A frequency-band modeling method for head-related transfer function based on spherical harmonic expansion

Abstract

The present application provides a head-related transfer function (HRTF) frequency band modeling method based on spherical harmonic expansion, wherein the method comprises: extracting the valley points of the HRTF amplitude spectrum of the mid-vertical plane and analyzing its center frequency; combining the distribution of the center frequency of the valley points with the division method of the equivalent rectangular bandwidth to obtain the target frequency band; using the spherical harmonic expansion to decompose the HRTF amplitude spectrum to different orders, and obtaining the spherical harmonic coefficients of the spherical harmonic basis functions corresponding to different orders by the least square method; according to the frequency range of the target frequency band, the spherical harmonic coefficients of the frequency points in the frequency band are retained at higher orders; based on the retained spherical harmonic coefficients, the HRTF amplitude spectrum corresponding to the target angle is obtained by using the inverse spherical harmonic transformation. The spherical harmonic modeling method based on the HRTF amplitude spectrum of the present invention achieves the goal of using fewer coefficients to model the HRTF by retaining higher-order coefficients of the target frequency band that affects binaural sound source localization.

Description

Technical Field

[0001] The present invention relates to a head-related transfer function frequency band modeling method based on spherical harmonic expansion. In particular, with regard to the problem of parameter quantity and computational complexity, the auditory localization characteristics are used to more accurately model the target frequency band, so as to increase the accuracy of sound source orientation perception by increasing a small number of parameters. The method provided by the present invention belongs to the field of audio signal processing. Background Art

[0002] Head Related Transfer Function (HRTF) plays an important role in spatial audio technology. It characterizes the process of sound waves from the sound source through physiological structures such as the head, auricle and torso to reach the eardrum of the human ear. HRTF is obtained by solving the sound signal collected by the microphone at the opening of the ear canal after the excitation signal is played by a spatially discrete speaker. Therefore, the existing HRTFs are all spatially discrete. However, in practical applications, spatially continuous HRTFs are often required for rendering binaural signals. The signal expansion method based on spherical harmonic basis functions is often used in the spatial modeling and interpolation of HRTF, but the modeling accuracy of this method is affected by the order of the spherical harmonic coefficients; in order to obtain a high-precision HRTF, a large number of spherical harmonic coefficients are often required, which affects the processing speed of the spatial audio system. Summary of the invention

[0003] The purpose of the present invention is to propose a frequency-band modeling method of head-related transfer function based on spherical harmonic expansion, which utilizes the sound source localization characteristics of the auditory system and uses more spherical harmonic coefficients to model the target frequency band, so as to achieve the goal of increasing the amount of parameters to improve the accuracy of sound source orientation perception under reasonable parameter quantity and computational complexity requirements.

[0004] To achieve the above object, the present invention proposes a head-related transfer function frequency band modeling method based on spherical harmonic expansion, the steps of which are as follows:

[0005] Step 1: Extract the valley point of the HRTF amplitude spectrum in the vertical plane and analyze its center frequency;

[0006] Step 2: Combine the distribution of valley center frequencies with the division method of equivalent rectangular bandwidth to obtain the target frequency band;

[0007] Step 3: Decompose the HRTF amplitude spectrum into different orders using spherical harmonic expansion, and obtain the spherical harmonic coefficients of the spherical harmonic basis functions corresponding to different orders by the least squares method;

[0008] Step 4: According to the frequency range of the target frequency band, the spherical harmonic coefficients of the frequency points within the frequency band are retained at a higher order;

[0009] Step 5: Based on the retained spherical harmonic coefficients, the HRTF amplitude spectrum corresponding to the target angle is obtained using the inverse spherical harmonic transform.

