Click here to purchase the entire book in PDF format. Practical Implementation Practically speaking, it is difficult to put four microphones (the omnidirectional and the three bidirectionals) in a single location in the recording space. If you're doing a panphonic recording, you can make a vertical array with the omni in between the two bidirectionals and come pretty close. There is also the small problem of the fact that the frequency responses of the bidirectionals and the omni won't match perfectly. This will make the contributions of the pressure and the velocity components frequency-dependent when you mix them to send to the loudspeakers. So, what we need is a smarter microphone arrangement, and at the same time (if we're smart enough), we need to match the frequency responses of the pressure and velocity components. It turns out that both of these goals are achievable (within reason). We start by building a tetrahedron. If you're not sure what that looks like, don't panic. Imagine a pyramid made of 4 equilateral triangles (normal pyramids have a square base - a tetrahedron has a triangular base). Then we make each face of the tetrahedron the diaphragm of a cardioid microphone. Remember that a cardioid microphone is one-half pressure and one-half velocity, therefore we have matched our components (in theory, at least...). We have cardioids pointing in the directions Left Front (LF) pointing upwards, Right Front (RF) pointing downwards, Left Back (LB) pointing downwards, and Right Back (RB) pointing upwards. This arrangement of four cardioid microphones in a single housing is what is typically called a soundfield microphone. Various versions of this arrangement have been made over the years by different companies. The signal consisting of the outputs of the four cardioids in the soundfield microphone make up what is commonly called an A-Format Ambisonics signal. These are typically converted into the B-Format using a standard set of equations given below [Rumsey, 2001]. $$W = 0.5(LF + LB + RF + RB)$$ (11.35) $$X = 0.5 ((LF - LB) + (RF-RB))$$ (11.36) $$Y = 0.5((LF - RB) - (RF - LB))$$ (11.37) $$Z = 0.5((LF - LB) + (RB - RF))$$ (11.38) There are some problems with this implementation. Firstly, we are oversimplifying a little too much when we think that the four cardioid capsules can be combined to give us a perfect B-Format signal. This is because the four capsules are just too far apart to be effective at synthesizing a virtual omni or bidirectional at high frequencies. We can't make the four cardioids coincident (they can't be in exactly the same place) so the theory falls apart a little bit here - but only for high frequencies. Secondly, nobody has ever built a perfect cardioid that is really a cardioid at all frequencies. Consequently, our dream of matching the pressure and velocity components falls apart a bit as well. Finally, there's a strange little problem that typically gets glossed over a bit in most discussions of soundfield microphones. You'll remember from earlier in this book that the output of a velocity transducer has a naturally rising response of 6 dB per octave. In other words, it has no low-end. In order to make bidirectional (as well as all other directional) microphones sound better, the manufacturers boost the low end using various methods, either acoustical or electrical. Therefore, an off-the-shelf bidirectional (or cardioid) microphone really doesn't behave ``correctly'' to be used in a theoretically ``correct'' Ambisonics system - it simply has too much low-end (and a messed-up low-frequency phase response to go with it...). The strange thing is that, if you build a system that uses ``correct'' velocity components with the rising 6 dB per octave response and listen to the output, it will sound too bright and thin. In order to make the Ambisonics output sound warm and fuzzy (and therefore good) you have to boost the low-frequency components in your velocity channels. Technically, this is incorrect, however, it sounds better, so people do it.