A New Method for Designing Flat Shelving and Peaking Filters Based on Allpass Filters

Two most commonly IIR filters used in audio equalization are shelving filters and peaking filters. Traditional design of shelving and peaking filters is based on the design of analog filters, mainly Butterworth filters, and bilinear transformation. In this way, it is well known the design of first order shelving filters and second order peaking filters. Additionally, the resulting filter can be efficiently implemented using allpass filter structures with a low sensitivity to the filter quantization and a low noise level. In this paper, we present a direct design of high order shelving and peaking filters with flat magnitude response in both passband and stop-band. The design is reduced to the design of one digital allpass filter with real coefficients. Using this allpass filter, we obtain two stable and real allpass filters, which are used to implement the resulting shelving and peaking filters. Additionally, closed form equations for the pole/zero computations are given. In contrast with others proposed methods, the design parameters for the shelving filter are the gains K_BdB and K_cdB at omega=0 and omega=pi, respectively, the passband droop A_p, stopband attenuation A_s, passband frequency omega_p, and stopband frequency omega _s, while for the peaking filter we have the gains K_BdB and K_cdB, the passband and stopband attenuation A_p and A_s, passband width W_p, stopband width W_s, and the central frequency omega₀. The proposed method is illustrated by means of examples. Finally, the appendix shows the MATLAB function ShelvingEq.m, which implements the proposed method for the design of shelving filters