Efficient Spectral Estimation of Non-Stationary Harmonic Signals Using Harmonic Transform

Michal Trzos, Hasan Khaddour


Non-stationary harmonic signals cannot be accuratelyrepresented by Fourier transform (FT). Fortunately, severalmethods for representing non-stationary harmonic signalsexist including Fan-Chirp trasnform (FChT) or Harmonic transform(HT). This article is focused on the Harmonic transform andits computation. Estimation of slope of fundamental frequencychange between analysed segments is essential for computationof the HT. The slope is estimated using several realisations ofHT and comparing the spectral flatness. Optimisation of thisprocedure is presented in the article.

Full Text:



M. Goodwin and M. Vetterli, “Time-frequency signal models for music analysis, transformation, and synthesis,” in proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1996, pp. 133–136.

G. Wakefield, “Time-pitch representations: acoustic signal processing and auditory representations,” in Time-Frequency and Time-Scale Analysis, 1998. Proceedings of the IEEE-SP International Symposium on, Oct. 1998, pp. 577–580.

A. Makur and S. Mitra, “Warped discrete-fourier transform: Theory and applications,” Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, vol. 48, no. 9, pp. 1086–1093, Sep. 2001.

L. Cohen, “The scale representation,” Signal Processing, IEEE Transactions on, vol. 41, no. 12, pp. 3275–3292, Dec. 1993.

T. Irino and R. D. Patterson, “Segregating information about the size and shape of the vocal tract using a time-domain auditory model: the stabilised wavelet-mellin transform,” Speech Commun., vol. 36, pp. 181–203, Mar. 2002.

A. De Sena and D. Rocchesso, “A study on using the mellin transform for vowel recognition,” in SMC05, International conference on Sound Music and Computing, Salerno, Italy, 2005.

F. Zhang, G. Bi, and Y. Chen, “Harmonic transform,” Vision, Image and Signal Processing, IEE Proceedings, vol. 151, no. 4, pp. 257–263, Aug. 2004.

D. Bailey and P. Swarztrauber, “The fractional fourier transform and applications,” SIAM Review, vol. 33, no. 3, pp. 389–404, Sep. 1995.

R. Tao, Y.-L. Li, and Y. Wang, “Short-time fractional fourier transform and its applications,” Signal Processing, IEEE Transactions on, vol. 58, no. 5, pp. 2568–2580, May 2010.

L. Weruaga and M. K´epesi, “Speech analysis with the short-time chirp transform,” in Eurospeech, Geneve, Sep. 2003, pp. 53–56.

M. K´epesi and L. Weruaga, “Speech analysis with the fast chirp transform,” 2004.

L. Weruaga and M. K´epesi, “The fan-chirp transform for non-stationary harmonic signals,” Signal Processing, vol. 87, no. 6, pp. 1504–1522, 2007.

M. K´epesi and L. Weruaga, “Adaptive chirp-based time–frequency analysis of speech signals,” Speech Communication, vol. 48, no. 5, pp. 474–492, 2006.

P. Zubrycki and A. Petrovsky, “Accurate estimation of harmonic amplitudes in voiced speech based on harmonic transform,” in Signals and Electronic Systems, 2008. ICSES ’08. International Conference on, Sep. 2008, pp. 47 –50.

——, “Accurate speech decomposition into periodic and aperiodic components based on discrete harmonic transform,” in 15th European Signal Processing Conference (EUSIPCO 2007), Pozna´n, Poland, 2007, pp. 2336–2340.

DOI: http://dx.doi.org/10.11601/ijates.v1i2-3.36


  • There are currently no refbacks.