CN103389155A - Digital image generation method of three-dimensional spatial distribution of sound quality objective parameters - Google Patents

Abstract

A digital image generation method of three-dimensional spatial distribution of sound quality objective parameters is performed according to the following steps of step1, recording holographic sound pressure data on the holographic measurement surface through a microphone array; step 2, performing acoustic amount reconstruction on a three-dimensional sound field; step 3, calculating the three-dimensional spatial distribution of the sound quality objective parameters such as loudness, sharpness and roughness of every point according to a sound pressure and sound quality objective parameter mapping model and obtained acoustic amount information in a three-dimensional space and providing in the form of a three-dimensional digital image to achieve three-dimensional spatial visualization of the sound quality objective parameters.

Description

The objective parameter three-dimensional spatial distribution of sound quality digital image generation method

Technical field:

The present invention relates to measurement assessment technique and the noise control technique of Nearfield acoustic holography, identification of sound source location technology, sound field visualization technique, the objective parameter of sound quality.

Background technology:

Traditional noise controls all to reduce sound pressure level that sound field responds as main target, and result of study shows that the reduction of sound pressure level can not substantially improve the subjective auditory perception of people to sound.Noise is not only relevant with sound pressure level for people's impact, also with the frequency of sound, forms, human auditory system's physical characteristics and psychological characteristic be relevant.The difference that two kinds of sound of same sound pressure level form due to frequency separately, the greatest differences that can cause people's loudness on mental impression, therefore need to introduce and can reflect that the people is to the quantizating index of sound subjectivity and objectivity impression-sound quality, as the reference to noise rating for the evaluation of noise.

The present invention is applied to that the objective parameter of sound quality in three-dimensional sound field distributes visual and with the space orientation of the closest sound source of people's auditory perception.When existing sound attributional analysis and measuring method are carried out the sound quality evaluation to the sound in the specified three-dimensional space, can only obtain the objective parameter information of sound quality of a certain measuring position of appointment in three dimensions, can not obtain distribution and the visual image of sound quality information in whole three dimensions, thereby not only can not estimate the sound quality quality of whole Enclosed Sound Field, more can not provide the locus with the sound source of sound correlation of attributes.

Summary of the invention:

The present invention will overcome the following shortcoming of prior art: overcome independent the use existing objective parameter measurement of sound quality, computational analysis and evaluation method and technology 1., sound quality profile and visual image in whole three dimensions can not be provided by one-shot measurement, the defect of the sound source position information relevant to the objective parameter of sound quality can not be provided.2. overcome the subjective auditory perception factor of not considering the people when independent employing near field acoustic holography methods analyst Enclosed Sound Field distributes, can not provide in sound field the defect with the closely-related sound source position of the subjective auditory perception of people.The invention provides the objective parameter three-dimensional digital image of the sound quality generation method that the near field acoustic holography method combines with the objective parametric analysis method of sound quality.

The objective parameter three-dimensional digital image of the sound quality generation method that the present invention proposes, its result of calculation is when providing the sound field distribution, also can provide the sound source spatial positional information that affects the subjective auditory perception maximum of people, and the image that the objective parameter of sound quality distributes in whole three dimensions is provided, thereby provides visual, the most directly instruct for noise reduction harmony quality improving.

The present invention carries out as follows:

1. utilize the holographic acoustic pressure data on microphone array (microphone array can be the spherical microphone array, hollow ball array of rigid surface, microphone array or the planar array conformal with the sound source structure) recording holographic measurement face.

Arrange spherical microphone array at Enclosed sound field, measure and record sound field acoustic pressure information.Can obtain holographic acoustic pressure data with plane microphone array and the conformal microphone array of other arbitrary shape in open and semi-open sound field.

2. three-dimensional sound field acoustics amount reconstruct

, according to the holographic acoustic pressure data that measure, obtain the distributed intelligence (acoustic pressure, normal direction particle rapidity and the normal direction sound intensity etc.) of Enclosed Sound Field acoustics amount by the near field acoustic holography method, and with the form of 3-D view, provide.

