Skip to content

Advertisement

  • Research Article
  • Open Access

An FIR Notch Filter for Adaptive Filtering of a Sinusoid in Correlated Noise

EURASIP Journal on Advances in Signal Processing20062006:038190

https://doi.org/10.1155/ASP/2006/38190

  • Received: 26 July 2005
  • Accepted: 18 February 2006
  • Published:

Abstract

A novel adaptive FIR filter for the estimation of a single-tone sinusoid corrupted by additive noise is described. The filter is based on an offline optimization procedure which, for a given notch frequency, computes the filter coefficients such that the frequency response is unity at that frequency and a weighted noise gain is minimized. A set of such coefficients is obtained for notch frequencies chosen at regular intervals in a given range. The filter coefficients corresponding to any frequency in the range are computed using an interpolation scheme. An adaptation algorithm is developed so that the filter tracks the sinusoid of unknown frequency. The algorithm first estimates the frequency of the sinusoid and then updates the filter coefficients using this estimate. An application of the algorithm to beamforming is included for angle-of-arrival estimation. Simulation results are presented for a sinusoid in correlated noise, and compared with those for the adaptive IIR notch filter.

Keywords

  • Additive Noise
  • Adaptive Filter
  • Interpolation Scheme
  • Filter Coefficient
  • Notch Filter

[123456789101112]

Authors’ Affiliations

(1)
Department of Electrical and Electronics Engineering, Mersin 10, Eastern Mediterranean University, Gazimagusa, Turkey

References

  1. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.MATHGoogle Scholar
  2. Haykin S: Adaptive Filter Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 2002.MATHGoogle Scholar
  3. Beaufays F: Transform-domain adaptive filters: an analytical approach. IEEE Transactions on Signal Processing 1995, 43(2):422-431. 10.1109/78.348125View ArticleGoogle Scholar
  4. Resende LS, Romano JMT, Bellanger MG: Split wiener filtering with application in adaptive systems. IEEE Transactions on Signal Processing 2004, 52(3):636-644. 10.1109/TSP.2003.822351MathSciNetView ArticleGoogle Scholar
  5. Nehorai A: A minimal parameter adaptive notch filter with constrained poles and zeros. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985, 33(4):983-996. 10.1109/TASSP.1985.1164643View ArticleGoogle Scholar
  6. Stoica P, Nehorai A: Performance analysis of an adaptive notch filter with constrained poles and zeros. IEEE Transactions on Acoustics, Speech, and Signal Processing 1988, 36(6):911-919. 10.1109/29.1602MathSciNetView ArticleMATHGoogle Scholar
  7. Li G: A stable and efficient adaptive notch filter for direct frequency estimation. IEEE Transactions on Signal Processing 1997, 45(8):2001-2009. 10.1109/78.611196View ArticleGoogle Scholar
  8. Mvuma A, Nishimura S, Hinamoto T: Adaptive IIR notch filter with controlled bandwidth for narrow-band interference suppression in DS CDMA system. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '03), May 2003, Bangkok, Thailand 4: IV-361-IV-364.Google Scholar
  9. Hocanin A, Kukrer O: Estimation of the frequency and waveform of a single-tone sinusoid using an offline-optimized adaptive filter. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 4: 349-352.Google Scholar
  10. Rafaely B, Elliot SJ: A computationally efficient frequency-domain LMS algorithm with constraints on the adaptive filter. IEEE Transactions on Signal Processing 2000, 48(6):1649-1655. 10.1109/78.845922View ArticleGoogle Scholar
  11. Papoulis A: Probability, Random Variables and Stochastic Processes. McGraw-Hill, NewYork, NY, USA; 1991.MATHGoogle Scholar
  12. Rickard JT, Zeidler JR: Second-order output statistics of the adaptive line enhancer. IEEE Transactions on Acoustics, Speech, and Signal Processing 1979, 27(1):31-39. 10.1109/TASSP.1979.1163203View ArticleMATHGoogle Scholar

Copyright

Advertisement