Nonlinear noise cancellation

Abstract

Noise or interference is often assumed to be a random process. Conventional linear filtering, control or prediction techniques are used to cancel or reduce the noise. However, some noise processes have been shown to be nonlinear and deterministic. These nonlinear deterministic noise processes appear to be random when analysed with second order statistics. As nonlinear processes are widespread in nature it may be beneficial to exploit the coherence of the nonlinear deterministic noise with nonlinear filtering techniques. The nonlinear deterministic noise processes used in this thesis are generated from nonlinear difference or differential equations which are derived from real world scenarios. Analysis tools from the theory of nonlinear dynamics are used to determine an appropriate sampling rate of the nonlinear deterministic noise processes and their embedding dimensions. Nonlinear models, such as the Volterra series filter and the radial basis function network are trained to model or predict the nonlinear deterministic noise process in order to reduce the noise in a system. The nonlinear models exploit the structure and determinism and, therefore, perform better than conventional linear techniques. These nonlinear techniques are applied to cancel broadband nonlinear deterministic noise which corrupts a narrowband signal. An existing filter method is investigated and compared with standard linear techniques. A new filter method is devised to overcome the restrictions of the existing filter method. This method combines standard signal processing concepts (filterbanks and multirate sampling) with linear and nonlinear modelling techniques. It overcomes the restrictions associated with linear techniques and hence produces better performance. Other schemes for cancelling broadband noise are devised and investigated using quantisers and cascaded radial basis function networks. Finally, a scheme is devised which enables the detection of a signal of interest buried in heavy chaotic noise. Active noise control is another application where the acoustic noise may be assumed to be a nonlinear deterministic process. One of the problems in active noise control is the inversion process of the transfer function of the loudspeaker. This transfer function may be nonminimum phase. Linear controllers only perform sub-optimally in modelling the noncausal inverse transfer function. To overcome this problem in conjunction with the assumption that the acoustic noise is nonlinear and deterministic a combined linear and nonlinear controller is devised. A mathematical expression for the combined controller is derived which consists of a linear system identification part and a nonlinear prediction part. The traditional filtered-x least mean squares scheme in active noise control does not allow the implementation of a nonlinear controller. Therefore, a control scheme is devised to allow a nonlinear controller in conjunction with an adaptive block least squares algorithm. Simulations demonstrate that the combined linear and nonlinear controller outperforms the conventional linear controller.