Spherical harmonics act as basis functions for building any microphone pattern
Evidence
All coincident multi-channel microphone techniques produce signals that can be transformed into B-format signals. B-format signals have directional patterns that have spherical harmonics. The zeroth-order harmonic is the omnidirectional pattern, the three first-order patterns are those of a dipole facing in each of the three directions of the axes of the Cartesian coordinate system, and second order patterns are more complicated, having the form of a quadrupole or a dipole-with-ring form, as shown in Figure 14.4. The directional patterns of signals are additive; when two signals are added, the directional pattern of the combined signal follows the combined directional pattern. For example, combining the omnidirectional and dipole patterns with equal gains produces a signal with a cardioid pattern. When higher-order components are recorded, more complex directional patterns are formed for the combined signals. The spherical harmonics can thus be seen as basis functions for the design of arbitrary patterns. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1855
Categorization
- DEFINE: Explains B-format spherical harmonics and the additive property of directional patterns as basis functions.
- XREF: Connects to Fourier-style decomposition thinking - spherical harmonics are the ‘Fourier series’ of sound field directionality. — connects to: Microphone construction determines directional sensitivity patterns like cardioid and dipole
- corroborated: 2 independent passages support this claim — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1855