JP6345634B2 - Sound field reproducing apparatus and method - Google Patents

Description

  The present invention relates to a sound field reproduction technique, and more particularly to a spatial multi-zone sound field reproduction technique.

  Spatial multi-zone sound field reproduction is a technique for reproducing a plurality of independent sound fields in a separated space by driving a speaker array (see, for example, Non-Patent Document 1). In the prior art, in order to reproduce a sound field in a plurality of areas, a circular array in which omnidirectional speakers are arranged in a circle at equal intervals so as to surround the reproduction area is used. In order to accurately reproduce the sound field up to the wave number k within the circumference of the radius R by the conventional circular array, a huge number of speakers of 2kR + 1 or more are required.

Y. J. Wu, et al. “Spatial Multizone Soundfield Reproduction: Theory and Design,” Speech and Audio Processing, IEEE Transactions on 19.6 (2011): 1711-1720.

  However, the conventional configuration has a problem that the degree of freedom in controlling the sound field is low. The subject of this invention is improving the control freedom degree of a sound field.

  A plurality of higher-order sound sources that reproduce an acoustic signal with a reproduction pattern, which is composed of any one of a plurality of independent radiation modes having different directivity patterns or a combination of at least some of the plurality of radiation modes, are used. The plurality of higher order sound sources are arranged on the circumference. The reproduction pattern is obtained by controlling the weight of each radiation mode in order to generate a desired sound field in a plurality of spatial regions.

  In the present invention, since the respective weights of the radiation modes of the higher-order sound source are controlled, the degree of freedom in controlling the sound field can be improved as compared with the conventional art.

FIG. 1 is a conceptual diagram for explaining the configuration of the sound field reproducing apparatus of the first embodiment. FIG. 2 is a block diagram illustrating the control unit of the embodiment. FIG. 3 is a geometric diagram relating to Theorem 1. 4A and 4B are conceptual diagrams for explaining the configuration of the sound field reproducing apparatuses of the second and third embodiments.

Embodiments of the present invention will be described below.
〔Overview〕
In this embodiment, sound field reproduction is performed using a plurality of higher order sources arranged on the circumference. An example of a higher order sound source is a higher order loudspeaker (for example, reference 1 “M. Poletti, T. Betlehem,“ Design of a prototype variable directivity loudspeaker for improved surround sound reproduction in rooms, ”AES 52nd. International Conference, Guildford, UK, 2013, September 2-4 "). Each higher-order sound source reproduces an acoustic signal with a “reproduction pattern” composed of any one of a plurality of independent radiation modes having different directivity patterns or a combination (linear sum) of at least a part of a plurality of radiation modes. . The “reproduction pattern” is obtained by controlling the weight of each radiation mode in order to generate a desired sound field in a plurality of spatial regions. Thereby, the control freedom degree of a sound field can be improved rather than before. For example, when using a circular array in which high-order sound sources of order N are arranged in a circle, when using a circular array of conventional omnidirectional speakers with the same radius of the circle containing the plurality of spatial regions, As compared with the above, it is possible to sufficiently suppress the external sound field of the circular array while reproducing the sound field having a bandwidth about N times as high as accuracy. Further, when the external sound field is not suppressed, a sound field having a bandwidth of about 2N times can be reproduced with high accuracy.

When controlling only the internal sound field of a circular array, for example for m∈ [−M _I (k), M _I (k)]
A pattern that uses the solution or approximate solution of w ⁽⁰⁾ _{n, u} (k) that satisfies the above as filter weights for the radiation mode m (n) at the wave number k of the higher-order sound source hs (u) is referred to as a “reproduction pattern”. . However, M _I (k) is a positive integer, and [−M _I (k), M _I (k)] is a closed interval composed of integers from −M _I (k) to M _I (k), The “plurality of high-order sound sources” are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and “multiple radiation modes” are 2N + 1 radiation modes m. (-N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is This is a value representing the size of the higher order sound source hs (u) (for example, the radius of the next sound source hs (u) or an approximate value thereof), and _RL is the radius of the circumference where a plurality of higher order sound sources are arranged. H _ι (·) is the first kind of Hankel function of order ι, H ' _ι (·) is the derivative (derivative) of the Hankel function H _ι (·), and i is the imaginary unit And e is ne Is the number of peers, theta _u is the argument of higher sound hs (u) relative to the origin, β ^{d m} _(k) is the polar region including a plurality of spatial regions where desired sound field is generated (r , Θ) is the expansion coefficient for m of the frequency domain signal S ^d (r, θ; k) of wave number k at k.

When controlling only the external sound field of a circular array, for example, for m∈ [−M _E (k), M _E (k)]

A pattern that uses a solution or approximate solution of w ⁽¹⁾ _{n, u} (k) that satisfies the above as a filter weight for the radiation mode m (n) at the wave number k of the higher-order sound source hs (u) is referred to as a “reproduction pattern”. . However, M _E (k) is a positive integer, and [−M _E (k), M _E (k)] is a closed interval composed of an integer from −M _E (k) to M _E (k), J _ι (·) is a Bessel function of order ι, and γ ^d _m (k) is a frequency domain signal S ^d (r, r, k) at polar coordinates (r, θ) of a region where a desired sound field is generated. θ: expansion coefficient of k) for m.

