JP6343771B2 - Head related transfer function modeling apparatus, method and program thereof - Google Patents

Description

  The present invention relates to modeling of a head related transfer function, and more particularly to a head related transfer function modeling apparatus, a method thereof, and a program thereof used for sound image localization technology and the like.

The head-related transfer function (HRTF) is an acoustic transfer function. Specifically, the head-related transfer function is calculated from the position corresponding to the center of the head when there is no head as a simulation. It is the acoustic transfer function to the binaural tympanic membrane position or the ear canal entrance.
The head-related transfer function modeling means expressing the head-related transfer function as a rational polynomial or a ratio thereof. The head-related transfer function and its model have a wide variety of applications such as a sound image localization technique that artificially arranges a sound image of an acoustic signal in space.

  In general, the transfer function G (q) of the system is defined by z-transformation of the impulse response g (k) of the system, and can be expressed as the following equation (1). Here, q is a shift operator.

  Equation (1) represents an infinite impulse response (IIR) model. On the other hand, in general, the head-related transfer function is truncated at an order M such that the impulse response sufficiently converges, and a rational polynomial is used to obtain a finite impulse response (FIR) as in the following equation (2). : Finite impulse response) model.

  The impulse response of the head-related transfer function is measured by applying an input signal from a speaker and collecting sound with, for example, microphones built in both ears of the dummy head. For example, when measured at a sampling frequency of 48 kHz, the length that provides sufficient convergence is approximately 512 samples. Therefore, the measurement signal is cut out by a rectangular window that is the same as or slightly longer than the number of samples, and the head-related transfer function becomes a high-order finite impulse response model such as 512th order or 1048th order.

  The head-related transfer function includes many feature quantities related to sound image localization perception, such as interaural time difference, level difference, and spectral cue on frequency characteristics. It has been confirmed by sound image localization experiments that these feature quantities are sufficiently preserved in modeling of the head-related transfer function by a sufficiently high-order finite impulse response model. Spectral cues and the like serve as clues for sound image localization perception in the identification of head-related transfer functions.

Conventionally, methods for modeling a head related transfer function are known (see, for example, Non-Patent Documents 1 and 2 and Patent Documents 1 and 2).
Non-Patent Document 1 discloses a method of modeling a head-related transfer function with a ratio of a rational polynomial using a pole / zero model as a method for modeling a head-related transfer function. Non-Patent Document 1 describes that the pole-zero model is defined by the following equation (3).

In Equation (3), C is a constant, p _k is a pole, and z _k is a zero point. Of these, the pole corresponds to resonance, and the zero point corresponds to time delay or anti-resonance.

  In the finite impulse response model expressed by the above equation (2), the impulse response is expressed using only the zero point. On the other hand, the head-related transfer function can be expressed with a smaller number of parameters by modeling using not only zeros but poles as in the pole-zero model shown in Equation (3), for example. In the technique described in Non-Patent Document 1, when the parameters of the pole-zero model are derived, a finite impulse response model is obtained as a primary model, and the error of each impulse response, that is, the sum of squares of output errors is minimized. Deriving parameters.

In the technique described in Non-Patent Document 2, the common pole zero (CAPZ: Common-acoustical-pole) in which the poles of the model are shared between the head-related transfer functions in each direction, assuming that the resonance does not depend on the direction. and zero) modeling. Non-Patent Document 2 describes that the common pole-zero model is defined by the following equation (4), where r _j is the position vector of the sound source receiving point position.

In Equation (4), the pole p _k does not depend on the direction, and only the zero point z _k changes according to the direction. Therefore, in this model, the number of parameters to be changed according to changes in the sound source and the sound receiving point is reduced. be able to. In the technique described in Non-Patent Document 2, when a common pole-zero model is derived, a finite impulse response model of a multi-directional head-related transfer function is obtained as a primary model, and a common pole-zero model is derived as an approximation thereof. In Non-Patent Document 2, at this time, the evaluation function is expressed by the following equation using the error of the impulse response between the finite impulse response model of each direction and the common pole-zero model, that is, the output error ε (r _j , k). It is described that it is expressed as (5).

  In Equation (5), R is the number of directions, and M is the order of the finite impulse response model. By minimizing J in this equation (5), the parameters of the common pole-zero model are derived.

  The technique described in Patent Document 1 relates to a method of simulating a basic vector extracted by using principal component analysis from a finite impulse response model of a plurality of head related transfer functions as a pole-zero model using a balance model approximation technique. It is. This basic vector is composed of one non-directional average basic vector and a plurality of directional basic vectors. Here, the non-directional average basic vector means a basic vector that represents a feature determined regardless of the direction of the sound source among the features of the modeled omnidirectional head-related transfer function. On the other hand, the directional basic vector is a basic vector typified by features determined by the direction of the sound source. The technique described in Patent Document 1 can simulate a head-related transfer function with few parameters as a pole-zero model by using a principal component analysis and a balance model approximation technique.

  Patent Document 2 discloses a method of generating a parameter representing a head-related transfer function by dividing a head impulse response signal into subbands in the frequency domain and obtaining parameters of each subband. In this method, fast Fourier transform bins are grouped into at least two subbands in the frequency domain, and parameters are determined based on the root mean square of the signal levels of the subbands. The technique described in Patent Document 2 can reduce the amount of calculation processing using the head-related transfer function by dividing the subband.

Japanese Patent No. 4681464 Japanese Patent No. 4912470

F. Asano, Y. Suzuki, and T. Sone, “Role of spectral cues in median plane localization,” J. Acoust. Soc. Am., Vol.88, pp.159-168 (1989) Y. Haneda, S. Makino, and Y. Kaneda, “Common-Acoustical-Pole and Zero Modeling of Head-Related Transfer Functions,” IEEE Trans. Vol. 7, No. 2 (1999)

In the modeling by the finite impulse response model of the head related transfer function represented by the above-described formula (2), since it is a higher order such as 512th order or 1048th order, the number of parameters is large. There is a problem that the amount of calculation in the used sound image localization method increases. In addition, since simulation of the head-related transfer function using this finite impulse response model does not consider noise, preprocessing such as synchronous addition is required to reduce the influence of noise. However, also in this case, it is assumed that the whiteness or average of noise is 0, and the reduction effect is limited.
Similarly, in the simulation of the head-related transfer function by any of the methods described in Non-Patent Documents 1 and 2 and Patent Documents 1 and 2, the influence of noise is not considered.

