TECHNICAL FIELD

The disclosure relates to a microphone array, in particular to a spherical microphone array for use in a modal beamforming system.
BACKGROUND

A microphonearraybased modal beamforming system commonly comprises a spherical microphone array of a multiplicity of microphones equally distributed over the surface of a solid or virtual sphere to convert sounds into electrical audio signals and a modal beamformer that combines the audio signals generated by the microphones to form an auditory scene representative of at least a portion of an acoustic sound field. This combination enables the reception of acoustic signals dependent on their direction of propagation. As such, microphone arrays are also sometimes referred to as spatial filters. Spherical microphone arrays exhibit low and highfrequency limitations so that the sound field can only be accurately described over a limited frequency range. Lowfrequency limitations essentially result when the directivity of the particular microphones of the array is poor compared to the wavelength and the high amplification necessary in this frequency range; this leads to high amplification of (self) noise and thus to the need to limit the usable frequency range up to a maximum lower frequency. Highfrequency issues can be explained by spatial aliasing effects. Similar to temporal aliasing, spatial aliasing occurs when a spatial function (e.g., the spherical harmonics) is undersampled. For example, at least 16 microphones are needed to distinguish 16 harmonics. In addition, the positions and, depending on the type of sphere used, the directivity of the microphones are important. A spatial aliasing frequency characterizes the upper critical frequency of the frequency range in which the spherical microphone array can be employed without generating any significant artifacts. Reducing the unwanted effects of spatial aliasing is widely desired.
SUMMARY

A spherical microphone array may include a sounddiffracting structure that has a closed threedimensional shape with a surface surrounding the shape and at least two differential microphones mounted flush on the surface of the sounddiffracting structure.

Other systems, methods, features and advantages will be or will become apparent to one with skill in the art upon examination of the following detailed description and figures. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention and be protected by the following claims.
BRIEF DESCRIPTION OF THE DRAWINGS

The system may be better understood with reference to the following description and drawings. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like referenced numerals designate corresponding parts throughout the different views.
 Figure 1 is a perspective view of a sixelement microphone array mounted in a spherical sounddiffracting structure.
 Figure 2 is a perspective view of a microphone array that has a sounddiffracting structure with the polyhedral shape of a 60sided pentakis dodecahedron.
 Figure 3 is a perspective view of a spherical sounddiffracting structure with indentations of the surface formed by conical cavities.
 Figure 4 is a crosssectional view of a rigid sphere with no indentation shapes and an integrated flushmounted microphone element.
 Figure 5 is a crosssectional view of a rigid sphere with an indentation shaped as an inverse spherical cap in which a differential microphone element is disposed at the bottom.
 Figure 6 is a crosssectional view of a rigid sphere with an indentation shaped as an inverse spherical cap in which two differential microphone elements are disposed, thereby forming a microphone patch.
 Figure 7 is a diagram illustrating directivity plots for a firstorder differential microphone in accordance with Equation (1), wherein α = 0.55.
 Figure 8 is a diagram illustrating directivity plots for a firstorder differential microphone in accordance with Equation (1), wherein α = 0.20.
 Figure 9 is a schematic sectional view of a first exemplary acoustically differentiating differential microphone element.
 Figure 10 is a schematic sectional view of a second exemplary acoustically differentiating differential microphone element.
 Figure 11 is a schematic sectional view of a first exemplary electrically differentiating differential microphone element.
 Figure 12 is a schematic sectional view of a second exemplary electrically differentiating differential microphone element.
DETAILED DESCRIPTION

A schematic illustration of a sixelement 3D microphone array 100 mounted in rigid sphere 101, which forms a sounddiffracting structure, is shown in Figure 1. Note that only three of the six microphone elements can be seen in the figure (i.e., microphones 102, 103 and 104), with the remaining three microphone elements being hidden on the back side of sphere 100. All six microphone elements are mounted flush on the surface of sphere 100 at points where an inscribed regular octahedron's vertices would contact the spherical surface. The individual microphone elements are differential microphone elements such as those shown in and described below in connection with Figures 812. In other exemplary microphone arrays, other conventional differential microphone elements may be used.

Figure 2 shows a perspective view of a 3D microphone array 200 that has the polyhedral shape of a 60sided pentakis dodecahedron. Although not shown in the figures, microphone array 200 of Figure 2 has a plurality of individual flushmounted microphone elements, analogous to elements 102, 103 and 104 of Figure 1, distributed around and integrated into different rigid triangular sections 201 of sphere 200, where zero, one or more microphone elements are mounted flush onto the surface of each different triangular section 201. Depending on the particular implementation, the microphone elements may be distributed uniformly or nonuniformly around the polyhedron, with each triangular section 201 having the same number of microphone elements or different triangular sections 201having different numbers of microphone elements, including some triangular sections 201 that have no microphone elements.