When performing simultaneous control of the internal / external sound field of a circular array, for example

Satisfy w ⁽²⁾ (k) or approximate solution element w ⁽²⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L) A pattern as a filter weight for the radiation mode m (n) at the wave number k of the sound source hs (u) is referred to as a “reproduction pattern”. For m∈ [−M _I (k), M _I (k)]
Is expressed as G (k) w ⁽⁰⁾ (k) = β ^d (k), G (k) is a matrix of (2M _I (k) +1) × L (2N + 1), and w ⁽⁰⁾ ( k) is a vertical vector consisting of L (2N + 1) w ⁽⁰⁾ _{n, u} (where n = −N,..., N, u = 1,..., L),

(·) ^T is the transpose of (·), and m∈ [−M _E (k), M _E (k)]

Is expressed as J (k) w ⁽¹⁾ (k) = γ ^d (k), J (k) is a matrix of (2M _E (k) +1) × L (2N + 1), and w ⁽¹⁾ ( k) is a vertical vector consisting of L (2N + 1) w ⁽¹⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L),

It is.

[First Embodiment]
A first embodiment will be described with reference to the drawings.
<Configuration>
As illustrated in FIG. 1, the sound field reproduction device 1 of the present embodiment includes a control unit 11 and L high-order sound sources (high-order speakers) 12-u arranged on the circumference (where u = 1). ,..., L). Each higher-order sound source 12-u is disposed, for example, in an anechoic environment or an environment similar thereto. However, each higher-order sound source 12-u may be arranged in a reverberant environment. As illustrated in FIG. 2, the control unit 11 includes a storage unit 111, a weight acquisition unit 112, a filtering unit 113-u, and a drive signal generation unit 114-u. The control unit 11 is, for example, a general-purpose or dedicated computer that includes a processor (hardware processor) such as a CPU (central processing unit) and a memory such as random-access memory (RAM) and read-only memory (ROM). It is configured by executing a predetermined program. The computer may include a single processor and memory, or may include a plurality of processors and memory. This program may be installed in a computer, or may be recorded in a ROM or the like in advance. In addition, some or all of the processing units are configured using an electronic circuit that realizes a processing function without using a program, instead of an electronic circuit (circuitry) that realizes a functional configuration by reading a program like a CPU. May be. In addition, an electronic circuit constituting one device may include a plurality of CPUs. 1 and 2 are examples of L = 15, this does not limit the present invention.

≪Geometric arrangement≫
Two-dimensional global (global) spatial regions, and S two-dimensional local (circular) desired spatial regions (circular regions) 14-1,. Assume a corresponding desired sound field. However, S is an integer of 2 or more. The radius and origin of the s-th (where s = 1,..., S) space region 14-s are expressed by R _z ^(s) and O _s , respectively. Here, O _s is located at polar coordinates (r ^(s0) , θ ^(s0) ) with respect to the global origin O. r ^(s0) and θ ^(s0) represent a radius vector and a declination angle, respectively. A local polar coordinate of an arbitrary observation point in the s-th spatial region 14-s is expressed as (R ^(s) , Ω ^(s) ). (R ^(s) , Ω ^(s) ) are polar coordinates centered on the local origin O _s , and R ^(s) and Ω ^(s) represent the radial and declination, respectively. Local polar coordinates (R ^(s) , Ω ^(s) ) are located at polar coordinates (r, θ) with respect to the global origin O. r and θ represent a radius vector and a declination angle, respectively. All the spatial regions 14-1,..., 14-S are present in a circular region having a radius R _P ≧ r with the global origin O as the center. R _P is all the spatial regions 14-1, ..., the radius of the circular area including the 14-S inwards. L pieces of high-order tone 12-u are arranged on the circumference of a radius R _L ≧ R _P from global origin O. The higher order sound sources 12-1, ..., 12-L may be arranged at equal intervals or may not be arranged at equal intervals. L is a positive integer. For example, L is an integer of 2 or more.

《Cylinder harmonic function expansion of internal / external sound field》
Development of the time-frequency domain signal S (r, θ; k) of the internal sound field at the wave number k of polar coordinates (r, θ) with respect to the origin O in the region r < _RL is as follows.

However, r and (theta) represent a moving radius and a declination, respectively. A _m (k) is an expansion coefficient (sound field coefficient) for m for uniquely expressing S (r, θ; k), and m is an integer.

The expansion of the time-frequency domain signal S (r, θ; k) of the external sound field in the polar coordinates (r, θ) with respect to the origin O in the region r> _RL is as follows.

Here, B _m (k) is an expansion coefficient (sound field coefficient) for m for uniquely expressing S (r, θ; k). H _m (·) is a first-type Hankel function of order m.

<< Expansion coefficient of plane wave >>
A time-frequency domain signal S ^{d (s)} (R ^(s) , Ω ^(s ) at a wave number k in polar coordinates (R ^(s) , Ω ^(s) ) representing a plane wave propagating from the direction of the vector r _s ^{→ );} k) can be expressed as follows.

It should be noted that, as in equation (3), of the "r _s ^→", "→" is it should be referred to directly above the original "r _s", on the constraints of the described notation, "→" and "r _s" It is written in the upper right of. Equation (3) can be transformed as follows by Jacobian-Anger expansion.

Where θ _s is the angle of the vector r _s ^{→ in} polar coordinates. That is, r _s ^→ = (r _s cos θ _s , r _s sin θ _s ), and r _s ^→ is represented by polar coordinates (r _s , θ _s ). Here, the time-frequency domain signal S ^{d (s)} (R ^(s) , Ω ^(s ) at the wave number k of polar coordinates (R ^(s) , Ω ^(s) ) representing the internal sound field of the spatial domain 14- ^{s. );} k) can be expressed as follows by a cylindrical harmonic expansion.

