Beamforming using a spherical microphone array based on legacy microphone characteristics

This paper presents a numerical approach that projects frequency-dependent directivity patterns of classic recording microphones onto steerable beams created with a spherical microphone array. In an anechoic chamber, the spatial and timbral characteristics of a legacy recording microphone and the characteristics of a 120-channel spherical microphone array were measured. Using a least-square matching approach, the measured frequency responses were used to calculate the set of filters that synthesize the desired legacy recording microphone characteristic from the 120-channel spherical microphone array. Synthesized microphone-beams are shown and compared with the measured characteristics of the original legacy microphones. Introduction Spherical microphone array technology allows for soundfield analysis and beamforming, and the creation of dynamic beams in any desired direction. Although flexible beamforming features may be desired in audio production, Tonmeisters tend to prefer first-order legacy recording microphones over novel microphone arrays. This preference is probably related to the familiarity in working with recording microphones. Contrary to engineering measurement applications that require neutral microphones with a flat frequency response, in sound recording, Tonmeister often desire microphones with “character”, expressed through parameters such as sensitivity, nonlinear distortions and off-axis frequency response. Consequently, the selection and placement of the “right” microphone becomes a highly subjective and irreversible decision. Because beamforming technology can capture a soundfield with a flexible directivity and steering orientation, these kinds of preproduction decisions can be moved to the production process. Unfortunately, beamforming technology has a reputation for not capturing the sound with the same character as recording microphones. This might be due to the fact that beamforming algorithms often prioritize the creation of highly directed beams while timbral features are of secondary importance. Although the authors are not aware of studies on the importance of specific microphone parameters on overall preference, research in sound reproduction quality suggests that timbral attributes are of higher importance than spatial attributes [1]. Also, an array’s performance and sound character may be affected by manufacturing differences of a large number of material components, such as capsules, microphonepreamps, or AD-converters. In this paper we use a spherical microphone array (the SAM-array) to synthesize the frequency-dependent directivity response of recording microphones. We first measured the frequency response of a recording microphone and the frequency response of our spherical microphone array. Then, using a numerical approach, we compute the best-fit filters for a filter-and-sum beamforming algorithm that matches the frequency response of the recording microphone. Theoretical results are compared with real-measurements. We also show how this virtual recording microphone can dynamically be re-oriented and how the desired microphone’s directivity pattern can be modified at run time. One might wonder why we we aim to simulate a recording microphone using a microphone array. As with many old synthesizers, tube amplifiers and other electro-acoustical instruments, there is a desire to simulate the complex behavior of rare, expensive and sensitive musical devices to enable their use in today’s digital audio workstation environments. A decade ago, the company Antares released the Microphone Modeler. This audio effect strived to virtually change the brand and type of the microphone used in a mono-channel recording. The user defines a) what microphone model was used within a recording and b) what microphone model is desired. Then the algorithm aimed to match the frequency response of both microphones to create the desired effect. Since the Microphone Modeler is discontinued, it was probably commercially not very successful. The algorithm only modeled the on-axis frequency response of the desired microphones using a one-channel input signal, neglecting other crucial microphone parameter such as the off-axis frequency response. 1http://www.antarestech. com/products/amm.shtml http://cnmat.berkeley. edu/publications/beamforming-using-spherical-microphone-array-based-legacy-microphonecharacteristics A recording microphone Microphones are categorized according to their ideal directivity Γ in classes as listed in Table 1. The directivity can be computed with Equation 1 with the angle of incidence δ. Omni Cardioid HyperFigure-8 directional cardioid a = 1.0 0.5 0.3 0.0 Table 1: Common first-order microphone directivity pattern Γi = a+ (1− a) · cos δi 0 ≤ a ≤ 1. (1) Manufacturers usually supply octave-smoothed, twodimensional cross-sections of the directivity pattern as a reference, because the directivity depends on frequency and microphone model. We measured the directivity of a popular large-diaphragm cardioid condenser microphone (2200 US$) from 576 directions in an anechoic chamber. The measurement procedure is described later in this paper. The horizontal polar patterns of the measurement compared with the specification sheet by the manufacturer shows a lot of resemblance across the entire frequency range (see Figure 1). However, these horizontal polar pattern do not reveal common axial asymmetries in the directivity, which are only visible in the spherical ballon plots (Figure 2). A transformation of this directivity pattern into spherical harmonics is visualized in Figure 3. One can see that most prominent contributions are of zero and first order spherical harmonics. This is expected, since the recording microphone has a cardioid characteristic which can be expressed with zero and first order spherical harmonics. Also clearly visible are the omnidirectional characteristic in low frequency bands due to the high contribution of the zero order harmonics, and an increasing contribution of the first order harmonics in the mid-frequencies around 1 kHz. Second order harmonics start to contribute at around 500 Hz to the the measured directivity pattern. It can be observed in Figure 2 how the recording microphone becomes increasingly directed for higher frequencies; the increase in directivity is expressed through additional contributions of higher spherical harmonics. 100 10 20 10 0 10 20 20 0 20 125 Hz 100 10 20 10 0 10 20 20 0 20 250 Hz 0 10 20 10 0 10 20 20 0 20 500 Hz 0 10 20 10 0 10 20 20 0 2