[0010] The specific steps of "extracting the valley point of the HRTF amplitude spectrum in the vertical plane and analyzing its center frequency" in step 1 are as follows:

[0011] The HRIR is obtained by removing the part of the head-related impulse response (HRIR) in the vertical plane of different subjects where the sampling value is approximately zero at the beginning (i.e., removing the transmission delay from the sound source to both ears). t ;

[0012] Calculating HRIR t The 10-12th order linear prediction residual r t , using a 1ms long half-Hanning window to intercept r t To eliminate the influence of trunk reflection on the spectrum valley point, we can get r t_w ;

[0013] Calculate r t_w The autocorrelation function r corr , using a 1ms long half-Hanning window to intercept r corr , we get r corr_w ;

[0014] Calculate r corr_w The group delay is determined by the minimum value of the group delay, which is the center frequency corresponding to the valley point of the HRTF amplitude spectrum.

[0015] The specific method of "combining the distribution of valley center frequencies with the division method of equivalent rectangular bandwidth to obtain the target frequency band" in step 2 is as follows:

[0016] According to the valley center frequency distribution obtained in step 1, combined with the auditory band division method under the Bark frequency scale, the 21st to 23rd critical frequency bands are selected as the target frequency bands.

[0017] The method of "using spherical harmonic expansion to decompose the HRTF amplitude spectrum into different orders" in step 3 is as follows:

[0018] Among them, the spherical harmonic expansion of the HRTF amplitude spectrum can be expressed as:

[0019]

[0020] Where k is the wave number, θ and They represent the horizontal angle and pitch angle of the corresponding HRTF, N represents the truncation order, are the desired spherical harmonic coefficients, represents the spherical harmonic basis function, n and m are integers, n represents the order of the spherical harmonic basis function, n≥0, m represents the degree of the spherical harmonic basis function, -n≤m≤n, Defined as:

[0021]

[0022] in, represents the adjoint Legendre polynomial of order n and degree m, is the real factor of spherical harmonics, defined as:

[0023]

[0024] The specific method of "obtaining the spherical harmonic coefficients of the spherical harmonic basis functions corresponding to different orders by the least squares method" in step 3 is as follows:

[0025] The spherical harmonic coefficients are expressed by the least squares method as follows:

[0026] a=(Y T Y+εD) -1 Y T h

[0027] where h = [H1, H2, ..., H L ] T represents the HRTF amplitude spectrum, H L represents the amplitude spectrum of the Lth HRTF, Y = [Y1, Y2, ..., Y L ] T represents the spherical harmonic basis function, Y L represents the Lth spherical harmonic basis function, represents the spherical harmonic coefficients, It is represented by the coefficients corresponding to the spherical harmonic basis functions of order N (subscript) and degree N (superscript), the subscript T represents the matrix transpose, D is the regularization matrix, and ε is the regularization control factor.

[0028] The method of "reserving the spherical harmonic coefficients of the frequency points in the target frequency band at a higher order according to the frequency range of the target frequency band" in step 4 is as follows:

[0029] The spherical harmonic coefficients of the target frequency band are retained using coefficients at least greater than 1st order.

[0030] The method of "obtaining the HRTF amplitude spectrum corresponding to the target angle by using the inverse spherical harmonic transform based on the retained spherical harmonic coefficients" in step 5 is as follows:

[0031] The calculation process is:

[0032]

[0033] Where f=ck represents the frequency, c represents the propagation speed of sound waves in the air, ROI represents the target frequency band, and N h With N l Respectively represent the retention order within and outside the target frequency band, Indicates that the horizontal angle is θ and the pitch angle is Modeling results of HRTF amplitude spectrum when the wave number is k.

[0034] The present invention proposes a frequency-band modeling method for head-related transfer function based on spherical harmonic expansion, and a method for modeling spatially discrete HRTF data based on spherical harmonic expansion. The spherical harmonic coefficients of the frequency band where the HRTF spectrum valley points are located are retained at a higher order by utilizing the perceptual characteristics of the auditory system, so that HRTF modeling with more accurate sound source orientation perception can be achieved using fewer spherical harmonic coefficients.

[0035] Through the above steps, the present invention realizes modeling suitable for HRTF and can greatly improve the sound source orientation rendering accuracy of HRTF while adding a few spherical harmonic coefficients to the frequency bands that are relatively important for orientation perception.

[0036] Based on the above steps, the head-related transfer function frequency band modeling method based on spherical harmonic expansion provided by the present invention can achieve the following effects:

[0037] 1. More accurate HRTF modeling in frequency bands that are relatively important for orientation perception.

