JP2018157309A - Microphone array - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a microphone array in which influence of spatial aliasing is low as compared with polyhedral derived arrangement and a degree of freedom of designing the number of microphone elements is enhanced.SOLUTION: A microphone array 1 is arranged at substantially equal intervals in an axial direction of a helical trajectory along a spiral orbit on a spherical surface, and, when projected onto a plane perpendicular to the axis of the helical trajectory, has a plurality of microphone elements arranged at an angular interval of substantially equal density around the axis.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a microphone array.

  As a method for collecting a three-dimensional sound field, a method using a multi-channel microphone in which microphone elements are arranged in a spherical shape is known (Patent Documents 1 and 2, and Non-Patent Document 1). In general, a recorded signal is encoded at a center position of a microphone array into a coefficient obtained by expanding a sound field into a spherical harmonic function, and a signal that restores the coefficient is reproduced by a speaker array surrounding the listener. High Order Ambisonics (HOA) that reproduces a three-dimensional sound field is known. Conventionally, the microphone array used in the HOA includes a plurality of microphone elements in a regular polyhedron (for example, a regular dodecahedron or a regular icosahedron), a semi-regular polyhedron (for example, a five-sided dodecahedron or a truncated icosahedron), or a so-called geodesic dome. Those arranged at the vertices of the regular polyhedron or semi-polyhedron are obtained by subdividing the surface to increase the number of vertices. Hereinafter, these arrangements are referred to as “polyhedral-derived arrangements”.

Japanese Patent Laid-Open No. 2006-82414 US Pat. No. 7,874,054

Shuichi Sakamoto, “SENZI: Three-dimensional sound space sound reproduction using a spherical microphone array”, Journal of the Acoustical Society of Japan, Acoustical Society of Japan, July 2014, Vol. 70, No. 7, pp. 379-384

  In the polyhedron-derived arrangement, the appearance of the effect of spatial aliasing in the high frequency region varies greatly depending on the direction of arrival of sound waves incident on the microphone array due to its high symmetry. Specifically, for example, the frequency characteristic of a signal encoded using HOA has strong sound source direction dependency. Further, the polyhedral-derived arrangement is limited in the number of microphone elements to be arranged due to its design principle. That is, there is a problem that only a known regular polyhedron or semi-regular polyhedron or an arrangement obtained by dividing the regular polyhedron can be used, and the degree of freedom in designing the number of microphone elements is low.

  In contrast, the present invention provides a microphone array that is less affected by spatial aliasing than a polyhedral-derived arrangement and has a higher degree of freedom in designing the number of microphone elements.

  The present invention is arranged at substantially equal intervals in the axial direction of the spiral trajectory along the spiral trajectory on the spherical surface, and when projected onto a plane perpendicular to the axis of the spiral trajectory, the density is approximately equal around the axis. A microphone array having a plurality of microphone elements arranged at angular intervals is provided.

  The plurality of microphone elements may be arranged according to a Fibonacci spiral.

  According to the present invention, it is possible to provide a microphone array in which the influence of spatial aliasing is low as compared with the polyhedral-derived arrangement and the degree of freedom in designing the number of microphone elements is increased.

FIG. 3 is a diagram illustrating the arrangement of microphone elements in the microphone array 1. The figure which shows another example of arrangement | positioning of the microphone element in the microphone array. The figure which illustrates the positional relationship of point P [0] and point P [1]. The figure which illustrates arrangement | positioning of point P [0]-point P [7]. The figure which shows regular dodecahedron vertex arrangement | positioning. The figure which shows regular icosahedron vertex arrangement | positioning. The figure which shows 5-sided dodecahedron arrangement. The figure which shows truncation icosahedron arrangement. The figure which shows geodesic dome arrangement | positioning. The figure which shows the reproduction error characteristic of the sound source in the geodesic dome arrangement | positioning which concerns on a comparative example. The figure which shows the reproduction error characteristic of the sound source in the Fibonacci spiral arrangement | positioning which concerns on one Example. The figure which illustrates arrangement | positioning of the microphone element which concerns on another embodiment. The figure which illustrates displacement angle delta [n]. The figure which shows the reproduction error characteristic of the sound source in the example of FIG.

FIG. 1 is a diagram illustrating the arrangement of microphone elements in a microphone array 1 according to an embodiment. FIG. 2 is a diagram illustrating another example of the arrangement of the microphone elements in the microphone array 1. In these drawings, the microphone element is represented by a point on the spherical surface S. 1, 2, 5-9, and 12, the microphone elements are arranged over the entire surface of the spherical surface S. In these drawings, the microphone elements arranged on the front surface and the back surface of the spherical surface S are distinguished by shading of dots. In the figure, the front microphone element is a microphone element at a position directly visible from the viewpoint, and the other microphone elements are rear microphone elements. A relatively dark point indicates the microphone element Pf disposed on the front surface, and a thin dot indicates the microphone element Pb disposed on the back surface. In the following, these are simply referred to as points P. FIG. 1 shows an example in which 32 microphone elements are arranged, and FIG. 2 shows an example in which 122 microphone elements are arranged. In these examples, the plurality of microphone elements are arranged along the Fibonacci spiral. Hereinafter, this arrangement is referred to as “Fibonacci spiral arrangement”. The position of the N microphone elements arranged on the spherical surface S is represented as a point P [n]. n is a natural number satisfying 0 ≦ n ≦ (N−1). According to the Fibonacci spiral arrangement, the coordinates of the point P [n] are expressed by the following equation (1). The value of N, that is, the number of microphone elements is not particularly limited, and the number of microphone elements can be designed freely. In equation (1), the center of the sphere is the origin O of the xyz coordinate system (not shown in FIG. 1), and the axial direction of the spiral is the z direction.

