Optimal Convolutive Filters for Real-Time Detection and Arrival Time Estimation of Transient Signals
Linear convolutive filters are fast in calculation and in application, and thus, often used for real-time processing of continuous data streams. In the case of transient signals, a filter has not only to detect the presence of a specific waveform, but to estimate its arrival time as well. In this study, a measure is presented which indicates the performance of detectors in achieving both of these tasks simultaneously. Furthermore, a new sub-class of linear filters within the class of filters which minimize the quadratic response is proposed. The proposed filters are more flexible than the existing ones, like the adaptive matched filter or the minimum power distortionless response beamformer, and prove to be superior with respect to that measure in certain settings. Simulations of a real-time scenario confirm the advantage of these filters as well as the usefulness of the performance measure.
[1] S. Z. Kalson, "An adaptive array detector with mismatched signal
rejection," IEEE Transactions on Aerospace and Electronic Systems,
vol. 28, pp. 195-207, 1992.
[2] W. Melvin, "A stap overview," IEEE Aerospace and Electronic Systems
Magazine, vol. 19, no. 1, pp. 19-35, 2004.
[3] D. Middleton and R. Esposito, "Simultaneous optimum detection and
estimation of signals in noise," IEEE Transactions on Information
Theory, vol. 14, 1968.
[4] B. Baygun and A. HeroIII, "Optimal simultaneous detection and estimation
under a false alarm constraint," IEEE Transaction on Information
Theory, vol. 41 (3), pp. 688 - 703, 1995.
[5] E. Fishler and H. Messer, "Detection and parameter estimation of a
transient signal using order statistics," IEEE Transactions on Signal
Processing, vol. 48, 2000.
[6] F. Nicolls, "Constraints and invariance in target detection," Ph.D. dissertation,
University of Cape Town, 2000.
[7] H. L. V. Trees, Detection, Estimation, and Modulation Theory Part IV
- Optimum Array Processing. JOHN WILEY & SONS, 2002.
[8] B. Friedlander and B. Porat, "Performance analysis of transcient detectors
based on linear data transformations," IEEE Transactions on
Information Theory, vol. 38 (2), pp. 665-673, 1992.
[9] B. Porat and B. Friedlander, "Performance analysis of a class of transcient
detection algorithms - a unified framework," IEEE Transactions
on Signal Processing, vol. 40 (10), 1992.
[10] Z. Wang and P. Willett, "A performance study of some transcient
detectors," IEEE Transactions on Signal Processing, vol. 48 (9), 2000.
[11] A. Yamazaki, T. Tajima, and K. Matsuoka, "Convolutive independent
component analysis of eeg data," SICE 2003 Annual Conference, vol. 2,
pp. 1227- 1231, 2003.
[12] P. H. Thakur, H. Lu, S. S. Hsiao, and K. O. Johnson, "Automated optimal
detection and classification of neural action potentials in extra-cellular
recordings." Journal of Neuroscience Methods, vol. 162, no. 1-2, pp.
364-376, 2007.
[13] M. Natora, F. Franke, M. Munk, and K. Obermayer, "Blind source
separation of sparse overcomplete mixtures and application to neural
recordings," Lecture Notes in Computer Science - Independent Component
Analysis and Signal Separation, vol. 5441, pp. 459-466, 2009.
[14] M. S. Pedersen, J. Larsen, U. Kjems, and L. C. Parra, A Survey of
Convolutive Blind Source Separation Methods, ser. Springer Handbook
of Speech Processing. Springer Press, Nov 2007.
[15] D. Scholnik, "Mixed-norm fir filter optimization using second-order
coneprogramming," ICASSP, IEEE International Conference on Acoustics,
Speech and Signal Processing - Proceedings, vol. 2, pp. 1525-1528,
2002.
[16] F. Robey, D. Fuhrmann, E. Kelly, and R. Nitzberg, "A cfar adaptive
matched filter detector," IEEE Transactions on Aerospace and Electronic
Systems, vol. 28 (1), pp. 208-216, 1992.
[17] O. Besson and F. Vincent, "Performance analysis of beamformers using
generalized loading of the covariance matrix in the presence of random
steering vector errors," IEEE Transactions on Signal Processing, vol. 53,
no. 2, pp. 452-459, 2005.
[18] T. Fawcett, "An introduction to roc analysis," Pattern recognition letters,
vol. 27 (8), pp. 861-874, 2006.
[19] R. Vollgraf and K. Obermayer, "Improved optimal linear filters for the
discrimination of multichannel waveform templates for spike-sorting
applications," IEEE Signal Processing Letters, vol. 13, no. 3, pp. 121-
124, 2006.
[20] F. Franke, M. Natora, C. Boucsein, M. Munk, and K. Obermayer, "An
online spike detection and spike classification algorithm capable of instantaneous
resolution of overlapping spikes," Journal of Computational
Neuroscience, 2009, in press.
[21] H. Luetkepohl, Handbook of Matrices. John Wiley and Sons, 1996.
[22] M. Ageel, "Variance upper bounds and a probability inequality for
discrete alpha-unimodality," Aplicationes Mathematicae, vol. 27, pp. 403
- 410, 2000.
[1] S. Z. Kalson, "An adaptive array detector with mismatched signal
rejection," IEEE Transactions on Aerospace and Electronic Systems,
vol. 28, pp. 195-207, 1992.
