Accurate cascade graphic equalizer

A graphic equalizer is a high-order filter controlling the gain of several frequency bands. For good accuracy, graphic equalizers consisting of cascaded IIR filters have been of very high order. A previously proposed parallel graphic equalizer entailing twice as many second-order filter sections as there are bands can have a maximum approximation error of less than 1 dB, but its design is complicated. This letter proposes a cascade graphic equalizer having an accuracy comparable to the best parallel graphic equalizer, although only one second-order section is assigned per command gain. A key idea is to use band filters whose interaction with the two neighboring filters at their center frequency is exactly controlled. The filter gains are obtained using the least-squares method with one iteration step, which involves linear interpolation of the target gain vector, inversion of a square matrix, and a few matrix multiplications. The proposed method is compared with previous designs and is shown to be the most accurate one. The new graphic equalizer is widely useful for audio and music processing.