JP7799501B2 - Sound field reproduction device and program - Google Patents

Description

The present invention relates to technology related to object acoustics in games, AR (Augmented Reality), VR (Virtual Reality), etc., and in particular to a sound field reproduction device and program that uses the spectral division method to model, describe, and reproduce sound sources that serve as objects.

Conventionally, sound field reproduction and synthesis methods are known that reproduce and synthesize a desired sound field in a sound field (a field in which sound is reproduced) using multiple speakers.

Figure 5 is a diagram explaining the sound field reproduction and synthesis method. The sound field formed by the emission of sound waves from a certain sound source (hereinafter referred to as "primary sound source 101") is called the "desired sound field." Furthermore, another location where the desired sound field is reproduced and synthesized using a speaker array (hereinafter referred to as "secondary sound source 102") consisting of speakers arranged in a line is called the "reproduced sound field."

The left side of Figure 5 shows a desired sound field formed by sound waves emitted from a bell, which is the primary sound source 101. The secondary sound source 102 shown on the left side of Figure 5 shows a case where a speaker placed in the reproduction sound field is reflected in the desired sound field, rather than a speaker placed in the desired sound field. Additionally, the right side of Figure 5 shows a reproduction sound field in which the desired sound field is reproduced and synthesized by driving the secondary sound source 102 when the desired sound field is formed by reproduction of the primary sound source 101.

Since it is usually difficult to perfectly match the entire sound field between the desired sound field and the reproduced sound field, a linear reference position such as that shown in Figure 5 is determined in advance. At this reference position, the drive signal for the secondary sound source is determined so that the sound (sound pressure) radiated from the primary sound source 101 matches the sound radiated from the secondary sound source 102. If the secondary sound source 102 is a linear speaker array, the reference position is also linear, parallel to the speaker array and at a certain distance away.

This allows the desired sound field to be reproduced at the reference position in the playback sound field. As the distance from the reference position increases, the error gradually increases and reproducibility decreases, but it is known that within a certain range, even if reproducibility decreases, this does not pose a major problem to the ear.

In order to match the sound of the desired sound field and the reproduced sound field at the reference position, it is necessary to compare the sound pressure at the reference position due to sound propagation from the primary sound source 101 with the sound pressure at the reference position due to sound propagation from the secondary sound source 102, and calculate a drive signal for the secondary sound source 102 that will match them.

In general, sound propagation is represented by an impulse response in the time domain, and by a transfer function in the time-frequency domain, where the time-domain impulse response is subjected to a time Fourier transform.

In this case, if the sound pressure (transfer function) in the sound field in the desired sound field is P, the transfer function from the secondary sound source 102 to each point in the sound field in the reproduction sound field is G, and the drive function (transfer function) of the secondary sound source 102 in the reproduction sound field is D, then the following equation can be expressed.
Here, ** represents a convolution operation.

Furthermore, if the results in the spatiotemporal frequency domain (wavenumber domain) obtained by spatial Fourier transforming P, G, and D in space are P, G, and D (hereinafter referred to as "angular spectra"), respectively, the convolution operation becomes a product operation, and the relationship is expressed by the following equation.

In other words, the angular spectrum D̂ of the driving function of the secondary sound source 102 is calculated so that the signal obtained by multiplying the angular spectrum D̂ of the driving function of the secondary sound source 102 by the angular spectrum Ĝ of the transfer function from the secondary sound source 102 to each point in the sound field matches the angular spectrum P̂ of the sound pressure in the desired sound field.

Therefore, the angular spectrum D of the driving function of the secondary sound source 102 is expressed by a division formula as follows:

This method of calculating the driving function by dividing the angular spectrum is called the "spectral division method." The signal (driving signal) for driving the speaker array, which is the secondary sound source 102, is obtained as a time signal by performing an inverse Fourier transform on the angular spectrum D of the driving function of the secondary sound source 102 in equation (3) above.

Fig. 6 is a diagram for explaining the arrangement of sound sources in a Cartesian coordinate system. When a stationary sound source is at the origin in the free space of the Cartesian coordinate system shown in Fig. 6, the impulse response between the coordinates (x, y, z) is expressed by the following equation:
δ(·) represents the unit impulse function.

The transfer function obtained by subjecting the impulse response of the above formula (4) to a time Fourier transform on the time axis is expressed by the following formula.
Here, ω represents the angular frequency and c represents the speed of sound.