The holographic acoustic pressure that adopts spherical microphone array to measure comes the three-dimensional acoustics amount of reconstruct to distribute, and the sound field transformation for mula is as follows:

$p_t(r,\mathrm{\θ},\mathrm{\φ},\mathrm{\ω})\≈\underset{n=0}{\overset{N}{\mathrm{\Σ}}}(j_n\left(\mathrm{kr}\right)-\frac{j_n^{\′}\left(\mathrm{ka}\right)}{h_n^{\′}\left(\mathrm{ka}\right)}{j}_n\left(\mathrm{kr}\right))\underset{m=-n}{\overset{n}{\mathrm{\Σ}}}{A}_{\mathrm{mn}}{Y}_n^m(\mathrm{\θ},\mathrm{\φ})---\left(1\right)$

A in formula _mnBy being arranged, following formula determines:

$A_{\mathrm{mn}}=\frac{{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\mathrm{\π}}{p}_t(a,\mathrm{\θ},\mathrm{\φ})Y_n^m{(\mathrm{\θ},\φ)}^{*}\sin \mathrm{\θd\θd\φ}}{(j_n\left(\mathrm{ka}\right)-\frac{j_n^{\′}\left(\mathrm{ka}\right)}{h_n^{\′}\left(\mathrm{ka}\right)}{h}_n\left(\mathrm{ka}\right))}---\left(2\right)$

In following formula: (r, θ, φ) is the spherical coordinates of three dimensions any point in sound field; A is the radius of spherical microphone array, and k is wave number, and k=ω/c, ω are angular frequency, and c is the velocity of sound, ω=2 π f, and f is frequency.p _t(a, θ, φ) lists the holographic acoustic pressure data of collection for microphone array; p _t(r, θ, φ, ω) is the reconstruct acoustic pressure that three dimensions assigned address (r, θ, φ) is located; For spheric harmonic function, j _n(kr) be the ball Bessel function, h _n(kr) be ball Hunk function; " * " represents conjugation, " ' " the expression derivative, N is spheric harmonic function expansion item number.The position of Reconstruction of Sound Field point in specifying whole three dimensions, the acoustic pressure that obtains whole sound field distributes.

3., according to the sound field information in the three dimensions that obtains in 2, calculate the distribution of the three dimensions objective parameter of each point sound quality (as loudness, sharpness, roughness etc.), and with the form of 3-D view, provide, realize the three-dimensional visualization of the objective parameter of sound quality.

In sound field, single-point sound quality loudness computation model is as follows:

$N_i^{\&prime;}=\left\{\begin{array}{cc}C[{(G{E}_i+2E_{\mathrm{THRQ}})}^{\mathrm{\&alpha;}}-{\left(2E_{\mathrm{THRQ}}\right)}^{\mathrm{\&alpha;}}]& E_{\mathrm{THRQ}}<E_i<{10}^{10}\\ C\left(\frac{2E_i}{E_i+E_{\mathrm{THRQ}}}\right)[{(G{E}_i+2E_{\mathrm{THRQ}})}^{\mathrm{\&alpha;}}-{\left(2E_{\mathrm{THRQ}}\right)}^{\mathrm{\&alpha;}}]& E_i<E_{\mathrm{THRQ}}\\ C{\left(\frac{E_i}{1.0707}\right)}^{0.2}& E_i>{10}^{10}\end{array}\right.---\left(3\right)$

N ' in following formula _iBe the characteristic loudness of i wave filter, E _THRQFor listening valve energy level, E _iFor the energy level of signal, unit is dB, and C is definite value 0.046871, works as f _iDuring 500Hz, E _THRQFor definite value 2.3067, cochlea low-frequency gain G is that 1, α is 0.2, and works as f _iDuring＜500Hz, E _THRQ, α all can obtain according to the discrete data interpolation calculation that ANSI provides.G is the cochlea low-frequency gain.Therefore total loudness formula is:

$N=0.2\underset{i=1}{\overset{372}{\mathrm{\&Sigma;}}}{N}_i^{\&prime;}---\left(4\right)$

According to the three-dimensional spatial distribution result of acoustic pressure in the sound field that calculates in 2, and in conjunction with the computation model of the objective parameter of single-point sound quality in space, set up the coupling three-dimensional matrice mapping model of sonic pressure field and loudness field in space, that is:

${[p_i(r,\mathrm{\&theta;},\mathrm{\&phi;},{\mathrm{\&omega;}}_1)\&CenterDot;\&CenterDot;p_i(r,\mathrm{\&theta;},\mathrm{\&phi;},{\mathrm{\&omega;}}_m)]}_{1\&times;m}{\left[\begin{array}{ccc}{w}_1& \&CenterDot;\&CenterDot;& w_{372}\\ w_1& \&CenterDot;\&CenterDot;& w_{372}\\ \&CenterDot;& \&CenterDot;\&CenterDot;& \&CenterDot;\\ w_1& \&CenterDot;\&CenterDot;& w_{372}\end{array}\right]}_{m\&times;372}={[{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003409046400041.png,HDA00003409046400051.png"\; state="\{\{state\}\}">N</figure-callout>}}_1^{\&prime;}(r,\mathrm{\&theta;},\mathrm{\&phi;})\&CenterDot;\&CenterDot;N_{372}^{\&prime;}(r,\mathrm{\&theta;},\mathrm{\&phi;})]}_{1\&times;372}---\left(5\right)$