  In addition, among the conventional techniques, in the modeling of the head related transfer function using a sufficiently high-order finite impulse response model, the features of the head related transfer function that are clues for sound image localization perception are sufficiently preserved. In the techniques described in Patent Documents 1 and 2 and Patent Documents 1 and 2, at least a spectral cue is not always stored. Here, the spectral cue is a specific peak P1 or notches N1 and N2 on the frequency characteristic of the head related transfer function as shown in FIG. Therefore, accurate modeling is considered important.

  The present invention has been made in view of the above problems, and is a model of a head-related transfer function that preserves the feature quantity related to sound image localization perception and considers the influence of noise. It is an object of the present invention to provide a head-related transfer function modeling device for obtaining a model capable of reducing the amount of calculation when used.

  In order to solve the above problems, the head related transfer function modeling apparatus according to the present invention inputs and outputs an input signal applied to a speaker and an output signal obtained by measuring a sound emitted from the speaker with a microphone. A head-related transfer function modeling device that uses the data as an asymptotic estimation method to model a head-related transfer function, comprising a high-order model estimation means and a reduction means, and the reduction means has a frequency A transfer function calculating means, a low-order model estimating means, and a low-order model searching means are provided.

According to such a configuration, the head related transfer function modeling apparatus uses the input / output data by the high order model estimating means to determine a head related transfer function and a noise model having a predetermined high order model order. The parameters of the higher-order model are estimated by the prediction error method.
With this high-order model estimation means, it is possible to obtain a highly accurate model in consideration of noise in the measurement of the head related transfer function.
Then, the head related transfer function modeling device derives the maximum likelihood estimated value by deriving the maximum likelihood estimated value using the high-order model estimated by the reduction means and the log likelihood function which is an evaluation function in the frequency domain. Reduce higher-order model.
Here, in the reduction means, the frequency transfer function of the higher order model is obtained by the frequency transfer function calculation means. Further, the reduction means obtains an estimated value of a lower-order model having an order lower than the higher-order model order by minimizing the log likelihood function by the lower-order model estimation means.
Then, in the reduction means, the low-order model search means updates the low-order order and repeats minimizing the log-likelihood function. An error of a feature amount related to sound image localization perception between the model and a higher-order reference model is obtained, and a low-order model when the error of the feature amount satisfies a predetermined allowable condition and becomes a minimum order Explore.

The present invention can also be realized by a head-related transfer function modeling method in which each unit of the head-related transfer function modeling apparatus executes processing.
The present invention can also be realized by a head-related transfer function modeling program that causes a computer to operate as each means of a head-related transfer function modeling apparatus.

  According to the present invention, the head-related transfer function is modeled by the asymptotic estimation method, so that the sound image is within a range in which an error from a higher-order model reference model such as the 512th order or 1024th order is allowed as the head-related transfer function. It is possible to obtain a low-order head-related transfer function model that takes into account noise and preserves the feature amount related to localization perception, and has a smaller number of parameters than conventional ones. Therefore, when the low-order model estimated as the head-related transfer function is used as a control target such as a sound image localization technique, the amount of calculation can be reduced.

It is a block diagram which shows typically the structure of the modeling apparatus of the head related transfer function which concerns on embodiment of this invention. It is drawing which shows typically the mode of the measurement of the input-output data of FIG. It is an example of the signal waveform of the input-output data of FIG. 1, (a) has extracted the input signal to a speaker, (b) has shown the extract of the output signal measured with the microphone. It is a block diagram which shows the structure of the model of a head-related transfer function, (a) shows the structure of FIR model, (b) has shown the structure of ARX model. It is a flowchart which shows the flow of the sound image localization control containing the modeling method of the head related transfer function which concerns on embodiment of this invention. 6 is a flowchart illustrating an example of a process for reducing the dimension of the ARX model in FIG. 5. It is a graph which shows an example of the spectrum distortion between the low-order model and high-order reference model of the estimated head-related transfer function. It is a graph which shows an example of the frequency characteristic of a head-related transfer function, Comprising: (b) is an Example, (a) has overlapped and showed the Example and the comparative example. It is a block diagram which shows typically an example of the sound image localization control to which the head-related transfer function estimated in this embodiment is applied. It is a figure which shows an example of a spectral cue.

  DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment for implementing a head related transfer function modeling apparatus of the present invention (hereinafter referred to as “embodiment”) will be described in detail with reference to the drawings.

  The head related transfer function modeling apparatus 1 shown in FIG. 1 uses asymptotic estimation using an input signal applied to a speaker and an output signal obtained by measuring a sound emitted from the speaker with a microphone as input / output data. The head-related transfer function is modeled by the method.

<Input / output data>
When the input / output data shown in FIG. 1 is measured in advance, the input signal u (k) is applied to, for example, one speaker SP installed in a predetermined direction in an acoustic anechoic room as illustrated in FIG. Apply. Here, k is a variable that identifies a sample associated with a time interval (sampling period) when sampling a continuous time signal of speech. k is a discrete value, and the number thereof is the number of data. Then, the sound emitted from the speaker SP is measured with a microphone installed at a position where it hits the ear of the dummy head D. The signal measured at this time is defined as an output signal y (k).

  In FIG. 2, the speaker SP is installed in the right 90 ° direction (that is, the left 270 ° direction) from the front of the dummy head D and is directed to the right ear of the dummy head D, but this is an example. By rotating the dummy head D relative to the speaker SP within a horizontal plane by a predetermined angle, it is possible to measure sound with microphones installed in the left and right ears from various directions. The relative distance and height between the speaker SP and the dummy head D are also variable.

