Low-complexity equalizers and applications

Abstract

Equalizers for audio signal processing play an important role in microphones, mixing systems, mastering processors, monitor loudspeakers, and consumer devices such as smart tablets, smart phones, wireless headphones, and hearing devices. We will introduce low-complexity filter designs for equalizers based on first- and second order recursive filters. Low-complexity filter design means having the lowest number of parameters and design equations for first- and second-order difference equation realizing prescribed filter transfer functions such as low-pass, high-pass, band-pass, and all-pass filters. Based on these basic filters, we derive all-pass realizations of these standard filters and then apply them to design parametric low- and high-frequency shelving filters and peak filters. These last two versions of weighting filters are based on three parameters, namely, the cut-off or center frequency, the bandwidth or Q factor, and the gain in dB for a low-, mid-, or high frequency band and are, therefore, named parametric equalizers. These parametric equalizers' PEQs occur in a channel-strip of a mixing console and are an integral part of the mixing process. We will describe several further applications of PEQs for amp and loudspeaker modeling, headphone equalization and head-related transfer function modeling, and audio coding. All applications allow a low-complexity filter design, parameter update, and efficient recursive filter implementations with much lower complexity compared to non-recursive filters.