Bamford used various analytical techniques to assess the ability of stereo, 5.1 and first and second order Ambisonics to recreate a plane wave [Bamford, 1995]. In general, it was found that the second order Ambisonics system produced the best results and was more consistent for different source angles. The results indicate that the upper frequency at which a plane wave is accurately reconstructed at the centre of the array, is increased when as the order of the Ambisonics system is raised. The performance of both Ambisonics systems deteriorated at higher frequencies but this effect was reduced with the higher order system.
Martin investigated the focus or source width of phantom images produced using amplitude panning, first and second order Ambisonics and some non-standard amplitude panning functions [Martin et al, 199b]. Listening tests were carried out in an acoustically treated, medium sized room with a small number of test subjects and a symmetrical eight channel array which was also used to produce interaural cross- correlation measurements. Overall, pair-wise amplitude panning was found to produce the most focussed source as it used a single loudspeaker when the source is positioned at a loudspeaker position, and a maximum of two loudspeakers in other directions. On the other hand, this produced a noticeable change in timbre as the source direction moves across a loudspeaker position. The second order Ambisonics system and a polarity restricted cosine panning function produced the most consistent images across all angles. The polarity restricted cosine function is essentially
amplitude panning with a consistent number of loudspeakers, similar to the spread function in Ville Pulkki’s VBAP. Martin recommended this algorithm as it produced the most consistent results and appeared less sensitive to listener position than the second order Ambisonics system. It should be noted that very little detail is given in terms of the precise ambisonic decoding scheme adopted. However, Martin mentions that anti-phase components were a disturbing factor in the listening tests with
Ambisonics, which suggests that a basic decoding scheme was used which optimizes the velocity component rV. It is perhaps not surprising, therefore, that the restricted
polarity cosine function was preferred, as this method contains no disturbing anti- phase components.
Dickins analysed the performance of first and second order Ambisonics and a custom non-negative least squares (NNLS) panning algorithm by measuring the directional energy vector magnitude rE [Dickins et al, 1999]. Two listening locations
have been considered, one in the sweet spot at the centre of the array, and another towards the rear of the array. The tests were carried out in an acoustically treated listening room. Martin suggests that in general a compromise must be made between optimizing the directionality of the source, and minimising panning artefacts as the source moves. The NNLS algorithm is therefore similar to Martin’s polarity restricted cosine function and Ville Pulkki’s VBAP in that it allows a trade-off between maximum directivity at loudspeaker positions and a more diffuse panning which is homogeneous in all directions. The NNLS algorithm was preferred to the second order Ambisonics system as it functioned well at off-centre listening positions and could be extended to non-symmetrical loudspeaker arrays. However, as with the tests carried out by Martin, little detail is given regarding the ambisonic decoding scheme used. A strict decoding scheme which optimized rV would be expected to
function poorly away from the sweet spot, while a decode which optimized rE would
be much more similar to the NNLS algorithm and would provide a better comparison.
Fig. 6.4 Mean ratings as reported by Guastavino
loudspeakers within an anechoic chamber [Guastavino et al, 2007]. A free verbalization task and a multiple comparison task was conducted with eleven experienced listeners. The subjects were first asked to rate recordings made with a Soundfield microphone, an ORTF stereo pair and binaural microphone in terms of various subjective measures such as envelopment, readability (meaning how well different sources in the scene can be distinguished) and naturalness. and an overall rating. The Soundfield recording was decoded using a single band in-phase decoding scheme. In a second experiment, subjects were asked to rate various monophonic signals positioned at various angles using amplitude panning, a Soundfield recording and a customised Transaural system. The results of the two experiments, shown in Figure 6.4 [Guastavino et al, 2007], indicate a strong contrast between Ambisonics and the other two techniques in that stereophony and transaural provide precise localization and a good readability but a lack of immersion and envelopment while Ambisonics provides a good sense of immersion and envelopment but poor
localization accuracy and readability of the scene. In a similar study conducted by Capra (see Figure 6.5) slightly better results were achieved for an Ambisonics system implemented using a dual-band shelf filter decoder [Capra et al, 2007].
