Hammerstein Model for Speech Coding

Abstract

<p/> <p>A nonlinear Hammerstein model is proposed for coding speech signals. Using Tsay's nonlinearity test, we first show that the great majority of speech frames contain nonlinearities (over 80% in our test data) when using 20-millisecond speech frames. Frame length correlates with the level of nonlinearity: the longer the frames the higher the percentage of nonlinear frames. Motivated by this result, we present a nonlinear structure using a frame-by-frame adaptive identification of the Hammerstein model parameters for speech coding. Finally, the proposed structure is compared with the LPC coding scheme for three phonemes /a/, /s/, and /k/ by calculating the Akaike information criterion of the corresponding residual signals. The tests show clearly that the residual of the nonlinear model presented in this paper contains significantly less information compared to that of the LPC scheme. The presented method is a potential tool to shape the residual signal in an encode-efficient form in speech coding.</p

System identification of Wiener systems with B-spline functions using De Boor recursion

“…The Hammerstein model, comprising a nonlinear static functional transformation followed by a linear dynamical model, has been applied to nonlinear plant/process modelling in a wide range of engineering problems (Balestrino, Landi, Ould-Zmirli, and Sani 2001;Bloemen, Van Den Boom, and Verbruggen 2001;Turunen, Tanttu, and Loula 2003). The Hammerstein model has been widely researched (Billings and Fakhouri 1979;Stoica and So¨derstro¨m 1982;Greblicki and Pawlak 1986;Greblicki 1989Greblicki , 2002Lang 1997;Verhaegen and Westwick 1996;Bai and Fu 2002;Chen 2004;Chaoui, Giri, Rochdi, Haloua, and Naitali 2005;Hong and Mitchell 2007).…”

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

“…It is a popular nonlinear plant/ process modelling approach for a wide range of biological/ engineering problems [10][11][12][13]. For example, it is a suitable model for signal processing applications involving any nonlinear distortion followed by a linear filter, the modelling of the human heart in order to regulate the heart rate during treadmill exercises [14] and the modelling of hydraulic actuator friction dynamics [15].…”

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

“…The Hammerstein model, comprising a nonlinear static functional transformation followed by a linear dynamical model, has been applied to nonlinear plant/process modelling in a wide range of biological/engineering problems (Hunter and Korenberg 1986;Balestrino, Landi, Ould-Zmirli and Sani 2001;Bloemen, van den Boom, and Verbruggen 2001;Turunen, Tanttu, and Loula 2003). For example, it is a suitable model for signal processing applications involving any nonlinear distortion followed by a linear filter, the modelling of the human heart in order to regulate the heart rate during treadmill exercises (Su 2007), and the modelling of hydraulic actuator friction dynamics (Kwak, Yagle, and Levitt 1998).…”