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Article: On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

TitleOn the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment
Authors
KeywordsAdaptive filters
Convergence performance analysis
Impulsive noise
M-estimation
TD normalized least mean M-estimate (TDNLMM)
Transform domain normalized least mean square (TDNLMS)
Issue Date2011
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/content/120889/
Citation
Journal Of Signal Processing Systems, 2011, v. 64 n. 3, p. 429-445 How to Cite?
AbstractThis paper studies the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm with general nonlinearity and the transform domain normalized least mean M-estimate (TDNLMM) algorithm in Gaussian inputs and additive Gaussian and impulsive noise environment. The TDNLMM algorithm, which is derived from robust M-estimation, has the advantage of improved performance over the conventional TDNLMS algorithm in combating impulsive noises. Using Price's theorem and its extension, the above algorithms can be treated in a single framework respectively for Gaussian and impulsive noise environments. Further, by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations which describe the mean and mean square behaviors of the TDNLMS and TDNLMM algorithms. These analytical results reveal the advantages of the TDNLMM algorithm in impulsive noise environment, and are in good agreement with computer simulation results. © 2010 The Author(s).
Persistent Identifierhttp://hdl.handle.net/10722/145084
ISSN
2015 Impact Factor: 0.508
2015 SCImago Journal Rankings: 0.262
ISI Accession Number ID
References

Widrow, B., McCool, J., Larimore, M. G., & Johnson, C. R., Jr. (1976). Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proceedings of IEEE, 64, 1151–1162. doi: 10.1109/PROC.1976.10286

Nagumo, J. I., & Noda, A. (1967). A learning method for system identification. IEEE Transactions on Automatic Control, AC-12, 282–287. doi: 10.1109/TAC.1967.1098599

Narayan, S., Peterson, A. M., & Narasimha, M. J. (1983). Transform domain LMS algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-31, 609–615. doi: 10.1109/TASSP.1983.1164121

Lee, J. C., & Un, C. K. (1986). Performance of transform-domain LMS adaptive digital filters. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(3), 499–510. doi: 10.1109/TASSP.1986.1164850

Boroujeny, B. F., & Gazor, S. (1992). Selection of orthonormal transforms for improving the performance of the transform domain normalized LMS algorithm. IEE Proceedings. Radar and Signal Processing, 139(5), 327–335. doi: 10.1049/ip-f-2.1992.0046

Pei, S. C., & Tseng, C. C. (1996). Transform domain adaptive linear phase filter. IEEE Transactions on Signal Processing, 44(12), 3142–3146. doi: 10.1109/78.553489

Marshall, D. F., Jenkins, W. K., & Murphy, J. J. (1989). The use of orthogonal transforms for improving performance of adaptive filters. IEEE Transactions on Circuits and Systems, 36(4), 474–484. doi: 10.1109/31.92880

Zou, Y., Chan, S. C., & Ng, T. S. (2000). Least mean M-estimate algorithms for robust adaptive filtering in impulsive noise. IEEE Transactions on Circuits and Systems II, 47, 1564–1569. doi: 10.1109/82.899657

Huber, P. J. (1981). Robust statistics. New York: John Wiley. doi: 10.1002/0471725250

Chan, S. C., & Zou, Y. (2004). A recursive least M-estimate algorithm for robust adaptive filtering in impulsive noise: fast algorithm and convergence performance analysis. IEEE Transactions on Signal Processing, 52(4), 975–991. doi: 10.1109/TSP.2004.823496

Price, R. (1958). A useful theorem for nonlinear devices having Gaussian inputs. IEEE Transactions on Information Theory, 4(2), 69–72. doi: 10.1109/TIT.1958.1057444

Price, R. (1964). Comment on: ’A useful theorem for nonlinear devices having Gaussian inputs’. IEEE Transactions on Information Theory, IT-10, 171. doi: 10.1109/TIT.1964.1053659

Haweel, T. I., & Clarkson, P. M. (1992). A class of order statistic LMS algorithms. IEEE Transactions on Signal Processing, 40(1), 44–53. doi: 10.1109/78.157180

Koike, S. (1997). Adaptive threshold nonlinear algorithm for adaptive filters with robustness against impulsive noise. IEEE Transactions on Signal Processing, 45(9), 2391–2395. doi: 10.1109/78.622963

Bershad, N. J. (1988). On error-saturation nonlinearities in LMS adaptation. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-36(4), 440–452. doi: 10.1109/29.1548

Mathews, V. J. (1991). Performance analysis of adaptive filters equipped with the dual sign algorithm. IEEE Transactions on Signal Processing, 39, 85–91. doi: 10.1109/78.80768

