An Audio Equalisation Linear Phase FIR Filter Design Method using RBF based Smoothing and Interpolation

A method for the design of audio equalisation linear phase FIR filters is developed by using a variant of the tuneable approximate piecewise linear regression (TAPLR) method to model the required FIR magnitude frequency response. This TAPLR model incorporates a set of contiguous piecewise linear (affine) sections which are coupled and smoothed by a single tuning parameter associated with a set of bandwidth weighted radial basis functions (RBFs) assigned to each linear section. The main difference between this variant and the original TAPLR method is that it incorporates RBFs with variable bandwidths that can be centred and set according to standard nonlinear frequency spacings as used for audio system response measurements, thereby producing a more accurate response model. The TAPLR smoothing mechanism is used to achieve the required degree of FIR filter band limiting to avoid aliasing effects and the Gibbs phenomenon. Some typical audio FIR filter design examples are provided to show the value and versatility of the method as compared with the standard windowing design approach.