Generalized harmonic analysis of Arc-Tangent Square Root (ATSR) nonlinear device for virtual bass system

Nowadays, portable devices demand small-sized and low-end loudspeaker, however, the physical acoustic bass (or low-frequency) reproduction is usually poor. Bass enhancement by equalization is not feasible, and may even overload or damage the loudspeaker. Bass enhancement for such low-end loudspeaker can be psychoacoustically accomplished by exploiting the missing fundamental phenomenon. These systems are known as virtual bass systems (VBS), and generally use nonlinear device (NLD) as the main processing block to generate harmonics for virtual pitch perception. One of the recently developed NLD is the Arc-Tangent Square Root (ATSR) function, which can be used to control the pitch perception by a set of parameters. Mathematical relation between the input and output of the NLD is derived under a single-tone analysis framework. A detailed study on how the parameters of this NLD affect the harmonic´s decay pattern and intensity is presented in this paper.