Cascaded warped-FIR and FIR filter structure for loudspeaker equalization with low computational cost requirements

This paper proposes an improved filter structure and methodology for the equalization of loudspeakers and other audio systems. It employs a cascaded structure of a finite impulse response (FIR) filter and a warped-FIR filter in order to obtain the best performance of both types of filters. In the task of loudspeaker equalization, FIR filters achieve excellent resolution and equalization at high frequencies, but at low frequencies the resolution obtained is too poor when evaluated in a logarithmic frequency axis, that could only be improved using high order filters. To solve this lack of resolution at low frequencies, warped-FIR filters have been employed, but at the expense of decreasing the resolution of the filter at high frequencies and increasing the complexity of the filter structure and its computational cost. The proposed combination of both types of filters, combined with the correct selection of their orders, and the λ value for the warped-FIR filter, allows the FIR filter to maintain its good resolution at high frequencies and achieve enough resolution at low frequencies with the warped-FIR filter. In this way, lower order filters with lower computational cost could be obtained than when using FIR or warped-FIR only. This approximation attains a more uniform resolution of the filter when evaluated in octaves, behaving much more like human hearing, than the linear frequency resolution obtained when employing only FIR filters.