Here, β _m ^d (k) is an expansion coefficient for m for uniquely expressing S ^{d (s)} (R ^(s) , Ω ^(s) ; k). From Equations (3), (4), and (5), the expansion coefficient β _m ^d (k) of the plane wave is given by

≪Linear sound source expansion coefficient≫
r _s ^→ = (in polar coordinates _{(r s, θ s))} (r s cosθ s, r s sinθ s) representing the sound field generated by the (point source in two-dimensional space domain) line source located, A time-frequency domain signal S ^{d (s)} (R ^(s) , Ω ^(s) ; k) at a wave number k in polar coordinates (R ^(s) , Ω ^(s) ) is expressed as follows.

However, R ^{→ (s)} = (R ^(s) cosΩ ^(s) , R ^(s) sinΩ ^(s) ), and R ^{→ (s)} is expressed in polar coordinates (R ^(s) , Ω ^(s) ) || (•) || represents the norm of (•). As shown in the equation (7), “→” in “R ^{→ (s)} ” should be described immediately above “R”, but “→” is changed to “R” due to the limitation of description. To the upper right. Here, the following relation is established by the addition theorem of the Hankel function.

Here, the time-frequency domain signal S ^{d (s)} (R ^(s) , Ω ^(s ) at the wave number k of polar coordinates (R ^(s) , Ω ^(s) ) representing the internal sound field of the spatial domain 14- ^{s. );} k) is expressed as follows.

Therefore, the expansion factor of the sound field by the line sound source is expressed as follows.

<< Expansion coefficient of sound field in each spatial area >>
A time-frequency domain signal S ^{d (s)} (R ^(s) , Ω ^(s) at wavenumber k in polar coordinates (R ^(s) , Ω ^(s) ) representing the desired sound field in the spatial domain 14-s; k) is expressed as follows by cylindrical harmonic function expansion.

However, J _m (•) is a Bessel function of degree m, and α _m ^{d (s)} (k) uniquely represents S ^{d (s)} (R ^(s) , Ω ^(s) ; k). Expansion coefficient (sound field coefficient) for m, and e is the Napier number (the base of natural logarithm). Expression (11) is a Fourier series expansion, which can represent an arbitrary two-dimensional sound field derived from an arbitrary number of cylindrical waves and plane waves. In addition, “ ^{d (s)} ” of “α _m ^{d (s)} (k)” should be written directly above “m”, but “α _m ^{d (s)} (k” is restricted due to the limitation of the description. ) ”. The same notation may be used for other symbols.

Equation (11) has an infinite number of orthogonal modes. However, due to the nature of the Bessel function and the fact that the sound field is limited in the spatial region where all sound sources are outside, this series expansion can be discontinued by a finite number of orthogonal modes. In this case, S ^{d (s)} (R ^(s) , Ω ^(s) ; k) can be approximated as follows.
However, M _s (k) is a positive integer. In this case, S ^{d (s)} (R ^(s) , Ω ^(s) ; k) is expressed by at least 2M _s (k) +1 modes. When M _s (k) = ceil (keR _z ^(s) / 2), the truncation error is 16.1% or less. However, ceil (•) is a ceiling function of (•).

≪Equivalent global sound field≫
An equivalent global sound field composed of the sound fields of the S spatial regions 14-1,..., S (multi-zone) described above is defined. That is, the sound field reproduction problem of the plurality of spatial regions 14-1,..., S is reduced to reproduction of a global desired sound field over the entire area. A time-frequency domain signal S ^d (r, θ; k) representing a desired global sound field is approximated by cylindrical harmonic function expansion as follows.

Here, β _m ^d (k) is an expansion coefficient (sound field coefficient) for m for uniquely expressing S ^d (r, θ; k). In this case, S ^d (r, θ; k) is expressed by at least 2M ₀ (k) +1 modes. For example, M ₀ (k) = ceil (keR _P / 2). If all multizone falls within a circular region of radius R _P, in order to reproduce the sound field in all multi-zone mode limitation by M 0 _(k) is
M ₀ (k) ≧ (M ₁ (k) + M ₂ (k) +... + M _S (k)) (14)
It is necessary to satisfy.

《Spatial harmonic coefficient conversion》
Consider a sound field in an area where no sound source exists. O _1, O ₂ as shown in FIG. 3, is the origin of the two coordinate systems, they have the axis of the same direction, which moves the O ₁ a known conversion is assumed to be O ₂ . When the polar coordinates (r ⁽¹⁾ , θ ⁽¹⁾ ) in the coordinate system with O ₁ as the origin are represented by the polar coordinates in the coordinate system with O ₂ as the origin, (r ⁽²⁾ , θ ⁽²⁾ ) and Become. Here, the polar coordinates of O ₂ with respect to O ₁ (r ⁽¹²⁾ , θ ⁽¹²⁾ ) are represented. Also, {α _m ⁽¹⁾ (k)} and {α _m ⁽²⁾ (k)} denote the sound field in the region where no sound source exists in the two coordinate systems with the origins as O ₁ and O ₂ , respectively. It is assumed that this is a set of expansion coefficients for m for uniquely expressing. In this case, the following theorems 1 and 2 hold.

[Theorem 1]
α _m ⁽¹⁾ (k) and α _m ⁽²⁾ (k) are related by:

However,

Where “*” represents discrete convolution at mode order m. T _m ⁽²¹⁾ represents a conversion operator from the origin O ₂ to O ₁ , and T _m ⁽¹²⁾ represents a conversion operator from the origin O ₁ to O ₂ .

[Theorem 2]
The polar coordinates of O ₁ with respect to O ₂ are expressed as (r ⁽²¹⁾ , θ ⁽²¹⁾ ),

And applying the theorem of Spatial Harmonic Coefficient Translation, the following relation can be derived.

Here, T _m ^(0s) is a conversion operator from a global coordinate system having O as the origin to a local coordinate system having O _s in the sth spatial region 14- _s as the origin.