[0038] 2: Improved HRTF spherical harmonic modeling method to achieve better HRTF azimuth rendering effect by adding fewer parameters.

[0039] 3: Using the frequency-band HRTF spherical harmonic modeling method can greatly reduce the computational complexity.

[0040] In summary, the present invention can model HRTF with fewer spherical harmonic coefficients to achieve higher positioning accuracy. Compared with the existing HRTF spherical harmonic domain modeling algorithm, the present invention has lower parameter quantity and lower computational complexity, thus showing wider applicability and stronger practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The following is a brief introduction to the drawings required for describing the embodiments or prior art.

[0042] Figure 1 A flowchart of a head-related transfer function frequency band modeling method based on spherical harmonic expansion provided in an embodiment of the present application. DETAILED DESCRIPTION

[0043] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar units or units with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as limiting the present application.

[0044] Figure 1 A flowchart of a head-related transfer function frequency band modeling method based on spherical harmonic expansion provided in an embodiment of the present application. Figure 1 The head-related transfer function frequency band modeling method shown in the figure has the following specific implementation steps S101-S105.

[0045] Step S101, extracting the valley points of the HRTF amplitude spectrum in the mid-vertical plane and analyzing the central frequency thereof.

[0046] Step S102: combining the distribution of the valley point center frequency with the division method of the equivalent rectangular bandwidth to obtain the target frequency band.

[0047] Step S103, decomposing the HRTF amplitude spectrum into different orders by using spherical harmonic expansion, and obtaining spherical harmonic coefficients of spherical harmonic basis functions corresponding to different orders by using the least square method.

[0048] Step S104: retaining higher-order spherical harmonic coefficients of frequency points within the target frequency band according to the frequency range of the target frequency band.

[0049] Step S105: Based on the retained spherical harmonic coefficients, an inverse spherical harmonic transform is used to obtain the HRTF amplitude spectrum corresponding to the target angle.

[0050] In a feasible implementation, before executing step S101, all head-related impulse responses (HRIRs) with a horizontal angle of 0° need to be selected from the database to extract valley points of the HRTF amplitude spectra in the vertical plane of different subjects and analyze their central frequencies.

[0051] In a feasible implementation, the HRIR is obtained by removing the portion of the HRIR sampling value at the initial stage of different subjects where the sampling value is approximately zero (i.e., removing the transmission delay from the sound source to the two ears). t ; Calculate HRIR t The 12th-order linear prediction residual r t , using a 1ms long half-Hanning window to intercept r t To eliminate the influence of trunk reflection on the spectrum valley point, we can get r t_w ; Calculate r t_w The autocorrelation function r corr , using a 1ms long half-Hanning window to intercept r corr , we get r corr_w ; Calculate r corr_wThe group delay is determined by the minimum value of the group delay, which is the center frequency corresponding to the valley point of the HRTF amplitude spectrum.

[0052] In a feasible implementation, the center frequencies corresponding to the valley points of the HRTF amplitude spectra of all subjects in the database are analyzed, and the 95% confidence interval of the center frequency distribution is selected, and the target frequency band is obtained by combining the division method of the equivalent rectangular bandwidth.

[0053] In a feasible implementation, based on the analyzed valley center frequency distribution and combined with the auditory band division method under the Bark frequency scale, the 21st to 23rd critical frequency bands (frequency range from 6.4kHz to 12kHz) are selected as the target frequency bands.

[0054] In a feasible implementation, the HRTF amplitude spectrum is decomposed into different orders using spherical harmonic expansion, and the spherical harmonic coefficients of the spherical harmonic basis functions corresponding to different orders are obtained by the least square method.

