Sparse Graphic Equalizer Design

A typical graphic equalizer frequency resolution is one-third octave comprising 31 bands. A previous design based on a least-squares optimization of the band-filter gains with a single second-order section per band has an accuracy of 1 dB. However, the design always uses all the band filters even when a small number of gains is adjusted. This letter proposes a sparse design of a one-third-octave graphic equalizer, where the number of active bands is minimized using orthogonal matching pursuit and linear programming before the least-squares gain optimization. In addition, the bandwidths of the high-frequency band filters are gain dependent in order to optimize their shape relative to an analog prototype. The optimal bandwidth is obtained with linear interpolation during the filter design. The proposed design achieves approximately the same or better accuracy in comparison to the state-of-the-art non-sparse design and can be used to automatically reduce the computational load of equalization when only some band filters are active.