The angular spectrum obtained by spatial Fourier transforming the transfer function of the above equation (5) in the x-axis direction is expressed by the following equation.
Here, H ₀ ⁽²⁾ (·) represents a special function (zeroth-order Hankel function of the second kind), and k _x represents the wave number in the x-axis direction. Note that evanescent waves when |k _x |≧k are not considered here.

On the other hand, when the sound source moves, the sound pressure at the position of coordinates (x, y, z) is expressed by the following equation, where the input signal (drive signal of the primary sound source 101, sound source signal) at time τ is s(τ) and the position of the primary sound source 101 is the sound source position r _s (τ) = ( _{x s} (τ), y _s (τ), z s (τ)).

The angular spectrum obtained by subjecting the sound pressure of the above equation (7) to a time Fourier transform on the time axis and then a spatial Fourier transform in the x-axis direction is expressed by the following equation (see Non-Patent Documents 1 and 2).

Firtha Gergely and Fiala Peter, “Sound Field Synthesis of Uniformly Moving Virtual Monopoles”, JAES Volume 63 Issue 1/2 pp. 46-53, January 2015 Sasaki, Matsui, Nakayama, "Reproduction of sound fields formed by moving sound sources using SDM," Acoustical Society of Japan 2021 Spring Meeting, Sound Lectures (Spring), 2-1P-5, 2021

As shown in Figure 6, the angular spectrum G from the speaker array, which is the secondary sound source 102 arranged linearly on the x-axis (the angular spectrum of the transfer function from the secondary sound source 102 to each point in the playback sound field) is expressed by the above equation (6). Furthermore, the angular spectrum P of the sound pressure formed by the propagation of sound from the moving primary sound source 101 (the angular spectrum of the sound pressure in the desired sound field) is expressed by the above equation (8).

When the equations (6) and (8) are substituted into the equation (3), the angular spectrum of the driving function (the angular spectrum of the driving function of the secondary sound source 102) D is expressed by the following equation.
However, as mentioned above, a reference position is usually set and a solution is found at that reference position.

As shown in FIG. 6, when the linear reference position is (x, _yr , _zr ), the above equation (9) can be expressed as follows:

When the primary sound source 101 moves, in order to synthesize its trajectory (movement trajectory) in the playback sound field, it is clear from equation (10) that the input signal s(τ) and the angular spectrum representing the trajectory must be integrated along the time axis. This integration process increases the amount of calculation required to derive the angular spectrum D of the driving function shown in equation (10).

The present invention was made to solve the above-mentioned problems, and its purpose is to provide a sound field reproduction device and program that can reduce the amount of calculation required to derive speaker drive signals when reproducing a desired sound field in a playback sound field using the spectral division method.

In order to solve the above-mentioned problem, a sound field reproduction device of claim 1 is a sound field reproduction device that generates a drive signal for reproducing a sound field formed by a moving primary sound source using a speaker array of a secondary sound source, wherein, when s(τ) is a sound source signal of the primary sound source at time τ, H ₀ ⁽²⁾ (.) is a zeroth-order Hankel function of the second kind, ω is an angular frequency, c is the speed of sound, k _x is a wave number in the x-axis direction, _yr , _zr are the y value and z value of a linear reference position, and (x _s (τ), y _s (τ), z _s (τ)) is the position of the primary sound source at time τ, the angular spectrum D(k _x , ω) of the drive function of the secondary sound source is expressed by the following equation of the angular spectrum by the spectral division method:
where the primary sound source and the secondary sound source are arranged on an xy plane and description of the z-axis is omitted, a position ( _xn , _yn ) of the primary sound source at time Tn of the _nth ( _n is an integer of _{1 or more} ) trajectory sampling of the primary sound source is input, and a movement speed calculation unit calculates a movement speed ( _vx , _vy ) of the primary sound source at time _Tn based on the positions ( _{xn -1 , yn-1 )} , ( _xn , _yn ) of the primary sound source at times _{Tn-1 and Tn} ; and a movement speed calculation unit that calculates the Hankel function _H0 ⁽²⁾ (·) is approximated by an exponential function, and the trajectory of the primary sound source is approximated by continuous uniform linear motion to obtain the following equation:
(F(ω) is expressed by the formula:
and a drive signal calculation unit that calculates the drive signal in the time domain by performing an inverse Fourier transform on the angular spectrum D( _{kx ,} ω) calculated by the drive function calculation unit.

