Discrete Phase-Locked Loop Systems and Spreadsheets
This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
McMaster University
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| Series: | Spreadsheets in Education |
| Online Access: | http://sie.scholasticahq.com/article/4530-discrete-phase-locked-loop-systems-and-spreadsheets.pdf |
| _version_ | 1797966378092724224 |
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| author | Sergei Abramovich Elena Kudryashova Gennady A Leonov Stephen J. Sugden |
| author_facet | Sergei Abramovich Elena Kudryashova Gennady A Leonov Stephen J. Sugden |
| author_sort | Sergei Abramovich |
| collection | DOAJ |
| description | This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behavior interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behavior of systems with different types of non-linear characteristic. |
| first_indexed | 2024-04-11T02:14:36Z |
| format | Article |
| id | doaj.art-001d671bd89e43feac9f6548bd261142 |
| institution | Directory Open Access Journal |
| issn | 1448-6156 |
| language | English |
| last_indexed | 2024-04-11T02:14:36Z |
| publisher | McMaster University |
| record_format | Article |
| series | Spreadsheets in Education |
| spelling | doaj.art-001d671bd89e43feac9f6548bd2611422023-01-03T01:20:49ZengMcMaster UniversitySpreadsheets in Education1448-6156Discrete Phase-Locked Loop Systems and SpreadsheetsSergei AbramovichElena KudryashovaGennady A LeonovStephen J. SugdenThis paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behavior interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behavior of systems with different types of non-linear characteristic.http://sie.scholasticahq.com/article/4530-discrete-phase-locked-loop-systems-and-spreadsheets.pdf |
| spellingShingle | Sergei Abramovich Elena Kudryashova Gennady A Leonov Stephen J. Sugden Discrete Phase-Locked Loop Systems and Spreadsheets Spreadsheets in Education |
| title | Discrete Phase-Locked Loop Systems and Spreadsheets |
| title_full | Discrete Phase-Locked Loop Systems and Spreadsheets |
| title_fullStr | Discrete Phase-Locked Loop Systems and Spreadsheets |
| title_full_unstemmed | Discrete Phase-Locked Loop Systems and Spreadsheets |
| title_short | Discrete Phase-Locked Loop Systems and Spreadsheets |
| title_sort | discrete phase locked loop systems and spreadsheets |
| url | http://sie.scholasticahq.com/article/4530-discrete-phase-locked-loop-systems-and-spreadsheets.pdf |
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