Parametric second- and fourth-order shelving filters for audio applications

In this paper, we develop a parametric recursive second-order lowpass/highpass shelving filters and fourth-order bandpass shelving filters. These filters allow a better frequency selectivity for audio equalization as compared to the well-known first-order lowpass/highpass shelving filters and second-order peak filters. In the parametric structures, the cut-off frequencies and the gain factors can be set independently. We derive the filter designs for the discrete-time implementation. Furthermore, we apply a technique for the implementation of delay-free loops which is necessary to yield the exact inverse filter to realize symmetric boost and cut of a frequency band.