  Unlike the polyhedron-derived arrangement, the Fibonacci spiral arrangement is an arrangement that does not start from the polyhedron. Therefore, the symmetry in the microphone element point group is lower than that in the polyhedral derivative arrangement. Due to this low symmetry, the dependence of the spatial aliasing on the sound source direction in the high frequency region is relaxed compared to the polyhedral-derived arrangement. In the Fibonacci spiral arrangement, the number of microphone elements can be increased or decreased by one unit, and the degree of freedom in design is high.

Here, it will be described that the Fibonacci spiral arrangement is an arrangement having substantially equal density in the vertical direction (z-axis direction) and the horizontal direction (xy plane) and low symmetry. The z-coordinate z [n] of the point P [n] is obtained from the equation (1):
And is an N-divided arrangement in the range of approximately ± 1 on the z-axis. As described above, the Fibonacci spiral arrangement has substantially the same density in the z-axis direction, and the N points P are arranged without overlapping in the orthogonal projection onto the z-axis.

  Next, consider an orthogonal projection of the point P onto the xy plane. As is clear from the equation (1), the radius r [n] in the polar coordinate display is not constant. However, in order to simplify the explanation, it is assumed that the radius r [n] is constant, and the point P [i ] And the point P [j] will be described below (where i ≠ j).

FIG. 3 is a diagram illustrating the positional relationship between the points P [0] and P [1]. Here, an angle Δθ formed by two line segments connecting the origin O and any two of the points P [i] and P [j] (hereinafter simply referred to as “points P [i] and P [j]”). (Referred to as “the angle formed by”) is as shown in the following equation (2).
When Δθ [i, j] is an integral multiple of 2π, the point P [i] and the point P [j] are arranged at the same angular position in the xy plane. Since (3-√5) is included, Δθ [i, j] does not become an integral multiple of 2π. Therefore, any two microphone elements are arranged without overlapping at the same angular position in the orthogonal projection onto the xy plane.

  Further, the angle Δθ (step size) formed by two adjacent points is Δθ = (3−√5) π from the equation (2). Since (3-√5) = 0.663 ..., Δθ is slightly larger than (3/4) π.

  FIG. 4 is a diagram illustrating the arrangement of the points P [0] to P [7]. When the step size is equal to (3/4) π, the points P are sequentially filled from the direction close to the diagonal, and finally, the circumference is equally divided into eight equal parts. However, in this case, since the points P [8] and after are repeatedly arranged at the same angular position, the arrangement is highly symmetric. If the Fibonacci spiral arrangement is used, the step size is an irrational number slightly larger than (3/4) π. Therefore, the points P [8] and after are not repeatedly arranged at the same angular position, and the density is substantially equal. In addition, the condition that the arrangement is low in symmetry is satisfied.

  5 to 9 are diagrams illustrating the polyhedral derivation arrangement. FIG. 5 shows a regular dodecahedron vertex arrangement. N = 20. FIG. 6 shows a regular icosahedron vertex arrangement. N = 12. FIG. 7 shows a five-sided dodecahedron arrangement. N = 32. FIG. 8 shows a truncated icosahedron arrangement (so-called soccer ball type). N = 60. FIG. 9 shows a geodesic dome arrangement. N = 122. In these arrangements, the number of microphone elements is determined, and the symmetry is high.

  The inventors of the present application evaluated the characteristics of the microphone array for the examples and comparative examples according to the present embodiment. For the evaluation, a simulation of sound field reproduction by HOA was used. In this simulation, the sound pressure radiated from a certain point sound source was calculated at the center position when there was no microphone array, and the sound pressure at the center position of the microphone array reproduced by HOA was calculated. The difference in amplitude characteristics was obtained from the difference between the two. This is hereinafter referred to as “reproduction error characteristic”. As the microphone array, a microphone array of a hard sphere baffle having a radius of 10 cm was used. In the simulation, the point sound sources were arranged in random 500 directions, and the average and standard deviation of the 500 points of data were calculated for each frequency.