As the input signal u (k), an M-sequence signal that is a pseudo white signal can be used.
As an example, FIG. 3A shows a waveform of an M-sequence signal having a shift register length of 15 (number of samples = 2 ¹⁵ −1). FIG. 3A shows a waveform of a part (100 samples) in the middle of the M-sequence signal. FIG. 3B shows a partial waveform of the output signal y (k) measured when the M series is applied to the speaker SP installed 30 ° to the left from the front of the dummy head D. . However, the waveforms shown in FIGS. 3A and 3B are obtained when the sampling frequency is 48 kHz.

<Asymptotic estimation method>
The asymptotic method is a known method as a modeling method for plant control, for example. In the asymptotic estimation method, first, the parameters of a higher-order model (for example, n-th order) taking into account the noise model are estimated for the input / output data obtained by the system identification experiment, and then the frequency characteristics based on the asymptotic theory. Reduce the dimension considering the above.

[Configuration of head transfer function modeling device]
The head-related transfer function modeling device 1 (hereinafter simply referred to as the modeling device 1) is, for example, a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), An HDD (Hard Disk Drive), an input / output interface, and the like are provided. Here, as shown in FIG. 1, the modeling apparatus 1 includes a high-order model estimation unit 10, a high-order setting unit 11, and a reduction order unit 20.

  The high-order model estimation means 10 estimates a high-order model for a head-related transfer function and a noise model having a predetermined high-order (n-th order) model order by using a prediction error method using input / output data. Is.

  Here, as a model having a noise model, a known model such as an ARX (Auto Regressive eXogenous) model shown in FIG. 4B can be used. In the ARX model, a noise model (1 / A (q) in the figure) is considered, and in this embodiment, the output signal measured by the microphone is treated as including the influence of noise.

  The conventional general head related transfer function modeling uses the FIR model shown in FIG. 4A, and an FIR filter has been mounted for sound image localization. The FIR model does not consider the noise model (1 / A (q)), but handles signals that are not affected by noise by performing preprocessing such as synchronous addition.

  The modeling apparatus 1 estimates the parameters of the higher-order model by the higher-order model estimation means 10 on the assumption that the order is reduced in the subsequent processing. Here, the reason why the parameters of the higher-order model are estimated is that, generally, the higher the model, the better the accuracy. In the prior art that does not consider the noise model, the head-related transfer function is a high-order finite impulse response model such as the 512th order or the 1048th order. In the present embodiment, a three-digit numerical value is empirically assumed as the higher order.

The prediction error method assumed in this embodiment is a general term for parameter estimation methods for calculating an estimated value that minimizes an evaluation criterion composed of prediction errors based on predicted values. As this prediction error method, a general method used for system identification can be used. When a quadratic function is used as a measure of the magnitude of the prediction error, the prediction error method is a least square method.
Here, the high-order model estimation unit 10 estimates the parameters by the least square method based on the system identification theory using the high-order ARX model.

  The higher-order model estimation means 10 is an ARX model defined by the following equation (6) based on input / output data {u (k), y (k); k = 1, 2,. Estimate the parameters of Here, u (k) is an input signal, y (k) is an output signal, and N is the number of data.

In Equation (6), A ^h (q) and B ^h (q) are elements (hereinafter simply referred to as models) constituting the system, and parameters {a _i }, {b _i } (i = 1). To n), respectively, are represented by the following formulas (7) and (8).

Further, in the above-described equation (6), normal white noise having an average value of 0 and a variance of σ ² _w is assumed as the disturbance w (k).
In equation (8), L represents a dead time.
In each of the above equations, the superscript h is an abbreviation for high, meaning that the order n of the models A ^h (q) and B ^h (q) is sufficiently high, that is, a high-order model. H is not a variable.

  In the present embodiment, the high-order setting unit 11 sets the model order input from the outside of the modeling apparatus 1 in the high-order model estimation unit 10. This model order (higher order n) is stored in the modeling apparatus 1 and read by the higher order model estimation means 10 during processing. Here, it is assumed that the high-order order n is 100, for example. Note that the higher-order order n may be input from outside the modeling apparatus 1 each time processing is performed.

Order model estimation means 10, as parameters of the ARX model, the equation parameters shown in _{(7) {a i} (} i = 1~100), parameters shown in the equation _{(8) {b i} (} i = 1 to 100) is estimated by the method of least squares.

The polynomial estimated from the equation (7) by the higher-order model estimation means 10 is denoted as A ^ ^h (q), and the polynomial estimated from the equation (8) is denoted as B ^ ^h (q). In the present specification, the symbol “^” arranged on the right of a certain character means a hat symbol arranged on the character immediately before. This hat symbol represents an estimated value.

When expressed in this way, the higher-order model for the transfer function G (q) to be controlled is expressed as G ^ ^h (q) and is expressed by the following equation (9a). Further, the high-order noise model for the noise model H (q) is expressed as H ^ ^h (q) and is expressed by the following equation (9b).

  In the case of the FIR model, normal white noise or average zero noise is assumed. Therefore, a relational expression corresponding to the equation (9a) is described as G (q) = B (q), and the equation ( The relational expression corresponding to 9b) is described as H (q) = 1. The relatively high-order FIR model is used as a reference for the low-order ARX model (hereinafter referred to as a high-order reference model), as will be described later.

The reduction means 20 obtains a higher-order model {G ^ ^h (q), H ^ ^h (q)} estimated by the higher-order model estimation means 10 and a log likelihood function that is an evaluation function in the frequency domain. It is used to reduce the higher-order model by deriving the maximum likelihood estimate.
As shown in FIG. 1, the order reduction means 20 includes a frequency transfer function calculation means 21, a low-order model estimation means 22, and a low-order model search means 23.

