TECHNICAL FIELD
[0001] The disclosure relates to a microphone array, in particular to a spherical microphone
array for use in a modal beamforming system.
BACKGROUND
[0002] A microphone-array-based 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 high-frequency limitations so
that the sound field can only be accurately described over a limited frequency range.
Low-frequency 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.
High-frequency 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 under-sampled. 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
[0003] A spherical microphone array may include a sound-diffracting structure that has a
closed three-dimensional shape with a surface surrounding the shape and at least two
differential microphones mounted flush on the surface of the sound-diffracting structure.
[0004] 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
[0005] 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 six-element microphone array mounted in a spherical
sound-diffracting structure.
Figure 2 is a perspective view of a microphone array that has a sound-diffracting
structure with the polyhedral shape of a 60-sided pentakis dodecahedron.
Figure 3 is a perspective view of a spherical sound-diffracting structure with indentations
of the surface formed by conical cavities.
Figure 4 is a cross-sectional view of a rigid sphere with no indentation shapes and
an integrated flush-mounted microphone element.
Figure 5 is a cross-sectional 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 cross-sectional 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 first-order differential
microphone in accordance with Equation (1), wherein α = 0.55.
Figure 8 is a diagram illustrating directivity plots for a first-order 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
[0006] A schematic illustration of a six-element 3D microphone array 100 mounted in rigid
sphere 101, which forms a sound-diffracting 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 8-12.
In other exemplary microphone arrays, other conventional differential microphone elements
may be used.
[0007] Figure 2 shows a perspective view of a 3D microphone array 200 that has the polyhedral
shape of a 60-sided pentakis dodecahedron. Although not shown in the figures, microphone
array 200 of Figure 2 has a plurality of individual flush-mounted 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 non-uniformly 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.
[0008] Figure 3 illustrates a 3D microphone array 300 that has a spherical sound-diffracting
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 sound-diffracting
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.
[0009] The microphone elements in the examples presented in Figures 1-3 are mounted flush
on the surface of the sound-diffracting structure (e.g., rigid spheres with or without
indentations) as shown in Figures 4-6. Flush-mounted 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.
[0010] In the exemplary microphone arrays shown in Figures 1-3, differential microphone
elements (also known as pressure gradient microphones) are employed. For example,
a first-order differential microphone element has a general directional pattern E,
which can be written as:
[0011] 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 first-order dipole sensor (i.e., the second term), which is the general form of
the first-order 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 sub-cardioid
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:
[0012] Figure 8 shows an illustrative directional response corresponding to this case, wherein
α = 0.20.
[0013] 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 tube-like member (e.g., a substantially u-curved 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 tube-like 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.
[0014] 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:
[0015] wherein
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:
[0016] 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
low-pass electronic circuit, the transfer function of material 906 is:
[0017] wherein R is the equivalent resistance and C is the equivalent capacitance. The phase
delay ψ due to this circuit is:
[0018] and time delay τ is given by:
[0019] Operating the filter in the passband (ω < 1/(RC)) leads to a time delay of
[0020] If the resistive material is selected to create a time delay given by τ = d/c, the
net pressure becomes:
[0021] The term 1+cos(ϕ) gives the familiar cardioid directivity pattern.
[0022] 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.
[0023] 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.
[0024] Differential microphone element 1000 may comprise a substantially u-curved 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 tube-like 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.
[0025] Differential microphone characteristics may be achieved not only with a purely acoustic
differential microphone assembly, but also electro-acoustically. Referring to Figure
11, an electro-acoustic first-order 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 all-pass filter or time delay circuit. The output
of differencing amplifier 1105 is passed through equalizing filter 1107 to compensate
for frequency-dependent gain values of the circuit.
[0026] Figure 12 shows a schematic diagram of another first-order full-band differential
microphone element 1200 based on an adaptive back-to-back 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 forward-facing 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 backward-facing cardioid signal.
[0027] 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.
1. A spherical microphone array comprising:
a sound-diffracting structure that has a closed three-dimensional shape with a surface
surrounding the shape; and
at least two differential microphones mounted flush on the surface of the sound-diffracting
structure.
2. The microphone array of claim 1, wherein the sound-diffracting structure has the shape
of a sphere or polyhedron.
3. The microphone array of claim 1 or 2, wherein at least one of the differential microphones
comprises two first omnidirectional microphones and a beamforming circuit, the two
first omnidirectional microphones and the beamforming circuit being configured to
provide a differential microphone output signal.
4. The microphone array of claim 1 or 2, wherein at least one of the differential microphones
comprises a tube-like member with two open ends and an omnidirectional microphone
disposed in the tube-like member between its two ends.
5. The microphone array of claim 3 or 4, wherein a second omnidirectional microphone
is disposed at a position with differing distances to the two ends of the tube-like
member.
6. The microphone array of claim 5, wherein an acoustic delay element is disposed between
one end of the tube-like member and the second omnidirectional microphone.
7. The microphone array of any of the preceding claims, wherein the tube-like member
is u-curved.
8. The microphone array of any of the preceding claims, further comprising at least one
indentation in the perimeter of the diffracting structure, wherein at least one differential
microphone is disposed in the at least one indentation.
9. The microphone array of any of the preceding claims, wherein the surface of the diffracting
structure has at least one indentation formed thereon and at least one differential
microphone is disposed in the at least one indentation.
10. The microphone array of claim 8, wherein the at least one indentation is shaped as
an inverse spherical cap or inverse circular paraboloid.
11. The microphone array of any of the preceding claims, wherein the walls of the indentation
are sound-reflective.