The sound field reproduction device of claim 2 is the sound field reproduction device of claim 1, further comprising: a buffer in which the drive signals are stored; and a drive signal writing unit that writes the drive signals calculated by the drive signal calculation unit into the buffer, wherein when the drive signal writing unit writes the calculated drive signals (D1 and D2) for the period from time T _n-1 to time T _n +a1, which exceeds time T n, calculated by the drive signal calculation unit in response to the signal s(τ) for the period from time T _{n -1 to} time T _n , into the buffer, the drive signal writing unit adds the calculated drive signal (D1) for the period from time T _n-1 to time T _n-1 +a2 to the drive signal (D0) for the period from time T _n-1 to time T _n-1 +a2, which exceeds time T _n-1 , which has already been written in the buffer, and writes the result, and also writes the calculated drive signal (D2) for the period from time T _{n-1 +a2 to time T n} +a1 as is.

Furthermore, the program of claim 3 provides a program for generating a drive signal for reproducing a sound field formed by a moving primary sound source using a speaker array of a secondary sound source, the program comprising: a computer constituting a sound field reproduction device that generates a drive signal for reproducing a sound field formed by a moving primary sound source using a speaker array of a secondary sound source; the computer program comprising: a sound source signal of the primary sound source at time τ; H ₀ ⁽²⁾ (·) being a zeroth-order Hankel function of the second kind; ω being an angular frequency; c being the speed of sound; k _x being the wave number in the x-axis direction; _yr , _zr being the y value and z value of a linear reference position; and (x _s (τ), y _s (τ), z _s (τ)) being the position of the primary sound source at time τ; the computer program comprising: a sound source signal of the primary sound source at time τ; H 0 ( ₂₎ (·) being a zeroth-order Hankel function of the second kind;
a movement speed calculation unit that inputs a position (x n , yn ) of the primary sound source at time T _n of the n-th (n is an integer of 1 or more) trajectory sampling of the primary sound source, and calculates a movement speed (v _x , v _y ) of the primary sound source at time _{T n based} on the positions (x _n-1 , yn _-1 ), ( _{x n} , _yn ) of the primary sound source at times T n-1 and _{T n} ; a signal s(τ) from time T _{n-1 to} time T _n , a position (x _s0 , y _s0 ) that is the position (x _n-1 , yn _-1 ) of the primary sound source at time T n-1, and a y value _yr that is preset, and calculates the Hankel function H ₀ ⁽²⁾ (·) is approximated by an exponential function, and the trajectory of the primary sound source is approximated by continuous uniform linear motion to obtain the following equation:
(F(ω) is expressed by the formula:
is a spectrum obtained by Fourier transforming the angular spectrum D( _kx , ω) of the driving function of the secondary sound source using a Fourier transform of the angular spectrum D(kx, ω) of the driving function of the secondary sound source, and a driving signal calculation unit that calculates the driving signal in the time domain by performing an inverse Fourier transform on the angular spectrum D( _kx , ω) calculated by the driving function calculation unit.

As described above, according to the present invention, when reproducing a desired sound field in a playback sound field using the spectral division method, the amount of calculation required to derive speaker drive signals can be reduced.

1 is a block diagram illustrating an example of the configuration of a sound field reproduction device according to an embodiment of the present invention. 10 is a flowchart illustrating an example of processing by the sound field reproduction device. FIG. 10 is a diagram illustrating an approximation of the trajectory of a primary sound source. 10A and 10B are diagrams illustrating an example of processing by a drive signal writing unit. FIG. 1 is a diagram illustrating a sound field reproduction and synthesis method. FIG. 2 is a diagram illustrating the arrangement of sound sources in a Cartesian coordinate system.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the present invention, when the primary sound source 101 moves on an arbitrary trajectory, the Hankel function H ₀ ⁽²⁾ (·) of the above-mentioned equation (10) is approximated by an exponential function, and the trajectory of the primary sound source 101 is approximated by continuous uniform linear motion, and the angular spectrum D of the driving function of the secondary sound source 102 is found by using the functions defined by these approximations.

