Warped IIR filter design with custom warping profiles and its application to room response modeling and equalization

In traditional warped FIR and IIR filters, the frequency-warping profile is adjusted by a single free parameter, leading to a less flexible allocation of frequency resolution. As an example, it is not possible to achieve a truly logarithmic frequency resolution, which would be often desired in audio applications. In this paper a new approach is presented for warped IIR filter design where the filter specification is transformed by any desired (e.g., logarithmic) frequency transformation, and a standard IIR filter is designed to this transformed specification. Then, the poles and zeros of this transformed filter are found and mapped back to the original frequency scale. Due to the approximations in mapping back the poles and zeros, the resulting transfer function shows some discrepancies from its optimal version. This is resolved by an additional optimization of the zeros of the final filter. Examples of loudspeaker–room response modeling and equalization are presented.