The latest research topic is Signal processing of nonlinear systems in the frequency domain, which focuses on the frequency domain analysis based design of nonlinear systems for signal processing objectives. In science and engineering fields, linear system theories in the frequency domain have been well established, and have wide applications in practice. The extension of frequency domain analysis methods to nonlinear systems started in 1950s when the concept of nonlinear transfer function, known as Generalized Frequency Response Functions (GFRFs), was first introduced (George 1959). Based on the Volterra series theory of nonlinear systems, many frequency domain analysis methods have been proposed (Bedrosian and Rice 1971, Bussgang et al 1974, Powers and Miksad 1987, Vinh et al 1987, Billings and Tsang 1989a and 1989b, Peyton Jones and Billings 1989, Billings et al 1990, Worden et al 1994, Lang and Billings 1996, Zhang et al 1995, Billings and Lang 1996a and 1996b). Several authors have derived some algorithms to estimate the GFRFs from input output data (Tick 1961, Kim and Powers 1988, Billings and Peyton Jones 1990, Nam and Powers 1994). These research studies have extended many linear systems frequency domain approaches to the nonlinear case.

Current studies based on Volterra series theories are basically related to low typically second order filter design in the time domain. There are few attempts to design nonlinear filters based on frequency domain objectives. For linear systems, it is well known that the output frequency range is exactly the same as that of the corresponding input, while for nonlinear systems, possible output frequency components are much richer than the frequency components of the input (Weiner and Spina 1980, Lang and Billings 1997). Previous studies regard the rich output frequency components as negative effects and try to avoid these effects in associated nonlinear filter designs.

However, the property of richer output frequencies with nonlinear systems can be an advantage to many engineering applications. The concept of Energy Transfer Filters was recently proposed based on this idea (Billings and Lang 2002). The fundamental principle of the energy transfer filters is that the energy in one frequency range can be moved or transferred to other frequency locations by exploiting nonlinear effects (Lang and Billings 2005). The practical significance is that energy could be transferred to desired frequency locations to meet the signal requirements of many engineering designs such as in the designs of communications and mechanical engineering.

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