Design of Audio Parametric Equalizer Filters Directly in the Digital Domain

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Most design procedures for a digital parametric equalizer begin with analog design techniques, followed by applying the bilinear transform to an analog prototype. As an alternative, an approximation to the parametric equalizer is sometimes designed using pole-zero placement techniques. In this paper, we present an exact derivation of the parametric equalizer without resorting to an analog prototype. We show that there are many solutions to the parametric equalizer design constraints as usually stated, but only one of which consistently yields stable, minimum phase behavior with the upper and lower cutoff frequencies positioned around the center frequency. The conditions for complex conjugate poles and zeros are found and the resultant pole zero placements are examined.