[0055] In one feasible implementation, the spherical harmonic expansion of the HRTF amplitude spectrum can be expressed as:

[0056]

[0057] Where k is the wave number, θ and They represent the horizontal angle and pitch angle of the corresponding HRTF respectively, N=4 represents the truncation order, are the desired spherical harmonic coefficients, represents the spherical harmonic basis function, n and m are integers, n represents the order of the spherical harmonic basis function, n≥0, m represents the degree of the spherical harmonic basis function, -n≤m≤n, Defined as:

[0058]

[0059] in, represents the adjoint Legendre polynomial of order n and degree m, is the real factor of spherical harmonics, defined as:

[0060]

[0061] In a feasible implementation, the spherical harmonic coefficients are expressed by the least square method as follows:

[0062] a=(Y T Y+εD) -1 Y T h

[0063] where h = [H1, H2, ..., H 25 ] T represents the HRTF amplitude spectrum, H25 represents the amplitude spectrum of the 25th HRTF, Y = [Y1, Y2, ..., Y 25 ] T represents the spherical harmonic basis function, Y 25 represents the 25th spherical harmonic basis function, represents the spherical harmonic coefficients, represents the coefficients corresponding to the spherical harmonic basis functions of order 4 (subscript) and degree 4 (superscript), the subscript T represents the matrix transpose, D is the regularization matrix, and ε is the regularization control factor.

[0064] In a feasible implementation, according to the frequency range of the target frequency band, the spherical harmonic coefficients of the frequency points in the frequency band are retained at a higher order, and the spherical harmonic coefficients of the target frequency band are retained using coefficients of at least order greater than 1.

[0065] In a feasible implementation, based on the retained spherical harmonic coefficients, the HRTF amplitude spectrum corresponding to the target angle is obtained by using the inverse spherical harmonic transform, and the calculation process is:

[0066]

[0067] Where f=ck represents the frequency, c represents the propagation speed of sound waves in the air, and ROI represents the target frequency band. Indicates that the horizontal angle is θ and the pitch angle is Modeling results of HRTF amplitude spectrum when the wave number is k, N h =4 and N l =3 represents the retention order within and outside the target frequency band, respectively, indicating that more accurate HRTF modeling is performed on the frequency band ROI that is relatively important for orientation perception.

[0068] In a feasible implementation, the auditory localization performance of the improved HRTF modeling method and the existing HRTF modeling method is compared based on the auditory localization model. The positioning effects of the three modeling results, HRTF obtained by 3rd-order spherical harmonic modeling (existing method), HRTF obtained by 4th-order spherical harmonic modeling (existing method), and HRTF with 4th-order modeling in the target frequency band and 3rd-order modeling in the non-target frequency band (improved method), are compared. The results show that the existing modeling method adds 1161 coefficients (the modeling order of the entire frequency band is increased from 3rd order to 4th order) to achieve a 3.61° positioning accuracy improvement, and the improved method adds 270 coefficients (only the modeling order of the target frequency band is increased from 3rd order to 4th order) to achieve a 1.89° positioning accuracy improvement. The improved method uses 1 / 4 of the additional coefficients to achieve a 1 / 2 positioning accuracy improvement. Therefore, compared with the existing HRTF spherical harmonic domain modeling algorithm, the invention has a lower parameter amount and lower computational complexity, and thus exhibits a wider range of applicability and stronger practicality.

[0069] The present invention is a method for modeling spatially discrete HRTF data based on spherical harmonic expansion. It utilizes the perceptual characteristics of the auditory system to retain the spherical harmonic coefficients of the frequency band where the HRTF spectrum valley points are located at a higher order, so that HRTF modeling with more accurate sound source orientation perception can be achieved with fewer spherical harmonic coefficients.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and do not limit it. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A frequency band modeling method of head-related transfer function based on spherical harmonic expansion, characterized in that: Here are the steps: Step 1: Extract the valley point of the HRTF amplitude spectrum in the vertical plane and analyze its center frequency; Step 2: Combine the distribution of valley center frequencies with the division method of equivalent rectangular bandwidth to obtain the target frequency band; Step 3: Decompose the HRTF amplitude spectrum into different orders using spherical harmonic expansion, and obtain the spherical harmonic coefficients of the spherical harmonic basis functions corresponding to different orders by the least squares method; Step 4: According to the frequency range of the target frequency band, the spherical harmonic coefficients of the frequency points within the frequency band are retained at a higher order; Step 5: Based on the retained spherical harmonic coefficients, the HRTF amplitude spectrum corresponding to the target angle is obtained using the inverse spherical harmonic transform.