The frequency transfer function calculating means 21 is a frequency transfer function G ^ ^h (e ^jω ) for the known higher order models {G ^ ^h (q), H ^ ^h (q)} estimated by the higher order model estimating means 10. , H ^ ^h (e ^jω ). The frequency transfer function calculating means 21 calculates, for example, a high-order frequency transfer function G ^ ^h (e ^jω ) that is the frequency response from the transfer function G ^ ^h (q) of the high-order model.

  The low-order model estimation unit 22 minimizes the log likelihood function, which is an evaluation function in the frequency domain, so that the model order (high-order order) of the high-order model estimated by the high-order model estimation unit 10 is smaller. This is to obtain an estimated value of a low-order model having a low order.

Here, the model order set in the higher-order model estimation means 10 is n (= 100). Further, the model order of an unknown low-order model to be estimated is set to m (0 <m <n). The m-th order low-order model is denoted as {G ^ ^l (q), H ^ ^l (q)}. Here, the superscript l is an abbreviation of low, meaning that the order m of G ^ ^l (q) and H ^ ^l (q) is lower than n, that is, a low-order model. And l is not a variable.
G ^ ^l (q) is an estimated value of the low-order model for the transfer function G (q) to be controlled, and H ^ ^l (q) is a low-order noise for the noise model H (q). This is an estimate of the model.

In this case, the frequency transfer function for the transfer function G ^ ^l (q) of the unknown low-order model to be estimated is further set as G ^ ^l (e ^jω ). Similarly, the unknown low-order model to be estimated is Let H ^ ^l (e ^jω ) be the frequency transfer function for the noise model H ^ ^l (q).

The log likelihood function described above is represented by V in the following equation (10). In the asymptotic theory, the higher order model (G ^ ^h ( ^ejω )) approximately follows a normal distribution in the frequency domain, so the lower order model (G ^ ^l ( ^ejω )) becomes asymptotically the maximum likelihood estimate. Become.

In equation (10), Φ _u (ω) is a power spectral density function of the input signal u (k). Φ _v (ω) is a power spectral density function of the noise v (k). This noise v (k) is expressed by the following equation (11).

Here, the noise v (k) is a normal white noise assumed as the disturbance w (k), and a noise-forming filter (a known high-order noise model H ^ ^h (estimated by the high-order model estimation means 10). q)) Noise after passing through.

The low-order model estimation unit 22 determines that the model order m (0 <m <n) of the unknown low-order model to be estimated is set to a predetermined value by the low-order model search unit 23. Is calculated, and when the model order m is the set value, an estimated value G ^ ^l (q) of the low-order model that minimizes V in Expression (10) is obtained. The estimated value G ^ ^l (q) of the low-order model is an output candidate of the modeling apparatus 1. In order to minimize the log likelihood function V, it is necessary to solve a nonlinear optimization problem. The solution method is not limited, but an example will be described later.

<Lower model search means 23>
The low-order model search means 23 updates the model order m of an unknown low-order model to be estimated and repeats minimizing the log-likelihood function V. An error of a feature amount related to sound image localization perception between the next model G ^ ^l (q) and a higher-order reference model is obtained, and the error of the feature amount satisfies a predetermined allowable condition and has a minimum order. It searches for a low-order model when The low-order model G ^ ^l (q) of the lowest order searched here is the output of the modeling apparatus 1.

  In this embodiment, an FIR model generally used in the acoustic field is used as an example of a higher-order reference model. The order of the FIR model as the higher-order reference model is 512th in consideration of sufficient convergence.

  Hereinafter, as an example, the feature amount related to sound image localization perception is the position of a spectral cue that is a peak and a notch on the frequency characteristic of the head-related transfer function. This is because accurate modeling of spectral cues is important in sound image localization technology that arranges sound images in space in a simulated manner.

  In the present embodiment, the spectral cue is stored when the low-order ARX model is estimated by reducing the order of the high-order ARX model. Here, the preservation of the spectral cue is determined in advance so that the spectral cue of the low-order ARX model to be estimated can reproduce the spectral cue of the high-order reference model (for example, a high-order FIR model) with a desired accuracy. Satisfying the specified acceptable conditions. The accuracy of reproducibility is appropriately set according to the desired effect of reducing the amount of calculation expected when applied to sound image localization and the like. By suppressing the deviation of the center frequency of both spectral cues to a desired allowable range, the low-order model estimated as the head-related transfer function has the desired accuracy, and the low-order model is converted into a sound image localization technique, etc. The amount of calculation when used as a control target can be reduced.

In the present embodiment, the low-order model search means 23 performs spectral distortion between the low-order model G ^ ^l (q) of each head-related transfer function estimated by the low-order model estimation means 22 and the high-order reference model. (SD: spectral distortion) is obtained, and the spectral distortion is equal to or less than a predetermined first threshold value, and the error between the spectral cue position and the higher-order reference model is equal to or less than a predetermined second threshold value. It was decided to search for a low-order model that satisfies the minimum order. Here, the spectral distortion SD is a physical index in which the difference in amplitude characteristics is evaluated for all frequency components in order to determine the degree of coincidence between two transfer functions. With this configuration, it is possible to reduce the amount of calculation and to guarantee the accuracy of the low-order model to be estimated.

  Therefore, in the present embodiment, as shown in FIG. 1, the low-order model search means 23 is a spectral distortion calculation means 24, a spectral distortion determination means 25, an acoustic feature quantity calculation means 26, and an acoustic feature quantity determination means 27. And so on.

Spectral distortion calculation means 24 calculates the spectral distortion SD by the following equation (12) when two head-related transfer functions H _X and H _Y are given.

In Expression (12), N represents the number of data in the head-related transfer function. The head-related transfer function H _X represents the frequency transfer function of the estimated lower-order model G ^ ^l (q) of the head-related transfer function, for example, and the head-related transfer function H _Y represents the frequency transfer function of the higher-order reference model, for example. Represents.