As a result, the function representing acoustic propagation from the primary sound source 101 can be expressed by a simpler function, and the trajectory of the primary sound source 101 is expressed as a trajectory of uniform linear motion, so the function reflecting these can be expressed by a simple formula.

In other words, as will be described later, the integral operation in equation (10) can be expressed as an operation that shifts the amplitude and phase of a specified function in the spatiotemporal frequency domain, thereby reducing the amount of calculation required for the spectral division method.

Summary of the Invention
First, we will explain the approximation of the angular spectrum D of the driving function of the secondary sound source 102 shown in equation (10). For simplicity of explanation, it is assumed that both the primary sound source 101 and the secondary sound source 102 are placed on the xy plane where z = _zn , and that the primary sound source 101 moves, and hence, description of the z axis will be omitted below.

In the above equation (10), the Hankel function H ₀ ⁽²⁾ (·) is approximated. The Hankel function H ₀ ⁽²⁾ (·) can be asymptotically (when the argument value is large) approximated by an exponential function as follows:
Here, a represents an argument (a>>0).

By applying the approximation of the formula (11) to the formula (10), the formula (10) can be expressed as follows:

Here, k _y is expressed by the following formula.

The trajectory of an arbitrary sound source position r _s (τ) is approximated by uniform linear motion, and the position (sound source position r _s (τ) following the trajectory of uniform linear motion) is defined as (x _s0 + v _x τ, y _s0 + v _y τ), where (x _s0 , y _s0 ) is the sound source position at time τ = 0, and v _x and v _y are the movement velocities in the x-axis and y-axis directions, respectively.

By approximating the trajectory of the sound source position r _s (τ) by uniform linear motion, the above equation (12) can be expressed as follows:

Here, the spectrum F(ω) is obtained by Fourier transforming the following f(τ):

In the above formula (15), f(τ) represents an equation in which the amplitude is corrected for the input signal s(τ). In other words, the angular spectrum D of the driving function of the secondary sound source 102 shown in the above formula (14) is expressed by the following frequency with respect to the spectrum F(ω):
and the following phase
It can be said that this represents a shifted expression of

In this way, by using equation (14) when calculating the angular spectrum D of the drive function of the secondary sound source 102, it is not necessary to perform the integration operation of equation (10), thereby reducing the amount of calculation required for its derivation. Therefore, when reproducing a desired sound field in a playback sound field using the spectral division method, it is possible to reduce the amount of calculation required to derive the speaker drive signal.

[Sound field reproduction device]
Next, a sound field reproduction device according to an embodiment of the present invention will be described. Fig. 1 is a block diagram showing an example of the configuration of a sound field reproduction device according to an embodiment of the present invention. Fig. 2 is a flowchart showing an example of processing by the sound field reproduction device, illustrating the flow of processing at time _Tn . This time _Tn is assumed to coincide with the timing of discretized trajectory sampling of the primary sound source 101.

This sound field reproduction device 1 comprises a movement speed calculation unit 10, a drive function calculation unit 11, a drive signal calculation unit 12, a drive signal writing unit 13, and a buffer (playback buffer) 14. The buffer 14 is a playback buffer that stores the drive signals of the secondary sound source 102 and uses these drive signals to play back the sound of the desired sound field in the playback sound field.

The movement velocity calculation unit 10 receives the position ( _xn , _yn ) of the primary sound source 101 at time (current time) _Tn (step S201). Then, the movement velocity calculation unit 10 calculates the movement velocity ( _vx , vy ₎ of the primary sound source 101 at time _Tn based on the positions ( _xn-1 , yn _-1 ), ( _xn , _yn ) of the primary sound source 101 at times Tn-1 and _Tn (step S202). The movement velocity calculation unit 10 outputs the movement velocity ( _vx , _vy ) of the primary sound _source 101 at time _Tn to the drive function calculation unit 11.

The moving speed v _x is the moving speed of the primary sound source 101 in the x-axis direction, and the moving speed v _y is the moving speed of the primary sound source 101 in the y-axis direction.