《Search for global sound field coefficient》
Coefficient conversion from α _m ^{d (s)} (k) to β _m ^d (k) is performed. The convolution of equation (18) is written as a linear sum as follows.

When this equation (19) is written down for S = 1,..., S, these simultaneous equations are constructed and expressed in matrix form as follows.
α ^d (k) = T (k) β ^d (k) (20)
However, the following is satisfied.

Equation (20) can be modified as follows.
β ^d (k) = T (k) ⁺ α ^d (k) (23)
Where T (k) ⁺ = [T (k) ^H T (k)] ⁻¹ T (k) ^H is a Moore-Peron's pseudo-inverse matrix of T (k), and (·) ^H is (·) Represents the complex conjugate transpose of.

<Description of high-order sound source>
The ideal form of the time frequency signal S _n (r, θ; k) at the wave number k in the polar coordinates (r, θ) representing the sound field by the radiation mode m (n) of the higher order sound source arranged at the origin O is It is expressed as follows.

An actual higher-order speaker can radiate a sound field with a far-field polar response having the form of cos (nθ) and sin (nθ). The response expressed by sin and cos can be easily obtained from the directivity of complex values. The radial velocity ν _r (θ) in the angle θ direction based on the radiation mode m (n) of the higher-order sound source having the radius R at the origin O is expressed as follows.

Where V ₀ is a constant and α _m is a coefficient of Fourier series expansion. Further, the external sound field at the wave number k in the two-dimensional polar coordinates (r, θ) is expressed in the form of the above-described equation (2), and the radiation speed is derived as follows.

Where ρ is a constant and c is the speed of sound. Equation (26) must be equal to Equation (25) with r = R. Therefore, the sound pressure at the wave number k in polar coordinates (r, θ) can be expressed by the following time-frequency signal.

Where t is an index representing time and ω is each speed. Each mode has a phase variation e ^imθ and a radiation variation H _m (kr), and the scale factor is αm / H _m ′ (kr). When generating a single higher-order sound source response e in ^θ , the following must be satisfied.

Real high-order sound sources with discrete drivers (eg, monopole speakers) can only produce the desired response up to a finite frequency. At higher frequencies, spatial aliasing occurs.

≪Description of higher-order sound source after conversion≫
Time-frequency domain representing a sound field at wavenumber k in polar coordinates (r, θ) generated by radiation mode m (n) of an ideal higher-order sound source arranged at polar coordinates (r _s , θ _s ) with respect to origin O The signal S _n (r, θ, r _s , θ _s ; k) can be expressed as follows with respect to the origin O by the cylindrical addition theorem.

R ^→ = (r cos θ, r sin θ), r _s ^→ = (r _s cos θ _s , r _s sin θ _s ), and β _s is the relationship between r ₀ ^→ and r _s ^→ The angle between and

It is expressed. here,
x _rot = x cos θ _s + ysin θ _s (31)
And,
y _rot = −xsin θ _s + y cos θ _s (32)
It is.

A general high-order sound source is a single speaker unit, and can generate radiation orders m (n) of all orders up to a given Nth order. An Nth single high-order sound source arranged at polar coordinates (r _s , θ _s ) having a radiation mode m (n) (n∈ [−N, N]) is represented by the following S _N (r, θ, A sound field of wave number k represented by r _s , θ _s ; k) can be generated in polar coordinates (r, θ).

However, w _n (k) represents a weight for the radiation mode m (n) and the wave number k. Expression (33) is expanded as follows.

A sound field represented by a time frequency domain signal S (r, θ; k) having a wave number k can be generated in polar coordinates (r, θ) by superimposing L-order higher-order sound sources.

However, θ _u is a declination angle of the polar coordinates (R _L , θ _u ) of the higher-order sound source 12-u with respect to the origin. This can be applied to approximation of a desired internal sound field and external sound field.

《Spatial multi-zone sound field reproduction by high-order sound source》
A desired sound field is reproduced in a desired spatial region 14-1,..., 14-S by a circular array composed of L high-order sound sources 12-1,. For this purpose, the weight w _n for each radiation mode m (n) (where n = −N,..., N) at the wave number k of each higher-order sound source 12-u (where u = 1,..., L). _{. u} (k) must be determined. Each high-order sound source 12-u can generate radiation modes m (−N),..., M (N) up to the Nth-order polar response. Weight w _{n. u} (k) is determined by minimizing the square error. In this embodiment, the external sound field of the circular array is not particularly controlled, and only the internal sound field of the circular array is controlled.

《Control of internal sound field of circular array》
In order to control a desired internal sound field without controlling the external sound field, a desired sum having an arbitrary expansion coefficient is obtained by linear summation of sound fields generated by the higher-order sound sources 12-1,. An internal sound field needs to be generated. Each higher-order sound source 12-u generates polar responses up to the Nth order, and a developed order representing the desired sound field is M _I (k). However, M _I (k) is a positive integer. In this case, it is necessary to match the right side of Equation (13) with the right side of Equation (35) (when r < _RL ). From this, the following relationship holds.

The equation (36) is written in matrix-vector format as follows.
G (k) w ⁽⁰⁾ (k) = β ^d (k) (37)
Here, G (k) is a matrix of (2M _I (k) +1) × L (2N + 1), and w ⁽⁰⁾ (k) is L (2N + 1) weights w ⁽⁰⁾ _{n, u} (k). (Where n = −N,..., N, u = 1,..., L),

It is.