Figure 3 illustrates a 3D microphone array 300 that has a spherical sounddiffracting structure 301 with microphones 302 embedded in cavities whose dimensions and shapes are optimized to tailor the directivity pattern. Figure 3 shows a circular conical cavity; however, a sectoral cavity or any other appropriately shaped cavity may alternatively be used to form an indentation of the spherical surface. The truncated conical shape of microphone array 300 is designed to increase directivity on both horizontal and vertical planes, whereas a sectoral cavity provides higher directivity on the horizontal plane. The cavity shape can be tailored and optimized to give the best compromise in terms of vertical and horizontal directivity. Directivity is achieved in sounddiffracting structure 301 of Figure 3 due to a combination of obstacle size and cavity design. A person of ordinary skill in the art will appreciate that there are a large variety of shapes of indentations that can be designed.

The microphone elements in the examples presented in Figures 13 are mounted flush on the surface of the sounddiffracting structure (e.g., rigid spheres with or without indentations) as shown in Figures 46. Flushmounted microphone elements are microphone elements that are mounted or integrated into the structure in such a way that there is substantially no protrusion from the surface. Figure 4 shows details of rigid sphere 400, which has no indentations, in which differential microphone element 401 is mounted flush on surface 402 of rigid sphere 400. Figure 5 shows details of rigid sphere 500, which has indentation 503, in which differential microphone element 501 is mounted flush on surface 502 of indentation 503 and thus of rigid sphere 500. Figure 6 shows details of rigid sphere 600, which has indentation 603, in which two differential microphone elements 601 and 604 are mounted flush on surface 602 of indentation 603 and thus of rigid sphere 600. Omnidirectional microphone elements can also be used instead of two differential microphone elements if their omnidirectional behavior is transformed into differential behavior by a corresponding electronic circuit or by software. The indentations may be shaped, for example, as inverse spherical caps or inverse circular paraboloids.

In the exemplary microphone arrays shown in
Figures 13, differential microphone elements (also known as pressure gradient microphones) are employed. For example, a firstorder differential microphone element has a general directional pattern E, which can be written as:
$$\mathrm{E}\left(\mathrm{\phi}\right)=\mathrm{\alpha}+\left(\mathrm{1}\mathrm{\alpha}\right)\mathrm{cos}\left(\mathrm{\phi}\right),$$

wherein ϕ is the azimuth spherical angle and, typically, 0 ≦ α ≦ 1 so that the response is normalized to have a maximum value of 1 at ϕ = 0°. Note that the directivity is independent of spherical elevation angle 8 due to an assumption of symmetrical rotation. The magnitude of Equation (1) is the parametric expression of the "limaçon of Pascal" algebraic curve, familiar to those skilled in the art. The two terms in Equation (1) can be seen to be the sum of an omnidirectional sensor (i.e., the first term) and a firstorder dipole sensor (i.e., the second term), which is the general form of the firstorder array. One implicit property of Equation (1) is that for 0 ≦ α ≦ 1, there is a maximum at 8 = 0 and a minimum at an angle between π/2 and π. For values of α > 0.5, the response has a minimum at π, although there is no zero in the response. A microphone with this type of directivity is typically referred to as a subcardioid microphone. An illustrative example of the response for this case is shown in
Figure 7, wherein α = 0.55. When α = 0.5, the parametric algebraic equation has a specific form, which is referred to as a cardioid. The cardioid pattern has a zero response at ϕ = 180°. For values of 0 ≦ α ≦ 0.5, there is a null at:
$${\mathrm{\phi}}_{\mathrm{null}}={\mathrm{cos}}^{\mathrm{1}}\left(\mathrm{\alpha}/\mathrm{\alpha}\mathrm{1}\right)\mathrm{.}$$

Figure 8 shows an illustrative directional response corresponding to this case, wherein α = 0.20.

Now referring to Figure 9, differential microphone element 900 may have directivity in the approximate shape of a cardioid. Differential microphone element 900 may be a tubelike member (e.g., a substantially ucurved tube 901) with two open ends, also herein referred to as sound inlet ports 902 and 903, and omnidirectional microphone 904 disposed in tube 901 between sound inlet ports 902 and 903 of the tubelike member. Sound inlet ports 902 and 903 are spaced at distance d apart and are defined by juxtaposed end sections of tube 901 that communicate with diaphragm 905 of microphone 904. The two sides 905a and 905b of microphone diaphragm 905 receive sound from the two respective inlet ports 902 and 903. The sound pressure driving the rear of the diaphragm travels through a resistive damping material 906, which is designed to provide a time delay (also referred to as acoustic delay). The dissipative, resistive damping material 906 may be designed to create a proper time delay in order for the net pressure to have the desired directivity.

