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

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.

References

  1. 1.

    Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.

    Google Scholar 

  2. 2.

    Haykin S: Adaptive Filter Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 2002.

    Google Scholar 

  3. 3.

    Beaufays F: Transform-domain adaptive filters: an analytical approach. IEEE Transactions on Signal Processing 1995, 43(2):422–431. 10.1109/78.348125

    Article  Google Scholar 

  4. 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.2003.822351

    MathSciNet  Article  Google Scholar 

  5. 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.1985.1164643

    Article  Google Scholar 

  6. 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. 10.1109/29.1602

    Article  Google Scholar 

  7. 7.

    Li G: A stable and efficient adaptive notch filter for direct frequency estimation. IEEE Transactions on Signal Processing 1997, 45(8):2001–2009. 10.1109/78.611196

    Article  Google Scholar 

  8. 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. 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. 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. 10.1109/78.845922

    Article  Google Scholar 

  11. 11.

    Papoulis A: Probability, Random Variables and Stochastic Processes. McGraw-Hill, NewYork, NY, USA; 1991.

    Google Scholar 

  12. 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.1979.1163203

    Article  Google Scholar 

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Correspondence to Osman Kukrer.

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Kukrer, O., Hocanin, A. An FIR Notch Filter for Adaptive Filtering of a Sinusoid in Correlated Noise. EURASIP J. Adv. Signal Process. 2006, 038190 (2006). https://doi.org/10.1155/ASP/2006/38190

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Keywords

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