Audio Equalization with Fixed-Pole Parallel Filters: An Efficient Alternative to Complex Smoothing

Recently, the fixed-pole design of parallel second-order filters has been proposed to accomplish arbitrary frequency resolution similarly to Kautz filters, at 2/3 of their computational cost. This paper relates the parallel filter to the complex smoothing of transfer functions. Complex smoothing is a well-established method for limiting the frequency resolution of audio transfer functions for analysis, modeling, and equalization purposes. It is shown that the parallel filter response is similar to the one obtained by complex smoothing the target response using a hanning window: a 1/β octave resolution is achieved by using β/2 pole pairs per octave in the parallel filter. Accordingly, the parallel filter can be either used as an efficient implementation of smoothed responses, or, it can be designed from the unsmoothed responses directly, eliminating the need of frequency-domain processing. In addition, the theoretical equivalence of parallel filters and Kautz filters is developed, and the formulas for converting between the parameters of the two structures are given. Examples of loudspeaker-room equalization are provided.