Variable-Octave Complex Smoothing for Loudspeaker-Room Response Equalization

In this paper we present a technique for processing room responses using a variable-octave complex-domain (viz., time-domain) smoother so as to design low-order FIR equalization filters. Traditional techniques for room response processing, for equalization and other applications such as auralization, have focused on a constant-octave (e.g., 1/3 octave) using only magnitude domain smoothing of these room responses. However, recent research by Olive [7] has shown that room responses need to be processed with a high frequency resolution (e.g., 1/20^th octave), especially in the low-frequency region, to characterize discrete room modes which are distinctly audible. Using such a high-resolution at higher frequencies of the room response results in relatively long model (or equivalently filter lengths) due to the undesirable over-fitting of the model in the high-frequency region. Moreover, auditory filters have wider bandwidth (viz., lower frequency resolution) in the high-frequency part of the human hearing. Hence, the present paper proposes a variable-octave complex-domain smoothing where a lower octave smoothing is performed in the high-frequency part of the room response. Thus this paper incorporates, simultaneously, the high low-frequency resolution requirement as well as the requirement of relatively lower-resolution fitting of the room response in the high-frequency part through a perceptually motivated approach. As will be shown, using this approach, there is a significant reduction in the filter order for loudspeaker-room equalization. A proposal for (i) an overall perceptually relevant smoothing scheme and, (ii)selection of the transition frequency between high- resolution smoothing (in the low-frequency region) and low- resolution smoothing in the high-frequency region will be presented.