Fig. 6.5 Localization accuracy results as reported by Capra
Pulkki carried out a number of listening tests in order to assess the validity of a binaural auditory model [Pulkki et al, 2005]. The experiment was conducted in an anechoic chamber using a symmetrical eight-channel array, first and second order
Ambisonics, amplitude panning (VBAP) and a spaced microphone technique. Although the primary aim of the experiment was to verify the binaural model, some interesting results were obtained. Lateral sources produced with the first order
Ambisonics system were found to be consistently biased toward the median plane and exhibited a strong frequency dependence. The second order system exhibited almost no bias, reduced frequency dependence and increased localization accuracy. The best average localization accuracy was obtained with amplitude panning, although the results for second order Ambisonics were equally good for frontal sources.
Jot compared a number of different amplitude panning and ambisonic techniques in terms of a number of objective localization criteria [Jot et al, 1999]. The comparisons were based on a single listener at the centre of a hexagonal
loudspeaker array. Noticeable improvements are obtained when raising Ambisonics from first-order to second order, with an average performance comparable to that of the six-channel pair-wise panning but more uniform across all azimuths. While amplitude panning produced more stable and accurately localized images at loudspeaker positions, it was less uniform and tended to reveal the loudspeaker locations. No technique produced particularly accurate localization cues at high frequencies.
6.4.1 Discussion
The results of the tests presented in the preceding Section indicate that Ambisonics is consistently preferred to amplitude panning for dynamically moving sources as it produces a more uniform phantom image and hence disguises the loudspeaker position. However, amplitude panning was also consistently preferred for static sources as this method uses fewer loudspeakers and so reduces the
localization blur. This would seem to support Martin’s view that in general a compromise must be made between optimizing the directionality of the source, and minimising panning artefacts as the source moves [Martin et al, 1999a]. The results which indicated that Ambisonics produced a more diffuse enveloping sound field but less tightly focussed sources is arguably another interpretation of the same
fundamental difference between the two spatialization techniques.
A number of alternative amplitude panning techniques were presented which attempt to reduce the timbral changes produced when a source is dynamically panned
to different positions [Pulkki, 2005; Martin, 1999a, Dickins et al, 1999]. These techniques are similar in that they can control the number of contributing
loudspeakers independently of the source azimuth. In this way, they can ensure that a minimum number of loudspeakers is always used, which then smoothes the perceived trajectory. This is clearly very similar to the Ambisonics approach of optimizing the energy vector rE for all directions, at the cost of reducing the maximum localization
accuracy that could be achieved at the loudspeaker positions. Pernaux point out that amplitude panning algorithms like VBAP can be considered as analogous to a local ambisonic velocity decode whereby only the loudspeakers closest to the source direction are used, and the requirement to optimize the velocity component (rV= 1) is
dropped [Pernaux et al, 1998]. They go on to develop a dual-band Vector Based Panning algorithm (VBP) which uses VBAP at low frequencies and a Vector Based Intensity panning algorithm (VBIP) at high frequencies, which like Ambisonics, ensures that θE =θV. The significant advantage of this system over Ambisonics is that
appropriate decoding factors can be more readily obtained for non-regular loudspeaker arrays.
Fig. 6.6 Ambisonic decoder directivity patterns where M is the system order These advanced amplitude panning schemes are highly reminiscent of
Ambisonics, and particularly higher order Ambisonics systems which are optimal for larger listening areas. Higher order systems increase the directivity of the response characteristic (see Figure 6.6 [Daniel, 2000]) which in turn reduces the number of
phase components Ambisonics becomes highly similar to these advanced amplitude panning techniques such as VBP. However, some tests have indicated that
Ambisonics was still preferred to VBP for moving sources [Pernaux et al, 1998].