Koike, S. (2006). Performance analysis of the normalized LMS algorithm for complex-domain adaptive filters in the presence of impulse noise at filter input. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science, E89-A(9), 2422–2428. doi: 10.1093/ietfec/e89-a.9.2422

Koike, S. (2006). Convergence analysis of adaptive filters using normalized sign-sign algorithm. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science, E88-A(11), 3218–3224. doi: 10.1093/ietfec/e88-a.11.3218

Bershad, N. J. (1986). Analysis of the normalized LMS algorithm with Gaussian inputs. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34, 793–806. doi: 10.1109/TASSP.1986.1164914

 

DC FieldValueLanguage
dc.contributor.authorChan, SCen_HK
dc.contributor.authorZhou, Yen_HK
dc.date.accessioned2012-02-21T05:43:41Z-
dc.date.available2012-02-21T05:43:41Z-
dc.date.issued2011en_HK
dc.identifier.citationJournal Of Signal Processing Systems, 2011, v. 64 n. 3, p. 429-445en_HK
dc.identifier.issn1939-8018en_HK
dc.identifier.urihttp://hdl.handle.net/10722/145084-
dc.description.abstractThis paper studies the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm with general nonlinearity and the transform domain normalized least mean M-estimate (TDNLMM) algorithm in Gaussian inputs and additive Gaussian and impulsive noise environment. The TDNLMM algorithm, which is derived from robust M-estimation, has the advantage of improved performance over the conventional TDNLMS algorithm in combating impulsive noises. Using Price's theorem and its extension, the above algorithms can be treated in a single framework respectively for Gaussian and impulsive noise environments. Further, by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations which describe the mean and mean square behaviors of the TDNLMS and TDNLMM algorithms. These analytical results reveal the advantages of the TDNLMM algorithm in impulsive noise environment, and are in good agreement with computer simulation results. © 2010 The Author(s).en_HK
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/content/120889/en_HK
dc.relation.ispartofJournal of Signal Processing Systemsen_HK
dc.rightsThe Author(s)en_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong Licenseen_US
dc.subjectAdaptive filtersen_HK
dc.subjectConvergence performance analysisen_HK
dc.subjectImpulsive noiseen_HK
dc.subjectM-estimationen_HK
dc.subjectTD normalized least mean M-estimate (TDNLMM)en_HK
dc.subjectTransform domain normalized least mean square (TDNLMS)en_HK
dc.titleOn the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environmenten_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4551/resserv?sid=springerlink&genre=article&atitle=On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment&title=Journal of Signal Processing Systems&issn=19398018&date=2011-09-01&volume=64&issue=3& spage=429&authors=S. C. Chan, Y. Zhouen_US
dc.identifier.emailChan, SC: ascchan@hkucc.hku.hken_HK
dc.identifier.emailZhou, Y: yizhou@eee.hku.hken_HK
dc.identifier.authorityChan, SC=rp00094en_HK
dc.identifier.authorityZhou, Y=rp00213en_HK
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1007/s11265-010-0494-5en_HK
dc.identifier.scopuseid_2-s2.0-84872437535en_HK
dc.identifier.hkuros195838-
dc.relation.referencesWidrow, B., McCool, J., Larimore, M. G., & Johnson, C. R., Jr. (1976). Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proceedings of IEEE, 64, 1151–1162.en_US
dc.relation.referencesdoi: 10.1109/PROC.1976.10286en_US
dc.relation.referencesPlackett, R. L. (1972). The discovery of the method of least-squares. Biometrika, 59(2), 239–251.en_US
dc.relation.referencesNagumo, J. I., & Noda, A. (1967). A learning method for system identification. IEEE Transactions on Automatic Control, AC-12, 282–287.en_US
dc.relation.referencesdoi: 10.1109/TAC.1967.1098599en_US
dc.relation.referencesNarayan, S., Peterson, A. M., & Narasimha, M. J. (1983). Transform domain LMS algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-31, 609–615.en_US
dc.relation.referencesdoi: 10.1109/TASSP.1983.1164121en_US
dc.relation.referencesLee, J. C., & Un, C. K. (1986). Performance of transform-domain LMS adaptive digital filters. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(3), 499–510.en_US