Specifically, the moving speed calculation unit 10 assumes that the primary sound source 101 is moving at a constant speed in a straight line between the trajectory sampling time T _n-1 immediately before the time T _n and the current time T _n , approximates the trajectory, and calculates the moving speed (v _x , v _y ) using the following equation:

3 is a diagram illustrating the approximation of the trajectory of the primary sound source 101. An arbitrary trajectory of the primary sound source 101 is sampled at a fixed trajectory sampling period (times T ₁ , T ₂ , ...). Then, the trajectory of the primary sound source 101 is approximated so that it moves at a constant speed in a straight line between the trajectory sampled positions during the time period between times T ₁ , T ₂ , ....

That is, the moving speed calculation unit 10 approximates an arbitrary trajectory of the primary sound source 101 to a trajectory of uniform linear motion at the trajectory sampling period, and calculates the moving speed (v _x , v _y ).

1 and 2, the driving function calculation unit 11 receives the moving velocity ( _vx , _vy ) of the primary sound source 101 at time _Tn from the moving velocity calculation unit 10, the position ( _xn , _yn ) of the primary sound source 101 at time _Tn , and also receives a preset sound speed c and a y value _yr of the reference position (x, _yr , _zr ). The driving function calculation unit 11 also receives an input signal s(τ), which is the sound source signal of the primary sound source 101 for the time period from time _Tn-1 to time _Tn (step S203).

The driving function calculation unit 11 sets the position (x _n-1 , y _n-1 ) of the primary sound source 101 at the trajectory sampling time T _n- 1 immediately before time T _n to the position (x _s0 , y _s0 ), and sets the timing of time T _n-1 as t=0.

The driving function calculation unit 11 calculates the angular spectrum D( _kx , _ω ) of the driving function of the secondary sound _source 102 using the wave number kx in the _x-axis direction and the angular frequency _ω as variables, using equations (14) and ₍₁₅ ) based on the moving speed ( _vx , vy) of the primary sound source 101 at time Tn, the input signal s(τ) in the time period from time _Tn-1 to time Tn, the position ( _xs0 , _ys0 ) which is the position (xn-1, _yn -1) of the primary sound source 101 at time _Tn -1, and the preset sound speed _c and the y value _yr of the reference position (x, _yr , zr) (step S204).

Specifically, the driving function calculation unit 11 obtains the spectrum F(ω) by Fourier transforming f(τ) in the above formula (15). Then, as shown in the above formula (14), the driving function calculation unit 11 obtains the angular spectrum D(k x , ω) of the driving function of the secondary sound source 102 by shifting the frequency shown in the above formula (16) and the phase shown in the above formula (17) with respect to the spectrum _F (ω).

The driving function calculation unit 11 outputs the angular spectrum D(k _x , ω) of the driving function of the secondary sound source 102 at time T _n to the driving signal calculation unit 12 .

The drive signal calculation unit 12 receives the angular spectrum D( _kx , ω) of the drive function of the secondary sound source 102 at time _Tn from the drive function calculation unit 11. The drive signal calculation unit 12 then performs an inverse Fourier transform on the angular spectrum D( _kx , ω) to generate a time domain drive signal D(x, t) for the secondary sound source 102 using the x value in xyz space and time t as variables (step S205).

Specifically, the drive signal calculation unit 12 obtains the drive function D( _x ,ω) in the time-frequency domain by performing an inverse Fourier transform on the angular spectrum D(kx,ω) of the drive function in the time-space frequency domain.The drive signal calculation unit 12 then obtains the drive signal D(x,t) in the time domain by performing an inverse Fourier transform on the drive function D(x,ω) in the time-frequency domain.This drive signal D(x,t) is calculated for each speaker (for each x (for each x coordinate value) specified by the position of the speaker) that constitutes the speaker array that is the secondary sound source 102.

The drive signal calculation unit 12 outputs the time domain drive signal D(x, t) of the secondary sound source 102 at time T _n to the drive signal writing unit 13 .

The drive signal writing unit 13 receives the time domain drive signal D(x, t) of the secondary sound source 102 at time _Tn from the drive signal calculation unit 12 and writes the drive signal D(x, t) into the buffer 14 (step S206).

4 is a diagram illustrating an example of processing by the drive signal writing unit 13. Here, the time domain drive signal D(x, t) of the secondary sound source 102 calculated by the drive signal calculation unit 12 and input to the drive signal writing unit 13 is a signal corresponding to the input signal s(τ) in the time period from time T _n-1 to time T _n .