Spectral distortion determination means 25 determines whether or not the spectral distortion SD calculated by the spectral distortion calculation means 24 is equal to or less than the first threshold value. Here, the first threshold value is not particularly limited. However, if the spectral distortion SD is less than about 3 dB, it can be considered that the two head-related transfer functions are in good agreement. Therefore, in the present embodiment, the first threshold is set to 3 dB as a typical example. Thus, when the spectral distortion SD is larger than 3 dB, the low-order model G ^ ^l (q) estimated at the model order m set at that time is NG and does not become the final output of the modeling apparatus 1. . Therefore, before selecting all possible values for m in the calculations of Equation (10) and Equation (12), the calculation is performed when the spectral distortion SD becomes greater than 3 dB as the model order m is updated. Can be terminated.

The acoustic feature quantity calculation means 26 uses the center frequency of the spectral cue in the frequency transfer function G ^ ^l (e ^jω ) for the low-order model G ^ ^l (q) to be estimated and the frequency transfer function for the high-order reference model. The difference from the center frequency of the spectral cue in is calculated as an error of the acoustic feature amount.

The acoustic feature amount determination unit 27 determines whether or not an error of the acoustic feature amount calculated by the acoustic feature amount calculation unit 26 (a shift in the center frequency of the spectral cue) is equal to or less than a second threshold value. Here, the second threshold value is not particularly limited. However, in the present embodiment, as a typical example, the second threshold value is one sample of the discrete frequency bin. That is, an error range of 1 sample was allowed at the center frequency of the spectral cue. Specifically, for example, when the sampling frequency is 48 kHz and the spectrum is obtained by discrete Fourier transform with the number of data N (512), the section of one sample can be 93.75 Hz. As a result, when the shift of the center frequency of the spectral cue is larger than one sample, the low-order model G ^ ^l (q) estimated at the model order m set at that time is NG and the modeling apparatus 1 It is not the final output. Therefore, in the process of calculating the shift of the center frequency of the spectral cue, the time when the shift of the center frequency of the spectral cue becomes greater than one sample as the model order m is updated before selecting all possible values as m. The operation can be terminated with.

  As described above, the low-order model search means 23 in FIG. 1 updates the model order m of the unknown low-order model to be estimated to minimize the log likelihood function V of the above-described equation (10). , The threshold value is determined for the difference between the spectral distortion SD and the center frequency of the spectral cue. At this time, the method of updating the model order m is not particularly limited.

  For example, after performing the process while updating the model order m for one of the threshold determination for the spectral distortion SD and the threshold determination for the shift of the center frequency of the spectral cue, the threshold determination while updating the model order m for the other Processing may be performed. Alternatively, when the model order m is set to a certain value, the model order m may be updated after performing both threshold determination processes.

Further, the order m may be monotonously decreased, monotonously increased, or increased / decreased.
Further, the order m may be shifted by 1 or may be shifted by 2 or more predetermined values. It is not always necessary to set the same number of shifts each time. For example, after shifting by 10 units, it may be shifted by 1 unit.
If it is clear that the final output of the modeling apparatus 1 is not obtained as described above, all m (0 <m <n) that can take values are not necessarily selected when the model order m is updated. Also good.

  In the present embodiment, as an example, when the low-order model search means 23 updates the low-order model order m in descending order from the high-order model order n side, and the spectral distortion SD becomes larger than the first threshold ( This is hereinafter referred to as an iterative stop condition), the log likelihood function V minimization processing is stopped, and the low-order model order m is set starting from the order when the spectral distortion SD is less than or equal to the first threshold (3 dB). By updating in ascending order, the order when the error from the higher-order reference model regarding the position of the spectral cue falls below the second threshold is determined as the lowest order. By doing in this way, it is possible to obtain | require efficiently the minimum order of the model order m.

(Solution method for minimization of log-likelihood function V in equation (10))
The solution method described here includes the following three procedures A-1, A-2, and A-3.

A-1. Input Filtering The input signal u (k) is filtered using the known high-order noise model H ^ ^h (q) estimated by the high-order model estimation means 10 as shown in the following equation (13). The signal u _f (k) that has passed through the filter of the high-order noise model H ^ ^h (q) is used as an input signal for the high-order model G ^ ^h (q) of the head-related transfer function.

A-2. Calculation of output The filtered signal u _f (k) shown in the equation (13) obtained in the procedure A-1 is used as a new input signal to the higher-order model G ^ ^h (q) of the head-related transfer function. The output signal y ^ _f (k) of the higher order model G ^ ^h (q) is calculated by the following equation (14).

A-3. Low-order model parameter estimation The new input / output signals {u _f (k), y ^ _f (k); k of the high-order model G ^ ^h (q) of the head-related transfer function by the procedures A-1 and A-2 = 1, 2,..., N}, the parameters of the low-order model obtained by reducing the high-order model G ^ ^h (q) using the new input / output signal are estimated by the output error method. To do. At this time, the loss function V ^OE of the output error method is expressed by the following equation (15).

Here, G ^ ^l (q) in the equation (15) is a low-order model of the head-related transfer function to be obtained, and is represented by the following equation (16). The low-order noise model H ^ ^l (q) is expressed by the following equation (17).

However, in formula (16), A ^l (q) and B ^l (q) are represented by formula (18) and formula (19), respectively, and in formula (17), C ^l (q), D ^l (q ) Is expressed by Expression (20) and Expression (21), respectively.

[Flow of sound image localization control]
Here, as an example of the application of the head-related transfer function and its model, a sound image localization technique that artificially arranges a sound image of an acoustic signal in space will be described. Specifically, the overall flow of the sound image localization control including the method of modeling the head-related transfer function by the modeling apparatus 1 will be described with reference to FIG. 5 (refer to FIGS. 1 to 3 as appropriate).
First, before the processing of the modeling apparatus 1, input / output data necessary for system identification is measured (step S100). As the measurement method, the method described with reference to FIG. 2 can be used. Specific examples of input / output data are shown in FIGS. 3 (a) and 3 (b).