A vector w ⁽⁰⁾ (k) composed of w ⁽⁰⁾ _{n, u} (k) (approximate solution or solution) that minimizes the square error of each element on the left side and right side of Expression (37) is as follows. .
w ⁽⁰⁾ (k) = G (k) ^H [G (k) G (k) ^H + λ (k) I] ⁻¹ β ^d (k) (38)
Here, I is a unit matrix of (2M _I (k) +1) × (2M _I (k) +1), and 2M _I (k) + 1 ≦ L (2N + 1). λ (k) is a regularization parameter, and when λ (k) = 0, equation (38) is the minimum norm solution. Λ (k) is used to reduce the weight solution when G (k) has a small singular value. The order M _I (k) required to reproduce the sound field inside the circular array is:

However, the right side of Expression (39) represents the ceiling function value of (ekR _L / 2). The order N increases with frequency,
2M _I (k) + 1 = βL (2N + 1), β <1 (40)
The order M _I (k) is limited by the relational expression. Therefore, the approximate value of the spatial Nyquist frequency is as follows.

<Operation>
W ⁽⁰⁾ _{n, u} (k) obtained as described above is stored in the storage unit 111 of the control unit 11 (FIG. 2). The input signal S (k) is also stored in the storage unit 111. Weight obtaining unit 112 from the storage unit 111 reads _{^{w (0) n, u (}} k), w (0) n, and sends u (k) to the filtering unit 113-u (although, u = 1, ..., L). The filtering unit 113-u reads the input signal S (k) from the storage unit 111, and sets the filter weight for the radiation mode m (ν) at the wave number k of the higher-order sound source 12-u to w ⁽⁰⁾ _{n, u} (k). _Is applied to the input signal S (k) to obtain the output signal S _νu (k). The processing of the filtering unit 113-u may be performed in the time domain or may be performed in the time frequency domain. Each higher-order sound source 12-u is formed by, for example, D _u speakers sp _u (χ) (provided that χ∈ [0, D _u −1]) arranged annularly at equal intervals on the outer periphery of a cylindrical baffle. It can be constituted by an annular array (for example, Reference 1). In this case, the weight of the acoustic signal of each speaker sp _u (χ) that radiates from the higher-order sound source 12-u in the radiation mode m (ν) is W _{u, χ} = (1 / iρcD _u ) e ^{−iνφ (χ)}
It becomes. However, χ∈ [0, D _u −1], and φ (χ) is an angle φ (χ) = 2χπ / D _u on the two-dimensional plane with respect to the center of the annular array forming the higher-order sound source 12- _u. It is. Ρ represents the density of air and c represents the speed of sound. In this example, the output signal S _νu (k) is as follows.
S _vu (k) = w ⁽⁰⁾ _{n, u} (k) W _{u, χ} S (k)

The output signal S _νu (k) or a combination (linear sum) thereof is sent to the drive signal generation unit 114-1, and the drive signal generation unit 114-1 outputs the drive signal S corresponding to the output signal S _νu (k) or a combination thereof. ' _νu (k) or a combination thereof is generated and output to the higher-order sound source 12-u. The higher order sound source 12-u radiates an acoustic signal having a reproduction pattern corresponding to the drive signal S ′ _νu (k) or a combination thereof. Thereby, a desired sound field is generated in the desired spatial region 14-1,..., 14-S, and spatial multi-zone sound field reproduction is realized. In this embodiment, each of the radiation modes m (ν) (where ν = 1,..., 2N _V +1) of the higher-order sound source 12-u (where u = 1,..., L) is controlled by G _νu (k). To do. This can improve the flexibility of the control of the mirror image due to reverberation, the number of high-order tone 12-u of order N _V required to reproduce an accurate sound field into a plurality of regions in the reverberation room (order N _V) L can be reduced to a maximum of N _V + 1 / compared with Non-Patent Document 1.

[Second Embodiment]
The second embodiment is a modification of the first embodiment. The difference of the second embodiment from the first embodiment is that a desired external sound field is controlled without controlling the internal sound field. Below, it demonstrates centering around difference with 1st Embodiment.

<Configuration>
As illustrated in FIG. 4A, the sound field reproduction device 2 of this embodiment includes a control unit 21 and L high-order sound sources 12-u arranged on the circumference (where u = 1,..., L). And have. As illustrated in FIG. 2, the control unit 21 includes a storage unit 111, a weight acquisition unit 212, a filtering unit 113-u, and a drive signal generation unit 114-u. The control unit 21 is configured by, for example, the above-described computer executing a predetermined program.

≪Geometric arrangement≫
The difference from the first embodiment is that one two-dimensional local desired spatial region (circular region) 24-1 and a corresponding desired sound field are assumed (FIG. 4A). ). However, the spatial region 24-1 exists outside a circular region having a radius R _P > r centered on the global origin O.

《Control of external sound field of circular array》
In order to control a desired external sound field without controlling the internal sound field, a desired sum having an arbitrary expansion coefficient is obtained by a linear sum of sound fields generated by the higher-order sound sources 12-1,. An external sound field needs to be generated. Each higher-order sound source 12-u generates polar responses up to the Nth order, and the expansion order expressing the desired sound field is M _E (k). However, M _E (k) is a positive integer. In this case, it is necessary to match the right side of Expression (13) with the right side of Expression (35) (when r> _RL ). From this, the following relationship holds.

The equation (42) is written in matrix-vector format as follows.
J (k) w ⁽¹⁾ (k) = γ ^d (k) (43)
Where G (k) is a matrix of (2M _I (k) +1) × L (2N + 1), and w ⁽¹⁾ (k) is L (2N + 1) weights w ⁽¹⁾ _{n, u} (k) (Where n = −N,..., N, u = 1,..., L),

And γ _m ^d (k) = β _m ^d (k).

