The accuracy of a graphic equalizer

The accuracy of a graphic equalizer can be improved by allowing filter gains to be different from command gains, and by then optimizing the filter gains for each command gain configuration. First Abel and Berners [51] and recently Oliver and Jot [63] have proposed to optimize the filter gains of the cascade graphic equalizer by solving a system of linear equations. This is made possible by the fact that the magnitude responses of the peak/notch filters at different gain settings (but with fixed center frequency and Q) are self-similar on the dB scale [51]. (However, Abel and Berners [51] used parametric sections characterized by crossover frequencies at which the filter gain is the square root of its extreme value. Doing so slightly better maintains the self similarity property, as Q varies a little with filter center frequency.)Thus, the magnitude responses of the peak/notch filters can be used as basis functions toapproximate the magnitude response of the graphic equalizer at the center frequencies. This can be written in the form hˆ = Bg, where hˆ is an M-by-1 vector of estimated dB magnitude response values at command frequencies, B is the M-by-M interaction matrix representing how much the response of each band filter leaks to other center frequencies in dB, and g is an M-by-1 vector of command gains in dB,