Subsequently, as a process of the modeling apparatus 1, a head related transfer function is modeled by an asymptotic estimation method using input / output data (step S200).
The process by the asymptotic estimation method (step S200) will be outlined. First, the process of estimating the parameters of the higher-order ARX model is performed (step S210: higher-order model estimation step), and then the lower dimension of the ARX model is based on the asymptotic theory. (Step S220: Reduction step).

More specifically, in step S210, in the modeling apparatus 1, the higher-order model estimation means 10 uses the input / output data to generate a head related transfer function having a predetermined higher-order (n-th) model order and The parameters {a _i } and {b _i } of the higher-order model (G ^ ^h (q), H ^ ^h (q)) for the noise model are estimated by the prediction error method.
In step S220, in the modeling apparatus 1, the reduction means 20 performs the estimated higher-order model (G ^ ^h (q), H ^ ^h (q)) and the logarithmic likelihood shown in the equation (10). The higher-order model is reduced in dimension by deriving the maximum likelihood estimate using the degree function V. Then, the modeling device 1 outputs a low-order model of the head related transfer function. The detailed flow of the ARX model reduction processing will be described later.

  Subsequently, the low-order ARX model of the head related transfer function estimated by the modeling apparatus 1 is applied to the sound image localization control target (step S300). Since this low-order ARX model is required as a model having a smaller number of parameters than the conventional model, the amount of computation when the low-order model estimated as the head-related transfer function is used as a control object such as a sound image localization technique is conventionally known. Can be reduced.

[Detailed flow of ARX model reduction processing]
Next, the detailed flow of ARX model reduction processing by the reduction means 20 of the modeling apparatus 1 will be described with reference to FIG. 6 (refer to FIGS. 1 to 3 and 5 as appropriate).
In the ARX model reduction processing (step S220), first, the frequency transfer function calculation means 21 of the modeling apparatus 1 uses the higher-order (n-order) model {G ^ ^h (q) obtained in step S210 of FIG. , H ^ ^h (q)}, the frequency transfer functions G ^ ^h ( ^ejω ), H ^ ^h ( ^ejω ) are obtained (step S221).

Then, the low-order model search means 23 sets the model order m (0 <m <n) (step S222). Here, as an example, n = 100, and therefore m = 99 is set. Then, the low-order model estimation means 22 minimizes the log likelihood function V shown in the above equation (10) when, for example, n = 100 and m = 99. A next model is estimated (step S223). As a result, the low-order model search means 23 obtains an estimated value G ^ ^l (q) of the low-order model when the set value is m = 99, for example.

Then, the low-order model search means 23 determines whether or not the iterative stop condition for the update of the model order m is satisfied (step S224). Specifically, the spectral distortion calculating means 24 calculates the spectral distortion SD of the 99th order model (H _X ) and the 100th order model (H _Y ) according to the above equation (12), and the spectral distortion determining means 25 is 3 dB. If it is determined that the value is greater than (first threshold), the repeated stop condition is satisfied.

  On the other hand, when the repeated stop condition is not satisfied (step S224: No), the low-order model order m is updated (step S225), and the process returns to step S223. Specifically, when the low-order model searching means 23 subtracts the value of the model order m by 1 and sets m = 98, the low-order model estimating means 22 is, for example, when n = 100 and m = 98. In step S222, the log-likelihood function V shown in the above equation (10) is minimized to estimate a low-order model in the case of a set value of m = 98, for example (step S222). In the case of No in step S224, subtraction is performed in the same manner.

  If the value of the model order m is further lowered in step S225 and the model continues to be reduced in dimension, the low-order model search unit 23 eventually determines that the iterative stop condition is satisfied (step S224: Yes). Specifically, it is determined that the spectral distortion determination means 25 is larger than 3 dB (first threshold).

In the case of Yes in step S224, the low-order model search means 23 adds “1” to the set value of the model order m at that time in step S226. The value of the model order m obtained by this addition is the lowest order when the spectral distortion SD is less than or equal to the first threshold (3 dB) in the low-order ARX model. Further, at this time, the low-order model search means 23 determines the order of the low-order model from the lowest order that satisfies the predetermined permissible condition with respect to the reference (high-order reference model) for the feature amount related to sound image localization perception. m is determined (step S226).
Specifically, the acoustic feature quantity calculating means 26 is the center of the spectral cue in the frequency transfer function G ^ ^l (e ^jω ) for the low-order model G ^ ^l (q) of the model order m set at that time. The difference between the frequency and the center frequency of the spectral cue in the frequency transfer function for the higher-order reference model (512th order FIR model) is calculated as an error of the acoustic feature quantity. Then, the acoustic feature amount determination unit 27 determines whether or not the shift in the center frequency of the spectral cues is equal to or less than one sample (second threshold).

  If the shift in the center frequency of the spectral cue is larger than one sample (second threshold value), the set value of the model order m at that time is too low, so the low-order model search means 23 sets the set value of the model order m at that time. "1" is added to. In the case of the value of the model order m obtained by this addition, the spectral distortion SD is naturally not more than the first threshold value (3 dB).

  Similarly, the acoustic feature quantity calculation means 26 calculates the shift of the center frequency of the spectral cue, and the acoustic feature quantity determination means 27 determines that the shift of the center frequency of the spectral cue is one sample (second threshold) or less. It is determined whether or not there is. In the case where the difference between the spectral cues is large, the value of the model order m is added in the same manner. Eventually, the acoustic feature quantity determination means 27 determines that the deviation has become one sample or less. The set value of the model order m at this time is the lowest order originally searched by the low-order model search means 23. Then, the modeling device 1 outputs a low-dimensional ARX model of the head related transfer function having the lowest order model order.