A vector w ⁽¹⁾ (k) composed of w ⁽¹⁾ _{n, u} (k) (approximate solution or solution) that minimizes the square error of each element on the left side and the right side of Equation (42) is as follows. .
w ⁽¹⁾ (k) = J (k) ^H [J (k) J (k) ^H + λ (k) I] ⁻¹ γ ^d (k) (44)
The order M _E (k) required to reproduce the sound field outside the circular array is:

The order N increases with frequency,
2M _E (k) + 1 = βL (2N + 1), β <1 (46)
The order M _E (k) is limited by the relational expression. Therefore, the approximate value of the spatial Nyquist frequency is as follows.

<Operation>
W ⁽¹⁾ _{n, u} (k) obtained as described above is stored in the storage unit 111 of the control unit 11 (FIG. 2). The input signal S (k) is also stored in the storage unit 111. Weight obtaining unit 212 from the storage unit 111 reads a _{^{w (1) n, u (}} k), w (1) n, and sends u (k) to the filtering unit 113-u (although, u = 1, ..., L). The filtering unit 113-u reads the input signal S (k) from the storage unit 111, and sets the filter weight for the radiation mode m (ν) at the wave number k of the higher-order sound source 12-u to w ⁽¹⁾ _{n, u} (k). _Is applied to the input signal S (k) to obtain the output signal S _νu (k). The subsequent processing is the same as in the first embodiment.

[Third Embodiment]
The third embodiment is a modification of the first embodiment. The difference of the third embodiment from the first embodiment is that both the internal sound field and the external sound field are controlled. Below, it demonstrates centering around difference with 1st Embodiment.

<Configuration>
As illustrated in FIG. 4B, the sound field reproduction device 3 of this embodiment includes a control unit 31 and L high-order sound sources 12-u arranged on the circumference (where u = 1,..., L). And have. As illustrated in FIG. 2, the control unit 21 includes a storage unit 111, a weight acquisition unit 312, a filtering unit 113-u, and a drive signal generation unit 114-u. The control unit 11 is configured by, for example, the above-described computer executing a predetermined program.

≪Geometric arrangement≫
The difference from the first embodiment is that there are S two-dimensional local desired local regions (circular regions) 34-1 to 34-S that do not overlap with each other and desired corresponding to them. This is a point where a sound field is assumed (FIG. 4A). However, the space regions 34-1,..., 34- (S-1) exist in a circular region having a radius R _P <r, and the space region 34-S exists outside a circular region having a radius R _P > r.

<< Simultaneous control of internal / external sound field of circular array >>
In this embodiment, the internal sound field and the external sound field are controlled separately. In this case, in order to generate a desired internal sound field having an arbitrary expansion coefficient and a desired external sound field having an arbitrary expansion coefficient, it is necessary to take a weighted sum of sound fields generated by higher-order sound sources. A combination of the above-described internal sound field control equation (formula (37)) and external sound field control equation (formula (43)) results in the following.

Where w ⁽²⁾ (k) is L (2N + 1) weights w ⁽²⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L ).

A vector w ⁽¹⁾ (k) composed of w ⁽¹⁾ _{n, u} (k) (approximate solution or solution) that minimizes the square error of each element on the left side and right side of Expression (48) is as follows. .
w ⁽²⁾ (k) = [Psi] ^H (k) [[Psi] (k) [Psi] ^H (k) + [lambda] (k) I] < ^-1 > [zeta] ^d (k) (49)
The order N increases with frequency,
2 (M _I (k) + M _E (k)) + 1 = βL (2N + 1), β <1 (50)
From the relational expression, the approximate value of the spatial Nyquist frequency is as follows.

<Operation>
W ⁽²⁾ _{n, u} (k) obtained as described above is stored in the storage unit 111 of the control unit 11 (FIG. 2). The input signal S (k) is also stored in the storage unit 111. Weight obtaining unit 312 from the storage unit 111 reads ^w _{(2) n,} u ^(k), and sends ^w _{(2) n,} u (k) of the filtering unit 113-u (although, u = 1, ..., L). The filtering unit 113-u reads the input signal S (k) from the storage unit 111, and sets the filter weight for the radiation mode m (ν) at the wave number k of the higher-order sound source 12-u to w ⁽²⁾ _{n, u} (k). _Is applied to the input signal S (k) to obtain the output signal S _νu (k). The subsequent processing is the same as in the first embodiment.

[Comparison of the fundamental limitations of multi-zone sound field reproduction with omnidirectional and higher order sound sources]
In spatial multi-zone sound field playback,

And M _I (k) = M ₀ (k) ≧ (M ₁ (k) + M ₂ (k) +... + M _S (k)) (53)
Thus, the center coordinates and the radius of each space area are obtained.

When a desired internal sound field is generated using L omnidirectional speakers, the approximate value of the spatial Nyquist frequency is

On the other hand, when a desired internal sound field is controlled without controlling the external sound field using L high-order sound sources 12-u (where u = 1,..., L), the approximate value of the spatial Nyquist frequency is ,

It becomes. Further, when both the internal sound field and the external sound field are controlled using L high-order sound sources 12-u (where u = 1,..., L), the approximate value of the spatial Nyquist frequency is

It becomes.

From equation (55), when the radius _{RL of} a circle containing a plurality of spatial regions is the same, a circular array of higher-order sound sources 12-u of order N is used, and the external sound field is not suppressed. Thus, it can be seen that a sound field having a bandwidth approximately 2N times the sound field reproduction by the circular array of omnidirectional speakers can be reproduced with high accuracy.

  Sound field reproduction using a circular array of omnidirectional speakers cannot suppress the external sound field. On the other hand, in this embodiment, the external sound field can be suppressed. According to the equation (56), when the external sound field is suppressed using a circular array of the high-order sound source 12-u of order N, the sound field reproduction by the circular array of the omnidirectional speaker is about N times. It can be seen that the bandwidth sound field can be reproduced with high accuracy.

