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Signal processing transforms the input signal to output signal using either linear transformation function or nonlinear transformation functions. If the input signal vector is $ \mathbf{x} $, the output signal vector transformed by linear matrix filter is given by

$ \mathbf{y} = \mathbf{W}\mathbf{x} $

where $ \mathbf{W} $ is the linear transformation matrix. For nonlinear signal processing, the output signal vector is given by

$ \mathbf{y} = f_w(\mathbf{x}) $

where $ f_w(.) $ is the nonlinear transformation function.