4, the time length (time length of drive signals _D1 and _{D2) of the time domain drive signal D(x, t) of the secondary sound source 102 corresponding to the processing at time T n (} processing in units of the time period from time T _{n-1 to time T n) can be longer than the time length from time T n-1} to time T _n . This is because of the influence of delays and the like caused by the difference between the distance from the primary sound source 101 to the reference position (x, _yr , _zr ) and the distance from the secondary sound source 102 to the reference position (x, _yr , _zr ).

In this case, among the drive signals already written to the buffer 14, the drive signal D0 in the time region beyond time _Tn-1 (the time region from time Tn _-1 to time Tn _{-1 +} a2) and the drive signal D1 in the time region from time _Tn-1 to time Tn-1+ _a2 among the drive signals D(x, t) calculated by the drive signal calculation unit 12 in processing time _Tn (drive signals D1 and D2 from time _Tn-1 to time _Tn +a1 beyond time Tn) will overlap on the time axis. a1 and a2 are positive real numbers.

Therefore, when the drive signal writing unit 13 writes the drive signals D(x, t) (D1 and D2) calculated by the drive signal calculation unit 12 in processing for time T _n into the buffer 14, it adds the drive signal D1 from time T _n-1 to time T n _{- 1 +a2, which is the same time period as the drive signal D0, to the drive signal D0 that has already been written to the buffer 14 and that is beyond time T n-1 ,} and writes the addition result into the buffer 14. Furthermore, the drive signal writing unit 13 writes the drive signal D2 from time T _n-1 +a2 onwards (the drive signal D2 from time T n-1 +a2 to time T _n +a1) directly into the buffer 14.

As a result, drive signal D0+D1 is written into buffer 14 as the drive signal for the time domain from time T _n-1 to time T _{n- 1} +a2, and drive signal D2 is written into buffer 14 as the drive signal for the time domain from time T _{n-1 +a2 to time T n} +a1.

Note that the buffer 14 shown in Figure 4 represents a buffer corresponding to each speaker that makes up the speaker array, which is the secondary sound source 102, and similar processing is performed for each speaker.

In other words, the drive signal calculation unit 12 calculates the time domain drive signal D(x, t) of the secondary sound source 102 for each speaker that makes up the speaker array (for each x (each x coordinate value) specified by the speaker's position) which is the secondary sound source 102. Then, the drive signal writing unit 13 writes the time domain drive signal D(x, t) of the secondary sound source 102 into the buffer 14 for each speaker that makes up the speaker array (for each secondary sound source 102).

Returning to Figures 1 and 2, the sound field reproduction device 1 determines whether the input signal s(τ) has a continuation (step S207), and if it determines that there is a continuation (step S207: Y), increments n to set it to n+1 (step S208), and proceeds to step S201.

As a result, the position (x _n , y _n ) of the primary sound source 101 at the next trajectory sampling time (current time) T _n is input, and the processing of steps S201 to S206 for that time T _n is performed. In this case, the input signal s(τ) is a signal in the time period from time T _n-1 to time T _n , with that time T _n being used as the reference.

If the sound field reproduction device 1 determines in step S207 that the input signal s(τ) does not have a continuation (step S207: N), the sound field reproduction device 1 terminates processing.

As described above, according to the sound field reproduction device 1 of the embodiment of the present invention, the movement speed calculation unit 10 inputs the position (x _n , y _n ) of the primary sound source 101 at the trajectory sampling time T _n , and calculates the movement speed (v _x , v y ) of the primary sound source 101 at the time T _n based on the positions (x n- ₁ , y _n-1 ), ( _{x n} , _{y n )} of the primary sound source 101 at the times T n-1 and T _n .

The driving function calculation unit 11 calculates the angular spectrum D(kx, ω) of the driving function of the secondary sound _source 102 using the equations ( ₁₄₎ and ₍₁₅ ) based on the moving velocity ( _vx , _vy ) of the primary sound source 101 at time _Tn , the input signal s(τ) for the time period from time Tn _{- 1} to time Tn, the position ( _xs0 , _ys0 ) which is the position (xn- ₁ , yn-1) of the primary sound source 101 at time Tn-1, and the predetermined sound speed c and the y value _yr of the reference position ( _x , yr, _zr ).