[Modifications, etc.]
The present invention is not limited to the embodiment described above. For example, the processing of the above-described control unit is not only executed in time series according to the description, but may also be executed in parallel or individually as required by the processing capability of the device that executes the processing. Needless to say, other modifications are possible without departing from the spirit of the present invention.

  When the configuration of the control unit is realized by a computer, the processing contents of the functions that these should have are described by a program. By executing this program on a computer, these processing functions are realized on the computer. The program describing the processing contents can be recorded on a computer-readable recording medium. An example of a computer-readable recording medium is a non-transitory recording medium. Examples of such a recording medium are a magnetic recording device, an optical disk, a magneto-optical recording medium, a semiconductor memory, and the like.

  This program is distributed, for example, by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, this computer reads a program stored in its own recording device and executes a process according to the read program. As another execution form of the program, the computer may read the program directly from the portable recording medium and execute processing according to the program, and each time the program is transferred from the server computer to the computer. The processing according to the received program may be executed sequentially. The above-described processing may be executed by a so-called ASP (Application Service Provider) type service that realizes a processing function only by an execution instruction and result acquisition without transferring a program from the server computer to the computer. Good.

  In the above embodiment, the processing functions of the apparatus are realized by executing a predetermined program on a computer. However, at least a part of these processing functions may be realized by hardware.

1-3 Sound field playback device

Claims (8)

A plurality of higher-order sound sources for reproducing an acoustic signal in a reproduction pattern, comprising any one of a plurality of independent radiation modes having different directivity patterns or a combination of at least a part of the plurality of radiation modes;
The plurality of higher order sound sources are arranged on a circumference,
The sound field reproducing apparatus, wherein the reproduction pattern is obtained by controlling the weights of the radiation modes in order to generate a desired sound field in a plurality of spatial regions. The sound field reproducing apparatus according to claim 1,
The plurality of high-order sound sources are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and the plurality of radiation modes are 2N + 1 radiation modes m ( -N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is the aforementioned Is a value representing the magnitude of the higher-order sound source hs (u), _RL is a value representing the radius of the circumference, H _ι (·) is a first-class Hankel function of degree ι, and H ′ _ι (·) Is the derivative of the Hankel function H _ι (·), i is the imaginary unit, e is the Napier number, and θ _u is the deflection angle of the higher order sound source hs (u) with respect to the origin , β ^{d m} _(k) is the desired sound field polar region including the plurality of spatial regions are generated (r, theta) in the wave number k of the frequency domain signal ^{S d (r, θ; k} ) a development coefficients for _{m, M} I (k) is a positive integer,
The reproduction pattern is for m∈ [−M _I (k), M _I (k)].
Sound field reproduction, which is a pattern in which a solution or approximate solution of w ⁽⁰⁾ _{n, u} (k) that satisfies the above is used as a filter weight for the radiation mode m (n) at the wave number k of the higher-order sound source hs (u) apparatus. A plurality of higher-order sound sources for reproducing an acoustic signal in a reproduction pattern, comprising any one of a plurality of independent radiation modes having different directivity patterns or a combination of at least a part of the plurality of radiation modes;
The plurality of higher order sound sources are arranged on a circumference,
The reproduction pattern is one in which each weight of the radiation mode is controlled in order to generate a desired sound field in a spatial domain,
The plurality of high-order sound sources are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and the plurality of radiation modes are 2N + 1 radiation modes m ( -N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is the aforementioned Is a value representing the magnitude of the higher-order sound source hs (u), _RL is a value representing the radius of the circumference, J _ι (·) is a Bessel function of degree ι, and H ′ _ι (·) is Is the derivative of the first kind of Hankel function of order ι, i is the imaginary unit, e is the Napier number, θ _u is the deflection angle of the higher order sound source hs (u), and γ ^d _m ( k) is an expansion coefficient for m of the frequency domain signal S ^d (r, θ; k) of wave number k at the polar coordinates (r, θ) in the region where the desired sound field is generated, and M _E (k ) Is positive Is a number,
The reproduction pattern is for m∈ [−M _E (k), M _E (k)].

Sound field reproduction, which is a pattern in which the solution or approximate solution of w ⁽¹⁾ _{n, u} (k) that satisfies the above is used as the filter weight for the radiation mode m (n) at the wave number k of the higher-order sound source hs (u) apparatus. The sound field reproducing apparatus according to claim 1,
The plurality of high-order sound sources are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and the plurality of radiation modes are 2N + 1 radiation modes m ( -N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is the aforementioned Is a value representing the magnitude of the higher-order sound source hs (u), _RL is a value representing the radius of the circumference, H _ι (·) is a first-class Hankel function of degree ι, and H ′ _ι (·) Is a derivative of the Hankel function H _ι (·), i is an imaginary unit, e is a Napier number, θ _u is a declination of the higher-order sound source hs (u), β ^{d m} _(k) is the desired sound field polar region including the plurality of spatial regions are generated (r, theta) frequency domain signal wave number k in ^{S d (r, θ; k} ) of m about An expansion _{coefficient, M} I (k) is a positive _{integer, m∈ [-M I (k)} , M I (k)] for
Is expressed as G (k) w ⁽⁰⁾ (k) = β ^d (k), G (k) is a matrix of (2M _I (k) +1) × L (2N + 1), and w ⁽⁰⁾ ( k) is a vertical vector composed of L (2N + 1) w ⁽⁰⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L),

(・) ^T is the transpose of (・),
γ ^d _m (k) is the frequency domain signal S ^d (r, θ; k) of wave number k at the polar coordinates (r, θ) of the region including the plurality of spatial regions where the desired sound field is generated. expansion coefficient for m, M _E (k) is a positive integer, and m∈ [−M _E (k), M _E (k)]

