A Tetrahedral Microphone Processor for Ambisonic Recording Fons ADRIAENSEN Laboratorio di Acustica ed Elettroacustica, Parma, Italy [email protected] Abstract Z LFU This paper introduces a Linux audio application that X provides an integrated solution for making full 3-D Ambisonics recordings by using a tetrahedral micro- phone. Apart from the basic A to B format conver- Y sion it performs a number of auxiliary functions such RBU as LF filtering, metering and monitoring, turning it into a complete Ambisonics recording processor. It also allows for calibration of an individual micro- phone unit based on measured impulse responses. A RFD new JACK backend required to make use of a partic- ular four-channel audio interface optimised for Am- LBD bisonic recording is also introduced. Keywords Ambisonics, tetrahedral microphone, recording. Figure 1: Tetrahedral mic geometry. 1 Introduction The standard first-order Ambisonics B-format consist of four signals named W, X, Y and Z. at the vertices of a regular tetrahedron and In acoustic field theory terms, W represents the pointing outwards, as shown schematically in pressure signal at a given point in space, and fig. 1. Figure 2 shows an example of how this X, Y, Z the three components of the velocity vec- may be realized in practice. tor at the same point, projected onto orthogo- Given the four A-format microphone signals nal axes. Conventionally X points forward, Y LF U, RF D, RBU and LBD1, we can find the left, and Z up. B-format signals from These four signals also correspond to the out- puts of four real microphones - an omnidirec- W 0 = LF U + RF D + RBU + LBD tional one for W , and three figure-of-eight ones X0 = LF U + RF D − RBU − LBD for X, Y and Z - provided one can find a way to 0 put these four microphones at exactly the same Y = LF U − RF D − RBU + LBD point in space. Z0 = LF U − RF D + RBU − LBD For horizontal-only surround recordings Z is not used, and it is possible to mount the three To find the correct W, X, Y, Z, we also need required mics close together in a vertical line to filter the outputs of this A-B matrix and so they are effectively coincident for sounds ar- apply some gain factors. Two types of filter riving from horizontal directions. But for full are required, one for the zero order component 3-D such a direct B-format setup is no longer W , and a second one for each first order one, practical. X, Y, Z. These filters will be discussed in more One solution, already developed by Michael detail in section 3. Gerzon e.a. in the early years of Ambisonics The first tetrahedral mics were manufactured [Gerzon, 1975], is to use a tetrahedral micro- by Calrec Ltd. in the UK, and their technology phone. This contains four cardioid or near- cardioid capsules mounted very close together 1LF U means left-front-up, etc. itoring functionality. Ambisonic microphones are often used for live recording, and in these circumstances one wants a system that is easy to set up and use, and that allows for verifi- cation of the recording chain. In practice the only other software needed should be the JACK server and a recording application such as Ar- dour. Figure 3 (next page) shows the processing chain implemented in Tetraproc. The high pass filters, the mute and invert switches, and the monitoring functions are controlled by the Figure 2: A tetrahedral mic (ST250). graphical user interface. All other modules are set up using a separate configuration window, and these settings are saved into configuration 2 files. These config files are also generated by a was later acquired by Soundfield Ltd. These separate calibration program discussed in sec- are quite expensive microphones, not only be- tion 4. cause of their high quality, but also because they need a hardware processing unit to perform 2.1 A to B format conversion the A to B-format conversion and filtering men- Going from the A-format microphone inputs to tioned above, and in particular because for best the B-format output, the following processing results each microphone needs to be calibrated steps are performed: individually and provided with a matched A-B matrix and/or filters. • High pass filtering. This has an ad- The Danish microphone manufacturers DPA3 justable cutoff frequency and a slope of 24 were the first to offer a tetrahedral mic without dB/oct. This is really an essential feature. a processing unit. It was a very high quality Figure-of-eight microphones having a good mic, but it is unfortunately no longer available. low frequency response are also excellent Soundfield Ltd. also produce such an A-format detectors of earthquakes, passing under- microphone, the SPS200-A. ground trains, waggling mic stands, slam- Recently, Core Sound4 has announced the rel- ming doors and air currents. These