The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Frequency-Warped Autoregressive Modeling and Filtering

Aki Härmä

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission for public examination and debate in Auditorium S4, Department of Electrical and Communications Engineering, Helsinki University of Technology, Espoo, Finland, on the 25th of May, 2001, at 12 o'clock noon.

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This thesis consists of an introduction and nine articles. The articles are related to the application of frequency-warping techniques to audio signal processing, and in particular, predictive coding of wideband audio signals. The introduction reviews the literature and summarizes the results of the articles.

Frequency-warping, or simply warping techniques are based on a modification of a conventional signal processing system so that the inherent frequency representation in the system is changed. It is demonstrated that this may be done for basically all traditional signal processing algorithms. In audio applications it is beneficial to modify the system so that the new frequency representation is close to that of human hearing. One of the articles is a tutorial paper on the use of warping techniques in audio applications.

Majority of the articles studies warped linear prediction, WLP, and its use in wideband audio coding. It is proposed that warped linear prediction would be particularly attractive method for low-delay wideband audio coding. Warping techniques are also applied to various modifications of classical linear predictive coding techniques. This was made possible partly by the introduction of a class of new implementation techniques for recursive filters in one of the articles. The proposed implementation algorithm for recursive filters having delay-free loops is a generic technique. This inspired to write an article which introduces a generalized warped linear predictive coding scheme. One example of the generalized approach is a linear predictive algorithm using almost logarithmic frequency representation.

This thesis consists of an overview and of the following 9 publications:

  1. A. Härmä, U. K. Laine, and M. Karjalainen, An experimental audio codec based on warped linear prediction of complex valued signals, in Proc. IEEE Int. Conf. Acoust. Speech and Signal Proc. (ICASSP'99), vol. 1, (Munich), pp. 323-327, 1997.
  2. A. Härmä, U. K. Laine, and M. Karjalainen, Backward adaptive warped lattice for wideband stereo coding, in Signal Processing IX: Theories and applications (EUSIPCO'98), (Greece), pp. 729-732, 1998.
  3. A. Härmä, U. K. Laine and M. Karjalainen, On the utilization of overshoot effects in low-delay audio coding, in Proc. IEEE Int. Conf. Acoust. Speech and Signal Proc. (ICASSP'99), vol. II, (Phoenix, Arizona), pp. 893-896, IEEE, March 1999.
  4. A. Härmä and U. K. Laine, Warped low-delay CELP for wide-band audio coding, in Proc. of the AES 17th Int. Conference: High-Quality Audio Coding, (Florence, Italy), pp. 207-215, September 2-5 1999.
  5. A. Härmä, M. Juntunen, P. Kaipio, Time-varying autoregressive modeling of audio and speech signals, Signal Processing X: theories and applications (EUSIPCO 2000), (Tampere, Finland), pp. 2037-2040, September 2000.
  6. A. Härmä, Implementation of frequency-warped recursive filters, Signal Processing, 80 (3), pp. 543-548, February 2000.
  7. A. Härmä, Linear predictive coding with modified filter structures, Report no. 59/Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, Espoo, Finland, 2001. (Submitted to IEEE Trans. Speech and Audio Processing, January 2000.)
  8. A. Härmä and U .K. Laine, A Comparison of warped and conventional linear predictive coding, IEEE Trans. Speech and Audio Processing, July 2001.
  9. A. Härmä, M. Karjalainen, L. Savioja, V. Välimäki, U. K. Laine, and J. Huopaniemi, Frequency-warped signal processing for audio applications, J. Audio Eng. Soc., Vol. 48 (11), pp. 1011-1031, November 2000.

Keywords: warping, delay-free loops, linear prediction, WLP, LPC, warped filters, audio signal processing

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© 2001 Helsinki University of Technology

Last update 2011-05-26