The formulas (14) and (15) are formulas obtained by approximating the Hankel function H ₀ ⁽²⁾ (•) of the formula (10) by an exponential function and approximating the trajectory of the primary sound source 101 by continuous uniform linear motion. The angular spectrum D(k _x , ω) of the formula (14) is expressed by an arithmetic expression in which the amplitude and phase of the spectrum F(ω) obtained by Fourier transforming the function f(τ) of the formula (15) are shifted.

The drive signal calculation unit 12 performs an inverse Fourier transform on the angular spectrum D(k _x , ω) of the drive function of the secondary sound source 102 at time T _n to obtain the time domain drive signal D(x, t) of the secondary sound source 102 at time T _n .

When the drive signal writing unit 13 writes the time domain drive signal D(x, t) (D1 and D2) of the secondary sound source 102 at time T _n into the buffer 14, for the drive signal D0 that has already been written in the buffer 14 and is beyond time T _n-1 , the drive signal writing unit 13 adds the drive signal D1 from time T _n-1 to time T _n-1 +a2, which is the same time period as the drive signal D0, to the drive signal D0 and writes it, and writes the drive signal D2 from time T _n-1 +a2 onwards as is.

In this way, in the sound field reproduction and synthesis method using a speaker array that is a linearly arranged secondary sound source 102, when the primary sound source 101 moves on an arbitrary trajectory, the function that represents the acoustic propagation from the primary sound source 101 is approximated, and the trajectory is approximated by a continuous uniform linear motion. This makes it possible to reduce the amount of calculation required to derive the angular spectrum D(k _x , ω) of the driving function of the secondary sound source 102.

In other words, when reproducing a desired sound field in a playback sound field using the vector division method, the amount of calculation required to derive speaker drive signals can be reduced.

Here, the trajectory of the primary sound source 101 is approximated to a straight line by continuous uniform linear motion, but experiments by the inventors of the present application have shown that this approximation can be made unnoticeable by shortening the interval between trajectory sampling times _Tn to a certain extent. Therefore, the processing according to the embodiment of the present invention can be implemented even in hardware and software with low machine power, and users of the sound field reproduction device 1 can enjoy sound field synthesis in a wide range of playback environments.

The present invention has been described above using embodiments, but the present invention is not limited to these embodiments and can be modified in various ways without departing from the technical concept thereof.

The hardware configuration of the sound field reproduction device 1 according to an embodiment of the present invention can be a conventional computer. The sound field reproduction device 1 is composed of a computer equipped with a CPU, a volatile storage medium such as RAM, a non-volatile storage medium such as ROM, an interface, etc.

The functions of the movement velocity calculation unit 10, drive function calculation unit 11, drive signal calculation unit 12, drive signal writing unit 13, and buffer 14 provided in the sound field reproduction device 1 are each realized by having the CPU execute a program that describes these functions.

These programs are stored on the storage medium and are read and executed by the CPU. These programs can also be stored and distributed on storage media such as magnetic disks (floppy disks, hard disks, etc.), optical disks (CD-ROMs, DVDs, etc.), and semiconductor memory, and can also be sent and received over a network.

1 Sound field reproduction device 10 Moving speed calculation unit 11 Driving function calculation unit 12 Driving signal calculation unit 13 Driving signal writing unit 14 Buffer 101 Primary sound source 102 Secondary sound source P Sound pressure P in desired sound field Angular spectrum G of sound pressure in desired sound field Transfer function G from secondary sound source to each point in reproduced sound field Angular spectrum D of transfer function from secondary sound source to each point in reproduced sound field Driving function D of secondary sound source Angular spectrum (x _n , _yn ) of driving function of secondary sound source Position (v _x , v _y ) Moving speed s(τ) of primary sound source Input signal (sound source signal of primary sound source)
c Sound speed (x, y _r , z _r ) Reference position

Claims (3)

