реверсивних фільтрів, що заснований на аналізі виразу норми знаменника гіперкомплексної передавальної функції. Згенеровані ГЧС дозволяють отримати повний набір ступенів оператора зсуву з передавальної функції фільтра, а також мають ізоморфні слабозаповнені таблиці Келі. Перехід до таких систем дозволяє помітно знизити кількість дійсних операцій при функціонуванні фільтра. Інститут проблем реєстрації інформації НАН України 2019-11-21 Article Article application/pdf http://drsp.ipri.kiev.ua/article/view/183470 10.35681/1560-9189.2019.21.3.183470 Data Recording, Storage & Processing; Vol. 21 No. 3 (2019); 20-30 Регистрация, хранение и обработка данных; Том 21 № 3 (2019); 20-30 Реєстрація, зберігання і обробка даних; Том 21 № 3 (2019); 20-30 1560-9189 uk http://drsp.ipri.kiev.ua/article/view/183470/184153 Авторське право (c) 2021 Реєстрація, зберігання і обробка даних |
| institution |
Data Recording, Storage & Processing |
| baseUrl_str |
|
| datestamp_date |
2019-12-10T13:03:03Z |
| collection |
OJS |
| language |
Ukrainian |
| topic |
hypercomplex numerical system linear convolution isomorphism multiplication bicomplex numbers quadriplex numbers computer algebra system |
| spellingShingle |
hypercomplex numerical system linear convolution isomorphism multiplication bicomplex numbers quadriplex numbers computer algebra system Kalinovsky, Ya. A. Boyarinova, Yu. E. Khitsko, Ya. V. Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| topic_facet |
гіперкомплексна числова система лінійна згортка ізоморфізм множення бікомплексні числа квадриплексні числа система комп’ютерної алгебри hypercomplex numerical system linear convolution isomorphism multiplication bicomplex numbers quadriplex numbers computer algebra system |
| format |
Article |
| author |
Kalinovsky, Ya. A. Boyarinova, Yu. E. Khitsko, Ya. V. |
| author_facet |
Kalinovsky, Ya. A. Boyarinova, Yu. E. Khitsko, Ya. V. |
| author_sort |
Kalinovsky, Ya. A. |
| title |
Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| title_short |
Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| title_full |
Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| title_fullStr |
Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| title_full_unstemmed |
Method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| title_sort |
method of hypercomplex numbers systems generation for modeling digital reversible filters of 4th order |
| title_alt |
Метод генерації гіперкомплексних числових систем для моделювання цифрових реверсивних фільтрів 4-го порядку |
| description |
A digital filter is a digital system used to filter a discrete signal. It can be implemented either by software or by specialized equipment.The use of hypercomplex numbers for building digital filter structures can provide significant benefits. Digital filters with hypercomplex parameters have higher speed and better performance in terms of total parametric sensitivity.Although in previous works software filter of 3th order structure synthesis algorithms were proposed, in this paper only software filter of 4th order structure synthesis algorithms are considered.Studies have shown that the expression analysis method for the transfer function denominator norms of the hypercomplex filter allows you to effectively select the hypercomplex number system, which has all the necessary properties.It is shown that only quadriplex number system K and hypercomplex number system obtained by auto doubling of a double-number system W are suitable for the structures synthesis of fourth-order hypercomplex digital filters. These hypercomplex number systems allow to get a complete set of filter transfer function shift operator steps. On the other hand, they have isomorphic weakly filled hypercomplex number systems. Transition to such systems can significantly reduce the number of real operations during the filter operation time.In the work, all transformations and calculations in the hypercomplex domain were performed using the software module for hypercomplex calculations in the Maple computer algebra framework. This fact confirms the efficiency of this software module. Tabl.: 2. Refs: 17 titles. |
| publisher |
Інститут проблем реєстрації інформації НАН України |
| publishDate |
2019 |
| url |
http://drsp.ipri.kiev.ua/article/view/183470 |
| work_keys_str_mv |
AT kalinovskyyaa methodofhypercomplexnumberssystemsgenerationformodelingdigitalreversiblefiltersof4thorder AT boyarinovayue methodofhypercomplexnumberssystemsgenerationformodelingdigitalreversiblefiltersof4thorder AT khitskoyav methodofhypercomplexnumberssystemsgenerationformodelingdigitalreversiblefiltersof4thorder AT kalinovskyyaa metodgeneracíígíperkompleksnihčislovihsistemdlâmodelûvannâcifrovihreversivnihfílʹtrív4goporâdku AT boyarinovayue metodgeneracíígíperkompleksnihčislovihsistemdlâmodelûvannâcifrovihreversivnihfílʹtrív4goporâdku AT khitskoyav metodgeneracíígíperkompleksnihčislovihsistemdlâmodelûvannâcifrovihreversivnihfílʹtrív4goporâdku |
| first_indexed |
2025-07-17T10:57:42Z |
| last_indexed |
2025-07-17T10:57:42Z |
| _version_ |
1850411385050103808 |