# ON THE INFLUENCE OF LOW FREQUENCY COMPONENTS IN THE WEIGHT BEHAVIOUR OF THE LMS ALGORITHM

### D. S. Brito, R. C. S. Freire, E. Aguiar, F. Lucena, A. K. Barros

#### 2009

#### Abstract

The Least Mean Square (LMS) algorithm is a very important tool in the estimation and filtering of biomedical signals. Amongst these signals are the periodic and quasiperiodic. For example, the LMS algorithm was used to estimate the coefficients of the Fourier series at a given frequency or even in a spectral analysis. In this paper we study the behavior of the weights of the LMS algorithm when the signal to be estimated acts at very low frequencies. We prove theoretically that lower frequency noise affects the estimation of the weights at higher frequencies. We carried out simulations and showed that experimental findings are in agreement with the theoretical results. Moreover, we exemplify the problem with electrocardiogram signals (ECG).

#### References

- Barros, A. K. and Ohnishi, N. (1997). Mse behavior of biomedical event-related filters. IEEE Transactions Biomedical Engineering, BME-44(9):848-855.
- Barros, A. K., Yoshizawa, M., and Yasuda, Y. (1995). Filtering non-correlated noise in impedance cardiography. IEEE Transactions on Biomedical Engineering, 42(3):324-327.
- Friesen, G., Jannett, T., Jadallah, M., Yates, S., Quint, S. R., and Nagle, H. (1990). A comparison of the noise sensitivity of nine qrs detection algorithms. IEEE Transactions on Biomedical Engineering, 37(1):85- 98.
- Goldberger, A. L., Amaral, L. A. N., Glass, L., Hausdorff, J. M., Ivanov, P. C., Mark, R. G., Mietus, J. E., Moody, G. B., Peng, C.-K., and Stanley, H. E. (2000 June 13). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation, 101(23):e215- e220. Circulation Electronic Pages: http:// circ.ahajournals.org/cgi/content/full/101/23/e215.
- Vaz, C. A., Kong, X., and Thakor, N. V. (1994). An adaptive estimation of periodic signals using a fourier linear combiner. IEEE Transactions on Signal Processing, 42(1):1-10.
- Vaz, C. A. and Thakor, N. V. (1989). Adaptive fourier estimation of time-varying evoked potentials. IEEE Transactions Biomedical Engineering, 36(4):448- 455.
- Widrow, B., Baudrenghien, P., Vetterli, M., and Titchener, P. (1987). Fundamental relations between the lms algorithm and dft. IEEE Transactions on Circuits and Systems, 7(Cas-34):814-820.
- Widrow, B. and Hoff Jr., M. E. T. (1960). Adaptive switching circuits. In Proceedings IRE WESCON Convention Record, pages 96-104, New York. INSTICC Press.
- Widrow, B., McCool, J. M., Larimore, M. G., and Johnson Jr., C. R. (1976). Stationary and nonstationary learning characteristics of the lms adaptive filter. In Procedings IRE WESCON Convention Record, pages 1151-1162. I Proc. of the IEEE.
- Widrow, B. and Stearns, S. D. (1985). Adaptive Signal Processing. Prentice-Hall Signal Processing Series, New Jersey - USA, 1st. edition.

#### Paper Citation

#### in Harvard Style

S. Brito D., C. S. Freire R., Aguiar E., Lucena F. and K. Barros A. (2009). **ON THE INFLUENCE OF LOW FREQUENCY COMPONENTS IN THE WEIGHT BEHAVIOUR OF THE LMS ALGORITHM** . In *Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2009)* ISBN 978-989-8111-65-4, pages 345-350. DOI: 10.5220/0001550803450350

#### in Bibtex Style

@conference{biosignals09,

author={D. S. Brito and R. C. S. Freire and E. Aguiar and F. Lucena and A. K. Barros},

title={ON THE INFLUENCE OF LOW FREQUENCY COMPONENTS IN THE WEIGHT BEHAVIOUR OF THE LMS ALGORITHM},

booktitle={Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2009)},

year={2009},

pages={345-350},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001550803450350},

isbn={978-989-8111-65-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2009)

TI - ON THE INFLUENCE OF LOW FREQUENCY COMPONENTS IN THE WEIGHT BEHAVIOUR OF THE LMS ALGORITHM

SN - 978-989-8111-65-4

AU - S. Brito D.

AU - C. S. Freire R.

AU - Aguiar E.

AU - Lucena F.

AU - K. Barros A.

PY - 2009

SP - 345

EP - 350

DO - 10.5220/0001550803450350