listener can clearly and accurately perceive the direction of the virtual source, in any direction. Most practical systems eliminate the height component and so simply require a number of loudspeakers to be placed around the audience. WFS differs from other systems in that it is based on linear arrays of loudspeakers rather than a small number of distributed loudspeakers. A WFS system which can position a virtual source in any direction in the horizontal plane requires therefore a very large number of loudspeakers placed in a linear array surrounding the audience. This was demonstrated by Verheijen who found that accurate synthesis is not possible for sources which do not lie in a straight line from the listener to the source, through the
synthesized is between two lines from the listener to the edges of the array, as shown in Figure 6.14. This area is further reduced if tapering windows are applied to the array to reduce truncation effects (see Section 3.2.2).
Fig. 6.14 Visibility of a virtual source in a WFS system
WFS can only accurately synthesize a sound field up to the spatial aliasing frequency, so clearly the high frequency content will be distorted in some way. Start reported that the imperfect reconstruction of the sound field above the spatial aliasing frequency gives rise to an increase in the apparent source width (ASW) due to the uncertain directionality of the high frequency content [Start, 1997]. Wittek points out that this must be taken into account when evaluating the localization accuracy of any WFS system [Wittek, 2003]. For example, a measure of the standard deviation in the reported directional data will not indicate whether listeners perceive a tightly focussed source within the range of directions reported, or a broad diffuse source distributed between the range of reported angles. As discussed earlier in Chapter Two,
locatedness is a measure of the degree to which an auditory event can be said to be clearly in a particular location [Blauert] and this parameter is sometimes used in the assessment of WFS systems to determine the focus or apparent width of the virtual source.
Some of the earliest perceptual experiments with WFS systems were carried out by Vogel [Vogel, 1993]. In an experiment with an array of twelve loudspeakers
despite the very low spatial aliasing frequency of 380Hz of this system. However, Wittek points out that as this system can only correctly synthesize frequencies below 380Hz, it cannot be assumed that WFS is responsible for the correct localization [Wittek, 2003]. For a WFS virtual source positioned behind the array, the
loudspeaker nearest to a direct line from the listener to the source will be producing the earliest and often the loudest signal. The precedence effect would therefore provide a localization cue at all frequencies, which, in this case, coincides with the source position specified by the WFS system. The mean directional error reported in Vogel’s test is no lower than what would be expected if the precedence effect was dominating localization and so these results do not indicate that localization accuracy is improved by this particular WFS system. This situation does not occur with focussed sources in front of the array, as in this case the first wavefront does not arrive from the same direction as the virtual source [Wittek, 2003].
Since these early tests further experiments have been carried out with loudspeaker arrays of greater size and resolution [Vogel, 1993; Huber, 2002]. The results of these tests demonstrated that localization accuracy was greater than the actual physical resolution of the loudspeaker array, no doubt due to the increased resolution of the array and the associated increase in the spatial aliasing frequency. The results of both these tests clearly indicate the importance of the spatial aliasing frequency in terms of the performance of the WFS system.
Start compared the minimal audible angle (MAA) of real sources and virtual sources produced using a WFS system [Start, 1997]. He found no difference between the MAA of a real source and the WFS source for a spatial aliasing frequency of 1.5kHz, for both broadband and low-pass-filtered noise signals. When the spatial aliasing frequency was reduced to 750Hz however, the MAA increased somewhat. Start suggested that this result implied that a spatial aliasing frequency of 1.5kHz would ensure that the dominant low frequency localization cues are satisfied and so the source will be accurately localized.
Huber conducted listening tests in an anechoic chamber to compare real sources, two-channel stereo, WFS with loudspeaker spacings of 4cm and 12cm, and an augmented WFS system based on Optimized Phantom Source Imaging (OPSI) [Huber, 2002]. OPSI uses amplitude panning to position the portion of the signal which lies above the sampling aliasing frequency [Wittek, 2002], thereby reducing the
in WFS systems. Figure 6.15 shows the scaled judgements of locatedness (which Huber refers to as localization quality) for each of the five systems. Clearly none are able to match the real source in terms of locatedness, however, a significant improvement is apparent when the loudspeaker spacing is reduced to 4cm (which results in a aliasing frequency of 3kHz). The worst results were achieved with stereo while the hybrid OPSI method was found to produce approximately the same results as the normal WFS system. Interestingly, the standard deviation in localization accuracy shown in Figure 6.16 does not indicate any differences between the real and WFS sources, which indicates the importance of assessing the perceptual sense of locatedness as well as the perceived direction.
A similar comparison test was carried out by Wittek on the localisation performance of various WFS systems compared to a real source, amplitude panning and a hybrid OPSI system (see Figure 6.17) [Wittek, 2007]. For the WFS systems, a virtual source was positioned one metre behind the array using loudspeaker arrays with a spatial aliasing frequency of 2.5kHz (labelled WFS12) and 7.5kHz (labelled WFS4) respectively. The OPSI signals were produced using the WFS12 system and three loudspeakers at spacings of 76cm to produce the phantom source with a
crossover frequency of 2kHz.
Fig. 6.17 Test setup for Wittek's listening tests
The results were similar to Huber's in that none of the systems matched the performance of a real source in terms of locatedness, but better results were reported with the WFS system than with amplitude panning (see Figure 6.18). As with Huber, better results were achieved when the spatial aliasing frequency was increased from 2.5kHz to 7.5kHz. Similarly, these differences are not evident when only the standard deviations of the measured auditory event directions are considered. No degradation in localization quality was found using the hybrid OPSI method.
Sanson examined localization inaccuracies in the synthesis of virtual sound sources using WFS at high frequencies [Sanson et al, 2008]. Objective and
perceptual analyses were carried out through a binaural simulation of the WFS array at the ears of the listener using individual head related transfer functions (HRTFs). The array could be configured for loudspeaker spacing of 15cm, resulting in an aliasing frequency around 1500Hz, or a loudspeaker spacing of 30cm results in an aliasing frequency around 700Hz. Two listener positions were evaluated, one central and one laterally displaced to the right by 1m. The results of the test indicated that localization accuracy was dependent on the listening position, the source position and the frequency content of the source signal. Localization accuracy decreased as the listener position moved laterally away from the centre point, As the source cut-off frequency was increased, localization at the off-centre position degraded, but not at the central listening position. The authors suggest that this is due to the unequal distribution of high frequency content at either ear when the listener is positioned at a non-central location. This would provide a conflicting localization cue relative to the low frequency content which is accurately reproduced by the WFS system. Clearly, technical solutions to the distorted high frequency content in WFS systems must address localization for off-centre listener positions.