[Specific example of ARX model reduction processing]
In order to confirm the effect of the present invention, a measurement signal is applied from one speaker SP installed in a 30 ° left direction from the front of the dummy head D at a position 1.3 m away from the center of the head of the dummy head D. The experiment was conducted. Then, sound was collected by a microphone built in the left ear of the dummy head D to obtain an output signal illustrated in FIG. The head-related transfer function was modeled by the modeling method according to the present embodiment using the input / output data at this time. In addition, a 512th order FIR model was obtained as a higher order reference model.

  Spectral distortion SD at each order with respect to a higher order model of n = 100 was obtained while monotonously decreasing the set value of model order m while repeating steps S223 to S225 of FIG. FIG. 7 shows a graph of SD change with respect to the model order m at this time. When the set value of the model order m was lowered to the 17th order, SD became larger than 3 dB. That is, the order at which SD becomes 3 dB or less was 18th or more. Note that the process of minimizing the log likelihood function V shown in the equation (10) was performed 83 times in accordance with the update of the model order m.

  Subsequently, a model that can capture the center frequency of the spectral cues within a range of one sample with a higher-order reference model (512th-order FIR model) was obtained. FIG. 10 shows frequency characteristics of the higher-order reference model (512th-order FIR model).

  Corresponding to step S226 in FIG. 6, the shift of the center frequency of the spectral cues was obtained by using the already obtained 18th-order or higher model as a search target. In the 18th, 19th, and 20th orders, the deviation of the spectral cues exceeded the allowable range, but in the 21st order, the deviation of the spectral cues could be captured within the range of one sample. That is, the process for obtaining the shift of the spectral queue related to the update of the model order m was performed only four times.

  The frequency characteristic of the 21st-order ARX model obtained from the above experiment is shown by a broken line in FIG. 8A shows the frequency characteristics (broken line) of the 21st-order ARX model shown in FIG. 8B and the frequency characteristics of the higher-order reference model (512th-order FIR model) shown in FIG. (Solid line) and superimposed. Distortion becomes conspicuous on the low frequency side. This is considered to be caused by the difference between models and the relatively large SD in a band with a small gain.

  As shown in FIG. 8A, it can be seen that the spectral queue is stored in the 21st-order ARX model. In addition, it has been confirmed that the number of parameters can be greatly reduced compared to a higher-order reference model that considers that the FIR model that has been used in the past is the 512th order.

  For the above experiment, an example of measurement in one direction was given. However, in practice, by repeating the procedure of rotating the dummy head clockwise by 5 ° and collecting sound in the same manner, after collecting the sound, The head-related transfer function in the direction of 72 in the horizontal plane at 5 ° intervals was measured. When the head-related transfer function from the direction of the horizontal plane 72 to the left ear was modeled, the average order of the orders considered to be appropriate in each direction was 20th.

[Specific example of sound image localization control using a low-order model of the head-related transfer function]
Here, a specific example of sound image localization control that applies a low-order model of the head-related transfer function estimated in this embodiment will be described.
As a system using a head-related transfer function, a system called a trans-oral system for realizing three-dimensional sound is known. FIG. 9 includes control points (hereinafter, the identifier is i, where i = 1,..., M) and secondary sound sources (hereinafter, the identifier is j, where j = 1,..., N). 1 shows a block diagram of a trans-oral playback system. Note that m may be equal to n.

  Here, the control points are, for example, the right ear position R and the left ear position L of the listener (listener) 90 shown in FIG. As an example, the control point is identified by the identifier i in the order of the right ear position and the left ear position of the listener 90, for example. In a simple example, assuming that one listener 90 is assumed and m = 2, it will be generalized.

The secondary sound source is a speaker shown in FIG. Here, as an example, the speaker SP _j is identified by the identifier _j in order from the right ear position L side of the listener 90. The sound source SS outputs a signal to the speaker SP _j (j = 1,..., N). The number of sound sources SS is not particularly limited. The speaker SP is, for example, a loud speaker.

In the figure, an element G _ij (q) of the system represents a head-related transfer function to be controlled using the shift operator q, and is transferred from the j-th speaker (secondary sound source) to the i-th control point (ear position). Represents an acoustic transfer function. One low-dimensional ARX model estimated by the modeling apparatus 1 corresponds to one G _ij (q). Element X _i (q) represents a desired transfer function at each control point.

The element H _ji (q) serves as a controller for crosstalk cancellation. In general, when a binaural signal is presented using a speaker, in addition to signal propagation from the speaker to the ipsilateral ear, leakage (crosstalk) to the contralateral ear also occurs. Therefore, it is necessary to perform compensation processing for suppressing the crosstalk and transmitting only a desired signal to each ear. This process is called crosstalk cancellation.
The element X _i (q) transmits an audio signal to be heard only by the right ear or the left ear of the listener 90 at each i-th control point after the crosstalk is suppressed by the controller H _ji (q). Represents a function.

  Therefore, the input / output signals of the system are expressed by the following relationships (22) to (26).

Here, the system input signal is a scalar u (k), and the system output signal y (k) is a one-dimensional matrix having m elements corresponding to the number of control points, as shown in Equation (23). (Column vector). Note that the column vector of y (k) is represented by the transposition T of the row vector in Equation (23). Further, k = 1, 2,..., N, and N is the number of data.
Expression (24) is represented by a column vector having m elements (X _i (q)) corresponding to the number of control points. This column vector is represented by a transposition T of the row vector.
Expression (25) is represented by a vector (matrix) having m × n elements (G _ij (q)) corresponding to the number of control points and the number of secondary sound sources.
Expression (26) is expressed by a vector (matrix) having n × m elements (H _ji (q)) corresponding to the number of secondary sound sources and the number of control points.

  In this system, the desired output signal shown on the left side of Equation (22) is a signal obtained by applying the desired transfer function shown in Equation (24) to the input signal u (k) after crosstalk cancellation. The following equation (27) is used.

