Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window
The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As a s...
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| Published in | The Journal of fourier analysis and applications Vol. 18; no. 3; pp. 456 - 470 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Boston
SP Birkhäuser Verlag Boston
01.06.2012
Springer |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1069-5869 1531-5851 |
| DOI | 10.1007/s00041-011-9210-5 |
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| Abstract | The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As a side result of these systematic developments of the subject, two new methods are presented here. Comparisons are made with respect to the computational complexity, and the running time of optimised implementations in the C programming language. The new algorithms have the lowest known computational complexity and running time when a long FIR window is used. The implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis. |
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| AbstractList | The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As a side result of these systematic developments of the subject, two new methods are presented here. Comparisons are made with respect to the computational complexity, and the running time of optimised implementations in the C programming language. The new algorithms have the lowest known computational complexity and running time when a long FIR window is used. The implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis. |
| Audience | Academic |
| Author | Søndergaard, Peter L. |
| Author_xml | – sequence: 1 givenname: Peter L. surname: Søndergaard fullname: Søndergaard, Peter L. email: ps@elektro.dtu.dk organization: Department of Electrical Engineering, Technical University of Denmark |
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| Cites_doi | 10.1002/spe.626 10.1109/78.533729 10.1006/jmaa.1995.1363 10.1016/0022-247X(92)90053-G 10.1137/1.9781611971514 10.1109/TSP.2009.2014282 10.1109/78.80904 10.1090/S0025-5718-1965-0178586-1 10.1109/PROC.1968.6477 10.1109/TAU.1973.1162474 10.1109/78.735301 10.1109/T-C.1974.223784 10.1109/TSP.2010.2043137 10.1109/PROC.1977.10770 10.1121/1.1939800 10.1109/TSP.2006.882087 10.1145/364096.364118 10.1145/77626.79170 10.1109/TAU.1967.1161905 10.1007/s00041-006-6069-y 10.1109/TASSP.1976.1162810 10.1016/0165-1684(96)00014-X 10.1007/978-1-4612-2016-9_2 10.1109/TSP.2008.928503 10.1007/978-1-4612-2016-9_9 10.1109/78.229898 10.1109/JPROC.2004.840301 10.1007/BF02475925 10.1016/j.cam.2011.09.011 10.1007/978-1-4612-0003-1 10.1007/978-0-8176-8224-8 10.1142/S0219691312500324 10.1016/0165-1684(95)00112-3 10.21236/ADA563016 |
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| Keywords | Discrete Gabor Transform 42C40 Algorithm 42C15 Implementation |
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| Snippet | The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development... |
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| SubjectTerms | Abstract Harmonic Analysis Algorithms Analysis Approximations and Expansions Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing |
| Title | Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window |
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