A parametric filter structure for first-order shelving and second-order peak filter transfer functions is derived. The approach is based on a decomposition of the transfer function into the minimum amount of direct branches and an all-pass section. It allows direct control of gain, bandwidth, and center/cutoff frequency for the boost case, and a coupled relation between gain and bandwidth for the cut case. Compared to other all-pass approaches, the new filter structure has fewer direct branches. Analytical formulas for the boost and cut case are derived.
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