dc.relation.referencesdoi: 10.1109/TASSP.1986.1164850en_US
dc.relation.referencesBoroujeny, B. F., & Gazor, S. (1992). Selection of orthonormal transforms for improving the performance of the transform domain normalized LMS algorithm. IEE Proceedings. Radar and Signal Processing, 139(5), 327–335.en_US
dc.relation.referencesdoi: 10.1049/ip-f-2.1992.0046en_US
dc.relation.referencesPei, S. C., & Tseng, C. C. (1996). Transform domain adaptive linear phase filter. IEEE Transactions on Signal Processing, 44(12), 3142–3146.en_US
dc.relation.referencesdoi: 10.1109/78.553489en_US
dc.relation.referencesMarshall, D. F., Jenkins, W. K., & Murphy, J. J. (1989). The use of orthogonal transforms for improving performance of adaptive filters. IEEE Transactions on Circuits and Systems, 36(4), 474–484.en_US
dc.relation.referencesdoi: 10.1109/31.92880en_US
dc.relation.referencesZou, Y., Chan, S. C., & Ng, T. S. (2000). Least mean M-estimate algorithms for robust adaptive filtering in impulsive noise. IEEE Transactions on Circuits and Systems II, 47, 1564–1569.en_US
dc.relation.referencesdoi: 10.1109/82.899657en_US
dc.relation.referencesHuber, P. J. (1981). Robust statistics. New York: John Wiley.en_US
dc.relation.referencesdoi: 10.1002/0471725250en_US
dc.relation.referencesChan, S. C., & Zou, Y. (2004). A recursive least M-estimate algorithm for robust adaptive filtering in impulsive noise: fast algorithm and convergence performance analysis. IEEE Transactions on Signal Processing, 52(4), 975–991.en_US
dc.relation.referencesdoi: 10.1109/TSP.2004.823496en_US
dc.relation.referencesPrice, R. (1958). A useful theorem for nonlinear devices having Gaussian inputs. IEEE Transactions on Information Theory, 4(2), 69–72.en_US
dc.relation.referencesdoi: 10.1109/TIT.1958.1057444en_US
dc.relation.referencesPrice, R. (1964). Comment on: ’A useful theorem for nonlinear devices having Gaussian inputs’. IEEE Transactions on Information Theory, IT-10, 171.en_US
dc.relation.referencesdoi: 10.1109/TIT.1964.1053659en_US
dc.relation.referencesHaweel, T. I., & Clarkson, P. M. (1992). A class of order statistic LMS algorithms. IEEE Transactions on Signal Processing, 40(1), 44–53.en_US
dc.relation.referencesdoi: 10.1109/78.157180en_US
dc.relation.referencesKoike, S. (1997). Adaptive threshold nonlinear algorithm for adaptive filters with robustness against impulsive noise. IEEE Transactions on Signal Processing, 45(9), 2391–2395.en_US
dc.relation.referencesdoi: 10.1109/78.622963en_US
dc.relation.referencesBershad, N. J. (1988). On error-saturation nonlinearities in LMS adaptation. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-36(4), 440–452.en_US
dc.relation.referencesdoi: 10.1109/29.1548en_US
dc.relation.referencesMathews, V. J. (1991). Performance analysis of adaptive filters equipped with the dual sign algorithm. IEEE Transactions on Signal Processing, 39, 85–91.en_US
dc.relation.referencesdoi: 10.1109/78.80768en_US
dc.relation.referencesKoike, S. (2006). Performance analysis of the normalized LMS algorithm for complex-domain adaptive filters in the presence of impulse noise at filter input. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science, E89-A(9), 2422–2428.en_US
dc.relation.referencesdoi: 10.1093/ietfec/e89-a.9.2422en_US
dc.relation.referencesKoike, S. (2006). Convergence analysis of adaptive filters using normalized sign-sign algorithm. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science, E88-A(11), 3218–3224.en_US
dc.relation.referencesdoi: 10.1093/ietfec/e88-a.11.3218en_US
dc.relation.referencesBershad, N. J. (1986). Analysis of the normalized LMS algorithm with Gaussian inputs. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34, 793–806.en_US
dc.relation.referencesdoi: 10.1109/TASSP.1986.1164914en_US
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dc.identifier.volume64en_US
dc.identifier.issue3en_US
dc.identifier.spage429en_HK
dc.identifier.epage445en_HK
dc.identifier.eissn1939-8115en_US
dc.identifier.isiWOS:000293711100012-
dc.publisher.placeUnited Statesen_HK
dc.description.otherSpringer Open Choice, 21 Feb 2012en_US
dc.identifier.scopusauthoridChan, SC=13310287100en_HK
dc.identifier.scopusauthoridZhou, Y=55209555200en_HK
dc.identifier.citeulike7376732-

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