Is expressed as J (k) w ⁽¹⁾ (k) = γ ^d (k), J (k) is a matrix of (2M _E (k) +1) × L (2N + 1), and w ⁽¹⁾ ( k) is a vertical vector consisting of L (2N + 1) w ⁽¹⁾ _{n, u} (where n = −N,..., N, u = 1,..., L),

And
The reproduction pattern is

W ⁽²⁾ (k) solution or approximate solution element w ⁽²⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L) satisfying The sound field reproducing device, which is a pattern with filter weights for the radiation mode m (n) at the wave number k of the next sound source hs (u). A plurality of higher-order sound sources arranged on the circumference is a reproduction pattern composed of any one of a plurality of independent radiation modes having different directivity patterns or a combination of at least a part of the plurality of radiation modes. Play an acoustic signal,
The sound field reproduction method, wherein the reproduction pattern is obtained by controlling the weights of the radiation modes in order to generate a desired sound field in a plurality of spatial regions. The sound field reproduction method according to claim 5,
The plurality of high-order sound sources are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and the plurality of radiation modes are 2N + 1 radiation modes m ( -N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is the aforementioned Is a value representing the magnitude of the higher-order sound source hs (u), _RL is a value representing the radius of the circumference, H _ι (·) is a first-class Hankel function of degree ι, and H ′ _ι (·) Is the derivative of the Hankel function H _ι (·), i is the imaginary unit, e is the Napier number, and θ _u is the deflection angle of the higher order sound source hs (u) with respect to the origin , β ^{d m} _(k) is the desired sound field polar region including the plurality of spatial regions are generated (r, theta) in the wave number k of the frequency domain signal ^{S d (r, θ; k} ) a development coefficients for _{m, M} I (k) is a positive integer,
The reproduction pattern is for m∈ [−M _I (k), M _I (k)].
Sound field reproduction, which is a pattern in which a solution or approximate solution of w ⁽⁰⁾ _{n, u} (k) that satisfies the above is used as a filter weight for the radiation mode m (n) at the wave number k of the higher-order sound source hs (u) Method. A plurality of higher-order sound sources arranged on the circumference is a reproduction pattern composed of any one of a plurality of independent radiation modes having different directivity patterns or a combination of at least a part of the plurality of radiation modes. Play an acoustic signal,
The reproduction pattern is one in which each weight of the radiation mode is controlled in order to generate a desired sound field in a spatial domain,
The plurality of high-order sound sources are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and the plurality of radiation modes are 2N + 1 radiation modes m ( -N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is the aforementioned Is a value representing the magnitude of the higher-order sound source hs (u), _RL is a value representing the radius of the circumference, J _ι (·) is a Bessel function of degree ι, and H ′ _ι (·) is Is the derivative of the first kind of Hankel function of order ι, i is the imaginary unit, e is the Napier number, θ _u is the deflection angle of the higher order sound source hs (u), and γ ^d _m ( k) is an expansion coefficient for m of the frequency domain signal S ^d (r, θ; k) of wave number k at the polar coordinates (r, θ) in the region where the desired sound field is generated, and M _E (k ) Is positive Is a number,
The reproduction pattern is for m∈ [−M _E (k), M _E (k)].

Sound field reproduction, which is a pattern in which the solution or approximate solution of w ⁽¹⁾ _{n, u} (k) that satisfies the above is used as the filter weight for the radiation mode m (n) at the wave number k of the higher-order sound source hs (u) Method. The sound field reproduction method according to claim 5,
The plurality of high-order sound sources are L high-order sound sources hs (1),..., Hs (L), L is a positive integer, and the plurality of radiation modes are 2N + 1 radiation modes m ( -N), ..., m (N), N is a positive integer, u = 1, ..., L, n = -N, ..., N, k is the wave number, and R is the aforementioned Is a value representing the magnitude of the higher-order sound source hs (u), _RL is a value representing the radius of the circumference, H _ι (·) is a first-class Hankel function of degree ι, and H ′ _ι (·) Is a derivative of the Hankel function H _ι (·), i is an imaginary unit, e is a Napier number, θ _u is a declination of the higher-order sound source hs (u), β ^{d m} _(k) is the desired sound field polar region including the plurality of spatial regions are generated (r, theta) frequency domain signal wave number k in ^{S d (r, θ; k} ) of m about An expansion _{coefficient, M} I (k) is a positive _{integer, m∈ [-M I (k)} , M I (k)] for
Is expressed as G (k) w ⁽⁰⁾ (k) = β ^d (k), G (k) is a matrix of (2M _I (k) +1) × L (2N + 1), and w ⁽⁰⁾ ( k) is a vertical vector composed of L (2N + 1) w ⁽⁰⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L),

(・) ^T is the transpose of (・),
γ ^d _m (k) is the frequency domain signal S ^d (r, θ; k) of wave number k at the polar coordinates (r, θ) of the region including the plurality of spatial regions where the desired sound field is generated. expansion coefficient for m, M _E (k) is a positive integer, and m∈ [−M _E (k), M _E (k)]

Is expressed as J (k) w ⁽¹⁾ (k) = γ ^d (k), J (k) is a matrix of (2M _E (k) +1) × L (2N + 1), and w ⁽¹⁾ ( k) is a vertical vector consisting of L (2N + 1) w ⁽¹⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L),

And
The reproduction pattern is

W ⁽²⁾ (k) solution or approximate solution element w ⁽²⁾ _{n, u} (k) (where n = −N,..., N, u = 1,..., L) satisfying A sound field reproduction method, which is a pattern with filter weights for the radiation mode m (n) at the wave number k of the next sound source hs (u).