[2] W. Melvin, "A stap overview," IEEE Aerospace and Electronic Systems
Magazine, vol. 19, no. 1, pp. 19-35, 2004.
[3] D. Middleton and R. Esposito, "Simultaneous optimum detection and
estimation of signals in noise," IEEE Transactions on Information
Theory, vol. 14, 1968.
[4] B. Baygun and A. HeroIII, "Optimal simultaneous detection and estimation
under a false alarm constraint," IEEE Transaction on Information
Theory, vol. 41 (3), pp. 688 - 703, 1995.
[5] E. Fishler and H. Messer, "Detection and parameter estimation of a
transient signal using order statistics," IEEE Transactions on Signal
Processing, vol. 48, 2000.
[6] F. Nicolls, "Constraints and invariance in target detection," Ph.D. dissertation,
University of Cape Town, 2000.
[7] H. L. V. Trees, Detection, Estimation, and Modulation Theory Part IV
- Optimum Array Processing. JOHN WILEY & SONS, 2002.
[8] B. Friedlander and B. Porat, "Performance analysis of transcient detectors
based on linear data transformations," IEEE Transactions on
Information Theory, vol. 38 (2), pp. 665-673, 1992.
[9] B. Porat and B. Friedlander, "Performance analysis of a class of transcient
detection algorithms - a unified framework," IEEE Transactions
on Signal Processing, vol. 40 (10), 1992.
[10] Z. Wang and P. Willett, "A performance study of some transcient
detectors," IEEE Transactions on Signal Processing, vol. 48 (9), 2000.
[11] A. Yamazaki, T. Tajima, and K. Matsuoka, "Convolutive independent
component analysis of eeg data," SICE 2003 Annual Conference, vol. 2,
pp. 1227- 1231, 2003.
[12] P. H. Thakur, H. Lu, S. S. Hsiao, and K. O. Johnson, "Automated optimal
detection and classification of neural action potentials in extra-cellular
recordings." Journal of Neuroscience Methods, vol. 162, no. 1-2, pp.
364-376, 2007.
[13] M. Natora, F. Franke, M. Munk, and K. Obermayer, "Blind source
separation of sparse overcomplete mixtures and application to neural
recordings," Lecture Notes in Computer Science - Independent Component
Analysis and Signal Separation, vol. 5441, pp. 459-466, 2009.
[14] M. S. Pedersen, J. Larsen, U. Kjems, and L. C. Parra, A Survey of
Convolutive Blind Source Separation Methods, ser. Springer Handbook
of Speech Processing. Springer Press, Nov 2007.
[15] D. Scholnik, "Mixed-norm fir filter optimization using second-order
coneprogramming," ICASSP, IEEE International Conference on Acoustics,
Speech and Signal Processing - Proceedings, vol. 2, pp. 1525-1528,
2002.
[16] F. Robey, D. Fuhrmann, E. Kelly, and R. Nitzberg, "A cfar adaptive
matched filter detector," IEEE Transactions on Aerospace and Electronic
Systems, vol. 28 (1), pp. 208-216, 1992.
[17] O. Besson and F. Vincent, "Performance analysis of beamformers using
generalized loading of the covariance matrix in the presence of random
steering vector errors," IEEE Transactions on Signal Processing, vol. 53,
no. 2, pp. 452-459, 2005.
[18] T. Fawcett, "An introduction to roc analysis," Pattern recognition letters,
vol. 27 (8), pp. 861-874, 2006.
[19] R. Vollgraf and K. Obermayer, "Improved optimal linear filters for the
discrimination of multichannel waveform templates for spike-sorting
applications," IEEE Signal Processing Letters, vol. 13, no. 3, pp. 121-
124, 2006.
[20] F. Franke, M. Natora, C. Boucsein, M. Munk, and K. Obermayer, "An
online spike detection and spike classification algorithm capable of instantaneous
resolution of overlapping spikes," Journal of Computational
Neuroscience, 2009, in press.
[21] H. Luetkepohl, Handbook of Matrices. John Wiley and Sons, 1996.
[22] M. Ageel, "Variance upper bounds and a probability inequality for
discrete alpha-unimodality," Aplicationes Mathematicae, vol. 27, pp. 403
- 410, 2000.
@article{"International Journal of Information, Control and Computer Sciences:61447", author = "Michal Natora and Felix Franke and Klaus Obermayer", title = "Optimal Convolutive Filters for Real-Time Detection and Arrival Time Estimation of Transient Signals", abstract = "Linear convolutive filters are fast in calculation and in application, and thus, often used for real-time processing of continuous data streams. In the case of transient signals, a filter has not only to detect the presence of a specific waveform, but to estimate its arrival time as well. In this study, a measure is presented which indicates the performance of detectors in achieving both of these tasks simultaneously. Furthermore, a new sub-class of linear filters within the class of filters which minimize the quadratic response is proposed. The proposed filters are more flexible than the existing ones, like the adaptive matched filter or the minimum power distortionless response beamformer, and prove to be superior with respect to that measure in certain settings. Simulations of a real-time scenario confirm the advantage of these filters as well as the usefulness of the performance measure.
", keywords = "Adaptive matched filter, minimum variance distortionless response, beam forming, Capon beam former, linear filters, performance measure.", volume = "3", number = "7", pages = "1818-6", }