can re- atively inexpensive Tetramic. It should be avail- sult in rather large amplitude signals, and able when this paper is presented, and its price cutting off low frequencies is the only way is expected to be below 1000 USD. It comes to get rid of them. Ideally this should be without a controller, and relies on a software done before AD-conversion, but not all au- solution for A to B-format conversion. dio interfaces provide such filters. Given such an application, this mic provides • Mute switches. For testing connections an affordable solution for Ambisonic recording. and verifying correct operation of the mi- While it was this announcement that triggered crophone it is convenient to be able to listen the development of the Tetraproc software pre- to selected inputs, hence the mute switches sented in this paper, it should be pointed out which are provided on the GUI. that this software can be used with any tetra- • Low frequency parametric filtering. hedral microphone. It is published under the This is provided to adjust the frequency re- GPL license, and in no way, either technically or sponse of the microphones in this region. commercially, linked to products of Core Sound The parameters provided are centre fre- or any other manufacturer. quency, bandwidth and gain. The same fil- tering is applied to all four channels. 2 Tetraproc processor architecture • A-format FIR filters. These are imple- Apart from the basic A to B format conversion, mented using fast FFT-based convolution Tetraproc also provides some convenient mon- and can be used to correct the frequency 2<http://www.soundfield.com> and phase response of the four microphones 3<http://www.dpamicrophones.com> using filters calculated from measured im- 4<http://www.core-sound.com> pulse responses. This will be mainly im- A-format in 4th order HP LF parametric Mute switches filter filter A Scalar matrix B-format out HF parametric Invert switches filters Convol. matrix B B-format in A B Meters Vol B-format monitoring Stereo decoder Stereo monitoring Figure 3: The Tetraproc processing chain portant in the medium and high frequency The output at this point is the B-format signal regions. that will be recorded. • A-B matrixing. This performs the A- 2.2 Monitoring functions B transformation already described in the Monitoring can be switched between the B- previous section. The actual matrix coeffi- format signal being recorded, or one being cients are modified to compensate for small played back. A virtual stereo microphone with gain and directivity mismatches between adjustable azimuth, elevation, microphone an- the four microphones. They are calculated gle and directivity is provided for stereo mon- by the calibration program described in itoring. This module also provides a volume section 4. control and optional low-frequency crosstalk for • B-format FIR filters. Again using fast headphone listening. convolution, these may be inserted to im- Four bargraph meters are provided on the plement Angelo Farina’s method (see next GUI. These show either the A-format signals, section) for obtaining the post-matrix fil- or the B-format signal being monitored. tering. They can be used together with the parametric sections that follow. 2.3 DSP implementation issues None of the processing steps above present any • HF parametric filtering. Two sections real difficulty, but some attention to detail is are provided in each channel to realize the required in order to obtain the highest quality. required post-matrix filters. Parameters The high pass filtering is implemented us- for these filters will be preset to sensible de- ing a filter architecture optimised for low fre- faults and can be tweaked for optimum per- quency filters described in [Adriaensen, 2006]. formance during the calibration of a tetra- It is used to avoid problems with filter coeffi- hedral microphone. cient and signal quantisation which may arise • X, Y, Z inversion switches. In some with some standard digital filter structures. cases it is required to invert some of the When both the A-format and B-format FIR first order signals, for example when the filters are enabled, they are combined together microphone is used upside down, hanging with the A-B matrix into a single four by four from its cable. convolution process. This doubles the number of convolutions, but is both more efficient and that would be required to do this. Gerzon pro- more accurate than using eight separate ones. vides design parameters for some analog filters, The parametric filter sections use the Mitra- but these do not match the diffuse field curves. Regalia architecture. The filters actually used in one of the products based on his work [Calrec Ltd., 1984] are again 3 Choice of the A-B matrix filters different.