Ports 902 and 903, which are separated by distance d, as mentioned above, create net pressure p
_{net} on the diaphragm, which may be expressed as:
$${p}_{\mathit{net}}={P}_{\mathit{net}}\cdot {e}^{\mathit{j\omega t}}=P\left(1{e}^{j\left(\mathit{\omega t}+\frac{d}{c}\omega \mathit{cos}\left(\varphi \right)\right)}\right){e}^{\mathit{j\omega t}}$$

wherein
$j=\sqrt{1},$ co is the frequency of the sound in radians/second, c is the speed of sound,
φ is the angle of incidence and τ is a time delay introduced by the resistive material. Since time delay τ and distance d between ports 12 and 14 are quite small, the argument of the exponential is small and allows Equation (3) to be approximated by:
$${p}_{\mathit{net}}\approx \mathit{Pj}\left(\mathit{\omega t}+\frac{d}{c}\mathit{\omega cos}\left(\varphi \right)\right){e}^{\mathit{j\omega t}}\mathrm{.}$$

Material 906 may be designed to create the proper time delay in order for the net pressure to have the desired directivity. If material 906 is represented by an equivalent lowpass electronic circuit, the transfer function of material 906 is:
$$H=\frac{1}{1+\mathit{j\omega RC}},$$

wherein R is the equivalent resistance and C is the equivalent capacitance. The phase delay ψ due to this circuit is:
$$\mathrm{\psi}=\mathrm{arctan}\left(\mathrm{\omega RC}\right)$$

and time delay τ is given by:
$$\tau =\frac{d\varphi}{d\omega}=\frac{1}{1+{\left(\mathit{\omega RC}\right)}^{2}}\frac{1}{\mathit{RC}}\mathrm{.}$$

Operating the filter in the passband (ω < 1/(RC)) leads to a time delay of
$$\tau =\frac{1}{\mathit{RC}}\mathrm{.}$$

If the resistive material is selected to create a time delay given by τ = d/c, the net pressure becomes:
$${P}_{\mathit{net}}=\mathit{j\omega}\frac{d}{c}\left(1+\mathit{cos}\left(\varphi \right)\right)\mathrm{.}$$

The term 1+cos(ϕ) gives the familiar cardioid directivity pattern.

It is important to note that the net pressure on the directional microphone is proportional to co and thus has a 6 dB per octave slope. The net pressure is also diminished in proportion to distance d between the ports. Reducing the overall size of the sensor thus results in a proportional loss of sensitivity.

Note that the 6 dB per octave slope and the dependence on dimension d remain even in microphones without the resistive material (τ = 0) in Equation (4). A microphone without the resistive material but with different distance between the omnidirectional microphone and the sound inlet ports is shown in Figure 10.

Differential microphone element 1000 may comprise a substantially ucurved tube 1001, with two sound inlet ports 1002 and 1003, and an omnidirectional microphone 1004 disposed in tube 1001 between sound inlet ports 1002 and 1003 of the tubelike member. Sound inlet ports 1002 and 1003 are spaced at distance d apart, and are defined by juxtaposed end sections of tube 1001 that communicate with diaphragm 1005 of microphone 1004. The two sides 1005a and 1005b of microphone diaphragm 1005 receive sound from the two respective inlet ports 1002 and 1003. The sound pressure driving rear side 1005b of the diaphragm travels a longer way compared to front side 1005a and thus provides a time delay relative to front side 1005a.

Differential microphone characteristics may be achieved not only with a purely acoustic differential microphone assembly, but also electroacoustically. Referring to Figure 11, an electroacoustic firstorder differential microphone element 1100 may include acoustics part 1101 and electronics part 1102. Acoustics part 1101 features two omnidirectional microphones 1103 and 1104 arranged at distance d from each other. Within electronics part 1102, the outputs of omnidirectional microphones 1003 and 1104 are subtracted from each other by differencing amplifier 1105. Before this subtraction, the output of omnidirectional microphone 1104 is passed through delay element 1106 to delay the outputs of the two omnidirectional microphones 1103 and 1104 relative to each other. This element may be, for example, an allpass filter or time delay circuit. The output of differencing amplifier 1105 is passed through equalizing filter 1107 to compensate for frequencydependent gain values of the circuit.

Figure 12 shows a schematic diagram of another firstorder fullband differential microphone element 1200 based on an adaptive backtoback cardioid system. In differential microphone element 1200, signals from two microphones 1201 and 1202 are delayed by time delay T at delay elements 1203 and 1204, respectively. The delayed signal from microphone 1201 is subtracted from the undelayed signal from microphone 1202 at subtraction element 1205 to form a forwardfacing cardioid signal. Similarly, the delayed signal from microphone 1202 is subtracted from the undelayed signal from microphone 1201 at subtraction element 1206 to form a backwardfacing cardioid signal.

While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.