Parametric Recursive Higher-Order Shelving Filters

The main characteristic of shelving filters, as commonly used in audio equalization, is to amplify or attenuate a certain frequency band by a given gain. For parametric equalizers, a filter structure is desirable that allows independent adjustment of the width and center frequency of the band, and the gain. In this paper, we present a design for arbitrary-order shelving filters and a suitable parametric structure. A low shelving filter design based on Butterworth filters is decomposed such that the gain can be easily adjusted. Transformation to the digital domain is performed, keeping gain and denormalized cut-off frequency independently controllable. Finally, we obtain mid and high shelving filters using a simple manipulation, providing the desired parametric filter structure.