  If the shift operator q is used in this way, the convolution operation in the time domain can be described in the form of a matrix product. Therefore, to obtain the controller of the system defined by the equation (26), an algebraic inverse matrix operation may be performed from the equation (27) and the equation (22). As a result, it is possible to design a controller of the system as described by the following equation (28).

  However, the controller shown in Expression (28) becomes unstable. In order to solve this problem, it is conceivable that after designing the unstable controller once, a transfer function having an unstable pole is extracted from each transfer function constituting the controller. Then, by approximating this as a delayed inverse system, a stable controller can be realized. In the present embodiment, the head-related transfer function is modeled using the ARX model shown in FIG. 4B, and an IIR filter is mounted for sound image localization.

  As described above, according to the head-related transfer function modeling apparatus according to the present embodiment, the head-related transfer function is modeled with a small number of parameters while preserving the spectral cue that is a feature amount related to sound image localization perception. Is possible. In addition, since noise in the measurement of the head-related transfer function is taken into consideration, it is expected to be a more precise model. Furthermore, since the number of parameters is small, it is possible to reduce the amount of calculation in a sound image localization method using a head-related transfer function.

  As mentioned above, although this invention was demonstrated based on embodiment, this invention is not limited to this. For example, although the spectral cue is exemplified as a feature quantity related to sound image localization perception used as an index when the low-order model search means 23 searches for a low-order model, other feature quantities included in the head-related transfer function, for example, binaural A time difference or a level difference may be used.

  Further, the head related transfer function modeling device 1 may be a circuit in which an electronic circuit is constructed in hardware by various electronic components, semiconductor devices, or the like. It may be realized by cooperation of a head transfer function modeling program described in a special computer language and a CPU that processes the program.

Further, the 512th-order FIR model has been specifically described as an example of the higher-order reference model. However, the higher-order reference model is not limited to this, and a noise model is considered even if it is an ARX model other than the FIR, for example. It may be a higher order model.
In addition, as an example of the application of the head related transfer function and its model, a sound image localization technique has been specifically described. However, the present invention is not limited to sound image localization, and for example, a head related transfer function such as a loudness meter is used. Applicable to all technologies.

  The head-related transfer function modeling apparatus according to the present invention can be used in general sound reproduction technology using headphones and sound reproduction technology using speakers.

DESCRIPTION OF SYMBOLS 1 Head transfer function modeling apparatus 10 Higher order model estimation means 11 Higher order setting means 20 Reduction means 21 Frequency transfer function calculation means 22 Lower order model estimation means 23 Lower order model search means 24 Spectral distortion calculation means 25 Spectral distortion Determination means 26 Acoustic feature quantity calculation means 27 Acoustic feature quantity determination means

Claims (6)

A head-related transfer function that models a head-related transfer function by an asymptotic estimation method using an input signal applied to the speaker and an output signal obtained by measuring the sound emitted from the speaker with a microphone as input / output data Modeling equipment,
High-order model estimation means for estimating a high-order model for a head-related transfer function and a noise model having a predetermined high-order model order using the input / output data by a prediction error method;
A reduction means for reducing the order of the higher-order model by deriving a maximum likelihood estimate using an estimated higher-order model and a log likelihood function that is an evaluation function in the frequency domain;
The reduction means is
A frequency transfer function calculating means for obtaining a frequency transfer function of the higher order model;
Low-order model estimation means for obtaining an estimated value of a lower-order model having a lower order than the higher-order model order by minimizing the log likelihood function;
Sound image localization perception between a low-order model of each head-related transfer function and a high-order reference model, each of which is estimated by updating the low-order order and minimizing the log likelihood function A low-order model search means for searching for a low-order model when the feature-value error satisfies a predetermined permissible condition and has a minimum order, respectively,
An apparatus for modeling a head-related transfer function.   2. The head related transfer function modeling apparatus according to claim 1, wherein the feature amount related to the perception of sound image localization is a position of a spectral cue which is a peak and a notch on a frequency characteristic of the head related transfer function. The low-order model search means includes
Spectral distortion between the low-order model of each head-related transfer function estimated by the low-order model estimation means and the high-order reference model is obtained, and the spectral distortion is equal to or less than a predetermined first threshold value. And searching for a low-order model when an error between the spectral cue position and the high-order reference model satisfies a condition equal to or smaller than a predetermined second threshold value and becomes a minimum order. The head related transfer function modeling apparatus according to claim 2. The low-order model search means includes
Updating the low-order order in descending order from the high-order model order side and stopping the log likelihood function minimization process when the spectral distortion is greater than the first threshold;
The low-order order is updated in ascending order starting from the order when the spectral distortion is less than or equal to the first threshold, and an error between the spectral reference position and the high-order reference model is the second order. 4. The head-related transfer function modeling apparatus according to claim 3, wherein an order when a value falls below a threshold is determined as the lowest order. A head-related transfer function that models a head-related transfer function by an asymptotic estimation method using an input signal applied to the speaker and an output signal obtained by measuring the sound emitted from the speaker with a microphone as input / output data Modeling method,
Using the input / output data, a high-order model estimation step for estimating a high-order model for a head-related transfer function and a noise model having a predetermined high-order model order by a prediction error method;
A lowering step for lowering the higher order model by deriving a maximum likelihood estimate using an estimated higher order model and a log likelihood function that is an evaluation function in the frequency domain, ,
The dimension reduction step includes:
A frequency transfer function calculating step for obtaining a frequency transfer function of the higher order model;
A low-order model estimation step for obtaining an estimated value of a low-order model of an order lower than the high-order model order by minimizing the log likelihood function;
Sound image localization perception between a low-order model of each head-related transfer function and a high-order reference model, each of which is estimated by updating the low-order order and minimizing the log likelihood function A low-order model search step for searching for a low-order model when the feature-value error satisfies a predetermined permissible condition and has a minimum order,
A method for modeling a head related transfer function, comprising:   A head transfer function modeling program for causing a computer to function as the head transfer function modeling device according to claim 1.

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