2. The head-related transfer function frequency band modeling method based on spherical harmonic expansion according to claim 1, characterized in that: Extract the valley point of the HRTF amplitude spectrum of the mid-plane as described in step 1 and analyze its center frequency. The specific method is as follows: remove the part of the head-related impulse response HRIR of the mid-plane of different subjects whose sampling value is approximately zero at the beginning stage, that is, remove the transmission delay from the sound source to the two ears, and obtain the HRIR t ; Calculating HRIR t The 10th to 12th order linear prediction residual r t , using a 1ms long half-Hanning window to intercept r t To eliminate the influence of trunk reflection on the spectrum valley point, we can get r t_w ; Calculate r t_w The autocorrelation function r corr , using a 1ms long half-Hanning window to intercept r corr , we get r corr_w ; Calculate r corr_w The group delay is determined by the minimum value of the group delay, which is the center frequency corresponding to the valley point of the HRTF amplitude spectrum.

3. The head-related transfer function frequency band modeling method based on spherical harmonic expansion according to claim 1, characterized in that: The target frequency band is obtained by combining the distribution of the valley center frequency and the division method of the equivalent rectangular bandwidth described in step 2. The specific method is as follows: According to the distribution of the valley center frequency obtained by the analysis in step 1, combined with the auditory band division method under the Bark frequency scale, the 21st to 23rd critical frequency bands are selected as the target frequency band.

4. The head-related transfer function frequency band modeling method based on spherical harmonic expansion according to claim 1, characterized in that: The HRTF amplitude spectrum is decomposed into different orders using spherical harmonic expansion as described in step 3. The method is as follows: The spherical harmonic expansion of the HRTF amplitude spectrum is expressed as: Where k is the wave number, θ and They represent the horizontal angle and pitch angle of the corresponding HRTF, N represents the truncation order, are the desired spherical harmonic coefficients, represents the spherical harmonic basis function, n and m are integers, n represents the order of the spherical harmonic basis function, n≥0, m represents the degree of the spherical harmonic basis function, -n≤m≤n, Defined as: in, represents the adjoint Legendre polynomial of order n and degree m, is the real factor of spherical harmonics, defined as:

5. The head-related transfer function frequency band modeling method based on spherical harmonic expansion according to claim 1, characterized in that: The spherical harmonic coefficients of the spherical harmonic basis functions corresponding to different orders are obtained by the least squares method as described in step 3. The specific steps are as follows: The spherical harmonic coefficients are expressed by the least squares method as follows: a=(Y T Y+εD) -1 Y T h where h = [H1, H2, ..., H L ] T represents the HRTF amplitude spectrum, H L represents the amplitude spectrum of the Lth HRTF, Y = [Y1, Y2, ..., Y L ] T represents the spherical harmonic basis function, Y L represents the Lth spherical harmonic basis function, represents the spherical harmonic coefficients, It is represented by the coefficients corresponding to the spherical harmonic basis functions, the subscript T represents the matrix transpose, D is the regularization matrix, and ε is the regularization control factor.

6. The head-related transfer function frequency band modeling method based on spherical harmonic expansion according to claim 1, characterized in that: According to the frequency range of the target frequency band as described in step 4, the spherical harmonic coefficients of the frequency points in the frequency band are retained at a higher order, and the method is as follows: the spherical harmonic coefficients of the target frequency band are retained using coefficients of at least order greater than 1.

7. The head-related transfer function frequency band modeling method based on spherical harmonic expansion according to claim 1, characterized in that: Based on the retained spherical harmonic coefficients described in step 5, the HRTF amplitude spectrum corresponding to the target angle is obtained by using the inverse spherical harmonic transformation, which is performed as follows: The calculation process is: Where f=ck represents the frequency, c represents the propagation speed of sound waves in the air, ROI represents the target frequency band, and N h With N l Respectively represent the retention order within and outside the target frequency band, Indicates that the horizontal angle is θ and the pitch angle is Modeling results of HRTF amplitude spectrum when the wave number is k.

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