  FIG. 10 is a diagram showing reproduction error characteristics of a sound source in a geodesic dome arrangement (FIG. 9) according to a comparative example. FIG. 11 is a diagram illustrating reproduction error characteristics of a sound source in the Fibonacci spiral arrangement (FIG. 2) according to an embodiment. In either case, N = 122 is shown. The vertical axis in the figure represents the reproduction error characteristic. When the reproduction error characteristic is 0 dB, this corresponds to the sound pressure being reproduced without error. In the figure, the solid line near 0 dB indicates the average reproduction error characteristic, the upper end of the area painted above and below the average reproduction error characteristic is a curve obtained by adding the standard deviation at each frequency to the average characteristic, and the lower end is the average characteristic to each frequency. The curve which subtracted the standard deviation in is shown. In FIG. 10, the peak of the standard deviation appears at a specific frequency, which indicates that the variance of the reproduction error is large at the specific frequency, that is, the spatial dependency of the spatial aliasing is large. On the other hand, in FIG. 11, the peak of the standard deviation is suppressed as compared with FIG. 10, and it can be seen that the dependence of the spatial aliasing on the sound source direction is reduced.

  The arrangement of microphone elements in the microphone array according to the present invention is not limited to strictly following the Fibonacci spiral arrangement described above, and various modifications can be made.

  FIG. 12 is a diagram illustrating the arrangement of microphone elements in a microphone array 1 according to another embodiment. FIG. 12 shows an example (N = 122) in which a displacement angle δ [n] is given as a random angular displacement (fluctuation) with respect to an ideal position according to the Fibonacci spiral arrangement shown in Equation (1). ing. The displacement angle δ [n] is a line segment connecting the ideal position Pi [n] of the microphone element and the center (origin O) of the microphone array (spherical surface S) and the (actual) microphone element after the displacement. An angle formed by a line segment connecting the position P [n] and the origin O.

FIG. 13 is a diagram illustrating the displacement angle δ [n]. In this example, the displacement angle δ [n] given to the point P [n] was obtained from a uniform distribution with the maximum displacement angle being 2.5% of the reference angle α and the average being zero. The reference angle α is obtained as follows. A distance from another point P closest to the point P [n] (microphone element) when viewed from one point P [n] is referred to as a distance between re-adjacent points at the point P [n]. The distance between re-adjacent points is obtained for all points P, and a combination of two points (a combination of microphone elements having the closest distance) that gives the minimum value is defined as a point P [n] and a point P [m]. An angle formed by a line segment connecting the point P [n] and the origin O and a line segment connecting the point P [m] and the origin O is the reference angle α. Here, the reason why the maximum displacement angle is set to 2.5% of the reference angle α is as follows. First, the maximum value (allowable displacement angle) of the displacement angle δ [n] allowed for the point P [n] is considered to be half of the angle (reference angle α) formed with the nearest neighbor point P [m]. This is because if the displacement more than this is allowed, the relationship with the position before the displacement becomes unclear. 5% of this allowable displacement angle (α / 2) was taken as the maximum displacement angle. Then, the maximum displacement angle δmax is
It is. That is, the maximum displacement angle is 2.5% of the angle between the two adjacent microphone elements. The value “5%” of the allowable displacement angle is an example of an error that does not affect the reproduction error. Further, here, the displacement points are sampled from the uniform distribution on the curved surface on the spherical surface S surrounded by the determined maximum displacement angle (the region on the spherical surface where the cone and the sphere with the center of the sphere as a vertex). The same displacement is allowed with respect to the angle at and the position in the z direction.

  FIG. 14 is a diagram showing reproduction error characteristics of the sound source in the example of FIG. The simulation was performed under the same conditions as in FIG. Even if a random angular displacement is given to the ideal position according to the Fibonacci spiral, the peak of the standard deviation is suppressed as in the result shown in FIG. 9, and the sound source direction dependence of spatial aliasing is suppressed. It can be seen that it has been reduced.

  The arrangement of the microphone elements in the microphone array according to the present invention is not limited to that based on the Fibonacci spiral. The plurality of microphone elements are arranged at substantially equal intervals in the axial direction of the spiral along the spiral trajectory on the spherical surface, and when projected onto a plane perpendicular to the axis of the spiral, the substantially equal density is centered on the axis. As long as these angular intervals are arranged, an arrangement based on a spiral trajectory other than the Fibonacci spiral may be used. Considering only improving the degree of freedom in designing the number of microphone elements, the angle Δθ (step size) formed by two adjacent points when projected onto the xy plane may be a rational number. However, an arrangement in which Δθ (step size) is an irrational number is preferable in order to suppress symmetry and reduce the sound source direction dependency of spatial aliasing. Further, “arranged along the spiral trajectory” does not mean that the microphone element is mathematically strictly arranged on the spiral trajectory, but is predetermined from the spiral trajectory as illustrated in FIG. It is also included that the microphone element is disposed at a position where the above displacement is given.

1 ... Microphone array

Claims (2)

Along the spiral trajectory on the spherical surface, they are arranged at substantially equal intervals in the axial direction of the spiral trajectory, and are projected at a substantially equal density angular interval around the axis when projected onto a plane perpendicular to the axis of the spiral trajectory. A microphone array having a plurality of microphone elements arranged. The microphone array according to claim 1, wherein the plurality of microphone elements are arranged according to a Fibonacci spiral.