Multicomponent AM-FM Modelling of Nonstationary Signals

Prof. Francesco Gianfelici, Aalborg University, Denmark

11 Nov 2010, 17:00; Location: S4|10-1

Multicomponent AM-FM models, also known as McAulay-Quatieri models in audio and speech processing, are highly parametric representations of non stationary signals that are able to effectively represent a large class of real phenomena with no limitations in terms of signal kind, applicative domain, and so on. During recent decades, the elegant formulation of these representations has attracted the attentions of many researchers in different areas, such as speech, image and signal processing, but also information theory, communications, biomedical and biometric engineering. The reason for this great interest, is related to the intrinsic nature of physical phenomena that are generally described by stochastic partial differential equations, whose these models may be considered, with no detriment to generality, a generical and suitable solution. The history of these models can be effectively classified according to the milestones that have been developed since 1978, when Teager published the mathematical formulation of the homonymous operator, also known as: i) Teager energy operator (TEO), or ii) Teager-Kaiser operator, for the systematic Kaiser works (during 78-82) that had been recognized as decisive for the TEO definition and development. In 1984 Bar-Ness et al. [1] proposed a suitable technique based on Phase Locked Loop (PLL) in order to separate two AM-FM components, where two couples of inphase and quadrature signals are used to extract the amplitude envelopes of the components, and feedback loops progressively correct the estimation: this technique represents one of the first works for two component AM-FM demodulation based on a pseudo-Hilbert approach. In 1986, Quatieri and McAulay discovered the relationships between the AM-FM modulations and the physiological properties of speech production and perception. The lack of empirical conditions and the suitability in many applications such as speech coding, synthesis and recognition has been recognized as one of the most important discoveries in audio and speech processing, and for this reason the multicomponent AM-FM models are also known as McAulay-Quatieri models. In this context, the great efforts that have been done by Maragos et al. (during 87-93) with the aim of improving the knowledge about TEO and its demodulation capabilities generated some works about the positivity of this operator and the effective filtering methodologies that have to be used, but also the development of suitable algorithms, such as Discrete Energy Separations Algorithm (DESA), and so on. Moreover, Bovik and Maragos defined an extension of DESA for the multicomponent demodulation [2], calledMultiband Energy Separation Algorithm (MESA), which exploits several properties of Gabor eigenfilters and the well-known half-pick condition that are related to the abovementioned Maragos works. In the years between 1998-2000 two novel techniques have been proposed: on the one hand Santhanam and Maragos presented an innovative approach [3], called Periodic Algebraic Separation and Energy Demodulation (PASED), which is able to outperform the demodulation capabilities of MESA; on the other hand, Huang et al. [4] proposed the Empirical Mode Decomposition (EMD) that is based on the iterative extraction of intrinsic modes, followed by the application of the Hilbert transform to compute a spectrum from them. A generalization of DESA for large frequency deviations was proposed by Santhanam [5] in 2004. Moreover, in 2004-2007 Bovik et al. published some results on the multidimensional demodulation. In 2007, Gianfelici et al. developed the Iterated Hilbert Transform (IHT) [6] that allows an asymptotically exact reconstruction of non-stationary signals as multicomponent AM-FM representations. This approach does not need the complex filter optimizations required by the other techniques and has higher performance than that obtained by current best practices. In this talk the impact of IHT on the milestones and the pioneering results of several decades of the advanced research done between MIT, Harvard, Bell-Labs, and NASA, will be analyzed. Past performance, open problems, and future trends of AM-FM models will be considered and discussed.


[1] Y. Bar-Ness, F. Cassara, H. Schachter, and R. DiFazio, “Crosscoupled phase-locked loop with closed loop amplitude control,” IEEE Trans. Commun., vol. 32, no. 2, pp. 195–199, Feb. 1984.

[2] A. C. Bovik, P. Maragos, and T. F. Quatieri, “AM-FM energy detection and separation in noise using multiband energy operators,” IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3245–3265, Dec. 1993.

[3] B. Santhanam and P. Maragos, “Multicomponent AM-FM demodulation via periodicity-based algebraic separation and EMD SNR energy-based demodulation,” IEEE Trans. Commun., vol. 48, no. 3, pp. 473–490, Mar. 2000.

[4] N. E. Huang et al., “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society of London—A, vol. 454, no. 1971, pp. 903–995, Mar. 1998.

[5] B. Santhanam, “Generalized energy demodulation for large frequency deviations and wideband signals,” IEEE Signal Process. Lett., vol. 11, no. 3, pp. 341–344, Mar. 2004.

[6] F. Gianfelici, et al., “Multicomponent AM-FM representations: An asymptotically exact approach,” IEEE Trans. Audio, Speech, Language Processing, vol. 15, no. 3, pp. 823–837, 2007.

[7] G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, Grado, Italy, Jun. 2003.

Category: CE Seminar


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