Skip to content

Advertisement

  • Research Article
  • Open Access

High-Selectivity Filter Banks for Spectral Analysis of Music Signals

  • Filipe C. C. B. Diniz1Email author,
  • Iuri Kothe1,
  • Sergio L. Netto1 and
  • Luiz W. P. Biscainho1
EURASIP Journal on Advances in Signal Processing20062007:094704

https://doi.org/10.1155/2007/94704

Received: 7 December 2005

Accepted: 10 September 2006

Published: 6 December 2006

Abstract

This paper approaches, under a unified framework, several algorithms for the spectral analysis of musical signals. Such algorithms include the fast Fourier transform (FFT), the fast filter bank (FFB), the constant- transform (C T), and the bounded- transform (B T), previously known from the associated literature. Two new methods are then introduced, namely, the constant- fast filter bank (C FFB) and the bounded- fast filter bank (B FFB), combining the positive characteristics of the previously mentioned algorithms. The provided analyses indicate that the proposed B FFB achieves an excellent compromise between the reduced computational effort of the FFT, the high selectivity of each output channel of the FFB, and the efficient distribution of frequency channels associated to the C T and B T methods. Examples are included to illustrate the performances of these methods in the spectral analysis of music signals.

Keywords

FourierFourier TransformInformation TechnologySpectral AnalysisFast Fourier Transform

[1234567891011121314151617]

Authors’ Affiliations

(1)
LPS-PEE/COPPE and DEL/Poli, Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil

References

  1. Farhang-Boroujeny B, Lim YC: A comment on the computational complexity of sliding FFT. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 1992,39(12):875-876. 10.1109/82.208583View ArticleMATHGoogle Scholar
  2. Lim YC, Farhang-Boroujeny B: Fast filter bank (FFB). IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 1992,39(5):316-318. 10.1109/82.142033View ArticleGoogle Scholar
  3. William D, Brown E: Theoretical Foundations of Music. Wadsworth, Belmont, Calif, USA; 1978.Google Scholar
  4. Brown JC:Calculation of a constant spectral transform. Journal of the Acoustical Society of America 1991,89(1):425-434. 10.1121/1.400476View ArticleGoogle Scholar
  5. Brown JC, Puckette MS:An efficient algorithm for the calculation of a constant transform. Journal of the Acoustical Society of America 1992,92(5):2698-2701. 10.1121/1.404385View ArticleGoogle Scholar
  6. Kashima KL, Mont-Reynaud B:The bounded- approach to time-varying spectral analysis. In Tech. Rep. STAN-M-28. Stanford University, Department of Music, Stanford, Calif, USA; 1985.Google Scholar
  7. Graziosi DB, Dos Santos CN, Netto SL, Biscainho LWP:A constant- spectral transformation with improved frequency response. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '04), May 2004, Vancouver, Canada 5: 544-547.Google Scholar
  8. Dos Santos CN, Netto SL, Biscainho LWP, Graziosi DB:A modified constant- transform for audio signals. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Canada 2: 469-472.Google Scholar
  9. Diniz FCCB, Kothe I, Biscainho LWP, Netto SL:A bounded- fast filter bank for audio signal analysis. Proceedings of IEEE International Telecommunications Symposium (ITS '06), September 2006, Fortaleza, Brazil 1:Google Scholar
  10. Diniz PSR, da Silva EAB, Netto SL: Digital Signal Processing: System Analysis and Design. Cambridge University Press, Cambridge, UK; 2002.View ArticleMATHGoogle Scholar
  11. Cooley JW, Tukey JW: An algorithm for the machine calculation of complex fourier series. Mathematics of Computation 1965,19(90):297-301. 10.1090/S0025-5718-1965-0178586-1MathSciNetView ArticleMATHGoogle Scholar
  12. Haykin S, Van Veen B: Signals and Systems. 2nd edition. John wiley & Sons, Hoboken, NJ, USA; 2002.MATHGoogle Scholar
  13. Vaidyanathan PP: Multirate Systems and Filter Banks. Prentice Hall, Upper Saddle River, NJ, USA; 1992.MATHGoogle Scholar
  14. Lim YC: Frequency-response masking approach for the synthesis of sharp linear phase digital filters. IEEE Transactions on Circuits and Systems 1986,33(4):357-364. 10.1109/TCS.1986.1085930View ArticleGoogle Scholar
  15. Lim YC, Farhang-Boroujeny B: Analysis and optimum design of the FFB. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '94), June 1994, London, UK 2: 509-512.View ArticleGoogle Scholar
  16. Wei LJ, Lim YC: Designing the fast filter bank with a minimum complexity criterion. Proceedings of the 7th International Symposium on Signal Processing and Its Applications (ISSPA '03), July 2003, Paris, France 2: 279-282.Google Scholar
  17. Lim YC, Wei LJ: Matrix formulation: fast filter bank. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Canada 5: 133-136.Google Scholar

Copyright

© Filipe C. C. B. Diniz et al. 2007

Advertisement