A sound field reproduction device that generates a drive signal for reproducing a sound field formed by a moving primary sound source using a speaker array of a secondary sound source,
Let s(τ) be the sound source signal of the primary sound source at time τ, H ₀ ⁽²⁾ (·) be the zeroth-order Hankel function of the second kind, ω be the angular frequency, c be the speed of sound, k _x be the wave number in the x-axis direction, _yr and _zr be the y and z values of a linear reference position, and (x _s (τ), y _s (τ), z _s (τ)) be the position of the primary sound source at the time τ,
The angular spectrum D(k _x , ω) of the driving function of the secondary sound source is expressed by the angular spectrum formula by the spectral division method:
When the primary sound source and the secondary sound source are arranged on an xy plane and the description regarding the z axis is omitted,
a movement speed calculation unit that receives a position ( _xn , _yn ) of the primary sound source at time _Tn of the nth (n is an integer of ₁ or more) trajectory sampling of the primary sound source and calculates a movement speed ( _vx , _vy ) of the primary sound source at time _Tn based on the positions ( _xn-1 , yn _-1 ), ( _xn , _yn ) of the primary sound source at times Tn-1 and _Tn ;
Based on the signal s(τ) from time T _n-1 to time _{T n} , the position (x _s0 , y _s0 ) which is the position (x _n-1 , y _n-1 ) of the primary sound source at time T n-1, and the preset sound speed c and the y value _yr of the reference position, the Hankel function H ₀ ⁽²⁾ (·) is approximated by an exponential function for the equation of the angular spectrum by the spectrum division method, and the trajectory of the primary sound source is approximated by continuous uniform linear motion to obtain the following equation:
(F(ω) is expressed by the formula:
a driving function calculation unit that calculates the angular spectrum D(k _x ,ω) of the driving function of the secondary sound source using the spectrum obtained by Fourier transform of
a drive signal calculation unit that calculates the drive signal in the time domain by performing an inverse Fourier transform on the angular spectrum D(k _x , ω) calculated by the drive function calculation unit;
A sound field reproduction device comprising: 2. The sound field reproduction device according to claim 1,
a buffer in which the drive signal is stored;
a drive signal writing unit that writes the drive signal calculated by the drive signal calculation unit into the buffer,
A sound field reproduction device characterized in that, when writing into the buffer the calculated drive signals (D1 and D2) for the period from time T _{n-1 to} time T _n +a1, which exceeds time T _n , calculated by the drive signal calculation unit in response to the signal s(τ) for the period from time T _{n -1} to time T n, the drive signal writing unit adds the calculated drive signal (D1) for the period from time T _n-1 to time T _n-1 +a2 to the drive signal (D0) for the period from time T _n-1 to time T _n-1 +a2, which exceeds time T _{n-1, which has already been written into the buffer, and writes the calculated drive signal (D2) for the period from time T n-1} +a2 to time T _n +a1 as is. a computer constituting a sound field reproduction device that generates a drive signal for reproducing a sound field formed by a moving primary sound source using a speaker array of a secondary sound source,
Let s(τ) be the sound source signal of the primary sound source at time τ, H ₀ ⁽²⁾ (·) be the zeroth-order Hankel function of the second kind, ω be the angular frequency, c be the speed of sound, k _x be the wave number in the x-axis direction, _yr and _zr be the y and z values of a linear reference position, and (x _s (τ), y _s (τ), z _s (τ)) be the position of the primary sound source at the time τ,
The angular spectrum D(k _x , ω) of the driving function of the secondary sound source is expressed by the angular spectrum formula by the spectral division method:
When the primary sound source and the secondary sound source are arranged on an xy plane and the description regarding the z axis is omitted,
a movement velocity calculation unit that inputs a position ( _xn , _yn ) of the primary sound source at time _Tn of the nth (n is an integer of ₁ or more) trajectory sampling of the primary sound source, and calculates a movement velocity ( _vx , _vy ) of the primary sound source at time _Tn based on the positions ( _xn-1 , yn _-1 ), ( _xn , _yn ) of the primary sound source at times Tn-1 and _Tn ;
Based on the signal s(τ) from time T _n-1 to time _{T n} , the position (x _s0 , y _s0 ) which is the position (x _n-1 , y _n-1 ) of the primary sound source at time T n-1, and the preset sound speed c and the y value _yr of the reference position, the Hankel function H ₀ ⁽²⁾ (·) is approximated by an exponential function for the equation of the angular spectrum by the spectrum division method, and the trajectory of the primary sound source is approximated by continuous uniform linear motion to obtain the following equation:
(F(ω) is expressed by the formula:
a driving function calculation unit that calculates the angular spectrum D(k _x ,ω) of the driving function of the secondary sound source using
A program for causing the program to function as a drive signal calculation unit that calculates the drive signal in the time domain by performing an inverse Fourier transform on the angular spectrum D(k _x , ω) calculated by the drive function calculation unit.