Click here to purchase the entire book in PDF format. Why Ambisonics cannot work Let's take a simple 1st-order panphonic Ambisonics system. We can use the equations given above to think of the system in a more holistic way. If we combine the sensitivity equations for the B-format signal with the mix equation for a loudspeaker in the playback system, we can make a plot of the gain applied to a signal as a function of the relationship between the angle to the sound source and the angle to the loudspeaker. That function looks like the graph in Figure 10.150. Figure 10.150: The sensitivity function combining the sensitivities of the B-format channels with the mix for the loudspeaker. So far, we have been considering the sound from a source recorded by a microphone at a single point in space, played back over loudspeakers and analyzed at a single point in space (the sweet spot). In doing this, we have found out that the soundfield at the sweet spot exactly matches the soundfield at the sweet spot within the constraints of the order of the Ambisonics system. Let's now change the analysis to consider what you actually hear. Instead of a single-point microphone, you have two ears, one on either side of your head. Let's look at two situations, a sound source directly in front of you and a sound source directly to the side. To simplify things, we'll put ourselves in an anechoic world. As we have already seen, a Head Related Transfer Function (or HRTF) is a description of what your head and ears do to a sound signal before hitting your eardrum. These HRTF's can be used in a number of ways, but for our purposes, we'll stick to impulse responses, showing what's happening in the time domain. The analysis you're about to read uses the HRTF database measured at MIT using a KEMAR dummy head. This is a public database available for download via the Internet[Gardner and Martin, 1995]. We'll begin by looking at the HRTF's of two sound sources, one directly in front of the listener and one directly to the right. The impulse responses for the resulting HRTF's for these two locations are shown in Figures 10.151 and 10.152 respectively. There are two things to notice about the two impulse responses shown in Figure 10.151 for a frontal sound source. Firstly, the times of arrival of the impulses at the two ears are identical. Secondly, the impulse responses themselves are identical throughout the entire length of the measurement. Figure 10.151: The impulse responses measured at the two ears of a KEMAR dummy head for a sound source directly in front[Gardner and Martin, 1995]. The top plot is the left ear and the bottom plot is the right ear. The x-axes are time, measured in samples. Let's consider the same two aspects for Figure 10.152 which shows the HRTF's for a sound source on the side of a listener. Notice in this case that the times of arrival of the impulses at the two ears different. Since the sound source is on the right side of the listener, the impulse arrives at the right ear before the left. This makes sense since the right ear is closer to sound sources on the right side of your head. Now take a look at the impulse response over time. The first big spike in the right ear goes positive. Similarly, the first big spike in the left ear also goes positive. This should not come as a surprise, since your eardrums are not bidirectional transducers. These interaural time differences (ITD's) are very significant components that our brains use in determining where a sound source is. Figure 10.152: The impulse responses measured at the two ears of a KEMAR dummy head for a sound source directly in to the right[Gardner and Martin, 1995]. The top plot is the left ear and the bottom plot is the right ear. The x-axes are time, measured in samples. Let's now consider a source directly in front of a soundfield microphone, recorded in 1st-order Ambisonics and played over an 8-channel loudspeaker configuration shown in Figure 10.153. Figure 10.153: The 8-channel Ambisonics loudspeaker configuration used in this analysis. If we assume that the sound source emits a perfect impulse and is recorded by a perfect soundfield microphone and subsequently reproduced by 8 perfect loudspeakers, we can use the same HRTF measurements to determine the resulting signal that arrives at the ears of the dummy head. Figure 10.154 shows the HRTF's for a sound source recorded and reproduced through such a system. Again, let's look at the same two characteristics of the impulse responses. The times of arrival of the impulse at the two ears are identical, as we would expect for a frontal sound source. Also, the two impulse responses are identical, also expected for a frontal sound source. So far, Ambisonics seems to be working... however, you may notice that the impulse responses in Figure 10.154 aren't identical to those in Figure 10.151. Frankly, however, this doesn't worry me too much. We'll move on... Figure 10.154: The impulse responses of a simulation of the signals at the two ears if you have a sound source in the front of the soundfield microphone. Figure 10.155 shows the HRTF's for a sound source 90$^{\circ }$ off to the side of a soundfield microphone and reproduced through the same 8-channel Ambisonics system. Again, we'll look at the same two characteristics of the impulse responses. Firstly, notice that the times of arrival of the pressure waves at the two ears is identical. This contrasts with the impulse responses in Figure 10.152. The interaural time differences that occur with real sources are eliminated in the Ambisonics system. This is caused by the fact that the soundfield microphone cannot detect time of arrival differences because it is in one location. Secondly, notice the differences in the impulse responses at the two ears. The initial spike in the right ear is positive whereas the first spike in the left ear is negative. This is caused by the fact that loudspeakers that are opposite each other in the listening space in a 1st-order Ambisonics system are opposite in polarity. This can be seen in the sensitivity function shown in Figure 10.150. The result of this opposite polarity is that sound sources on the sides sound similar to a stereo signal normally described as being ``out of phase'' where the two channels are opposite in polarity [Martin et al., 1999]. Figure 10.155: The impulse responses of a simulation of the signals at the two ears if you have a sound source on the side of the soundfield microphone. Notice that there are no time differences and that the two ears are basically opposite in polarity. This is very different from the situation shown in Figure 10.152. In the interest of fairness, a couple of things should be pointed out here. The first is that these problems are most evident in 1st-order Ambisonics systems, The higher the order, the less problematic they are. However, for the time being, it is impossible to do a recording in a real space in any Ambisonics system higher than 1st-order. Work has been done to develop coefficients that avoid polarity differences in the system [Malham, 1999] and people are developing fancy ways of synthesizing higher-order directional microphones using multiple transducers, however, these systems have associated problems that will not be discussed here.