Robust Inverse Filter Design Based on Energy Density Control

3-D audio systems, which provide a listener with 3-D sound illusion at arbitrary locations, are an important part of immersive interfaces. 3-D audio systems can use headphones or loudspeakers to present the 3-D sound. A main limitation of producing 3-D sound through loudspeakers is distortion caused by room acoustics. Various methods of designing inverse filters that can equalize the room response have been suggested. One of the common problems of the previous methods is the restriction on the listener to sit in a relatively narrow equalization zone. The problems were mainly caused by the fact that equalization was conducted by controlling sound pressure at discrete points, and the points were not ideal locations to obtain global control of the pressure field. Most inverse filtering approaches are based on the cost function defined by using acoustic pressure. These inverse filtering systems typically minimize the squared acoustic pressure at a control point using the least square (LS) optimization Nelson et al. (1992)Nelson et al. (1995)Kirkeby et al. (1998). These systems, however, often produce distortions such as boosting at certain frequencies in the vicinity of the control point, because the room transfer function (RTF), being defined in an acoustic pressure field, changes drastically with variation in source and receiver positions inside a space. Thus, a listener’s slight movement easily harms the inverse filtering performance. To overcome the problem of distortion, an alternative equalization method called joint LS Abe et al. (1997)Ward (2000), was presented, in which a sum of the squared pressures at several control points is minimized. A major disadvantage of this approach is that global control over control points can be partly effective, sometimes; it is not guaranteed. Recently, the filters for crosstalk cancellation were designed using the minimax optimization Rao et al. (2007). The minimax approach is known to provide better channel separation in low-frequency than LS approach with marginal improvement Rao et al. (2007). But it still inherits the distortion problems mentioned previously, since it is also based on acoustic pressure at the control point. Another approach to the problem of room transfer function (RTF) variations with source and receiver position is equalization via a vector quantization (VQ) method Mourjopoulos (1994), in which an inverse filter is updated during operation using an RTF codebook generated by using the VQ method. Although the inverse filtering using VQ methods can resolve the problems of previous methods by making them effective for all possible source and receiver positions inside the enclosure, the method needs large sets of off-line measurements of RTFs to make the RTF codebook and additional tracking modules to find receiver positions. 29