Least squares IIR filter design on a logarithmic frequency scale

A technique is described for designing infinite impulse response (IIR) digital filters where the arbitrary desired frequency response is approximated with respect to the log of frequency. The technique uses the inverse of a spectral transformation to produce a prewarped specification, from which a prototype filter is designed using a suitable least-squares algorithm. The forward spectral transformation is then used on the filter to realign its frequency response with the original specification. The prewarping operation reduces the frequency resolution required in the filter design process, making it possible to use efficient, optimal design techniques that use a linear frequency scale. An algorithm is presented for the computation of the spectral transformation parameters which maximize the advantages of the prewarping operation. The error weighting function it introduces is derived and compensated for in the filter design process. The utility of the method is demonstrated with a design example