Or be abbreviated as:

P _iW=N′ (6)

In formula: (r, θ, φ) is the spherical coordinates that three dimensions i is ordered, ω _mFor angular frequency, ω _m=2 π f _m, f _mFor frequency, m=1,2 ... M, M are that frequency corresponding to different sound sources forms number.p _iFor the acoustic pressure under the arbitrary frequency in i point place in sound field, P _iFor the vector that the acoustic pressure reconstruction value under each frequency of i point place in sound field forms, W is the auditory filter matrix that is comprised of 372 wave filter w, the response of expression people ear to all frequencies in audio-band, and N ' is the characteristic loudness vector.Just can obtain the loudness of sound field specified point by formula (4) to the every summation in characteristic loudness vector N ', and sound field three dimensions node is repeated this computation process, just can obtain sound field loudness distributed in three dimensions result.The objective amount distributed in three dimensions of other sound quality result also can adopt with loudness and calculate similar analysis process acquisition, sees accompanying drawing 1.

Can provide the objective value of consult volume of sound quality of each position in detected space by said method, and with the form of 3-D view, provide its space distribution, and then can identify the sound source position that the subjective sense of hearing of people is had the greatest impact.

Description of drawings:

Fig. 1. the calculation flow chart of the objective parameter distributed in three dimensions of sound quality of the present invention

Fig. 2. the spherical microphone array schematic diagram

Fig. 3. spherical microphone array and double sound source sound field distribution schematic diagram

The loudness of Fig. 4 (a) .3.5kHz (69dB) and 1kHz (75dB) two point sound source sound fields and the contrast of acoustic pressure result of calculation

The sharpness of Fig. 4 (b) .3.5kHz (69dB) and 1kHz (75dB) two point sound source sound fields and the contrast of acoustic pressure result of calculation

The loudness of Fig. 4 (c) .3.5kHz (70dB) and 7kHz (76dB) two point sound source sound fields and the contrast of acoustic pressure result of calculation

The sharpness of Fig. 4 (d) .3.5kHz (70dB) and 7kHz (76dB) two point sound source sound fields and the contrast of acoustic pressure result of calculation

Specific embodiments:

The invention will be further described below by specific embodiment.With reference to accompanying drawing:

The objective parameter three-dimensional digital image of the sound quality generation method that the present invention proposes, its result of calculation is when providing the sound field distribution, also can provide the sound source spatial positional information that affects the subjective auditory perception maximum of people, and the image that the objective parameter of sound quality distributes in whole three dimensions is provided, thereby provides visual, the most directly instruct for noise reduction harmony quality improving.

The present invention carries out as follows:

1. utilize the holographic acoustic pressure data on microphone array (microphone array can be the spherical microphone array, hollow ball array of rigid surface, microphone array or the planar array conformal with the sound source structure) recording holographic measurement face.

Arrange spherical microphone array at Enclosed sound field, measure and record sound field acoustic pressure information.Can obtain holographic acoustic pressure data with plane microphone array and the conformal microphone array of other arbitrary shape in open and semi-open sound field.

2. three-dimensional sound field acoustics amount reconstruct

, according to the holographic acoustic pressure data that measure, obtain the distributed intelligence (acoustic pressure, normal direction particle rapidity and the normal direction sound intensity etc.) of Enclosed Sound Field acoustics amount by the near field acoustic holography method, and with the form of 3-D view, provide.

The holographic acoustic pressure that adopts spherical microphone array to measure comes the three-dimensional acoustics amount of reconstruct to distribute, and the sound field transformation for mula is as follows:

$p_t(r,\mathrm{\&theta;},\mathrm{\&phi;},\mathrm{\&omega;})\&ap;\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}(j_n\left(\mathrm{kr}\right)-\frac{j_n^{\&prime;}\left(\mathrm{ka}\right)}{h_n^{\&prime;}\left(\mathrm{ka}\right)}{j}_n\left(\mathrm{kr}\right))\underset{m=-n}{\overset{n}{\mathrm{\&Sigma;}}}{A}_{\mathrm{mn}}{Y}_n^m(\mathrm{\&theta;},\mathrm{\&phi;})---\left(1\right)$

A in formula _mnBy being arranged, following formula determines:

$A_{\mathrm{mn}}=\frac{{\&Integral;}_0^{2\mathrm{\&pi;}}{\&Integral;}_0^{\mathrm{\&pi;}}{p}_t(a,\mathrm{\&theta;},\mathrm{\&phi;})Y_n^m{(\mathrm{\&theta;},\&phi;)}^{*}\sin \mathrm{\&theta;d\&theta;d\&phi;}}{(j_n\left(\mathrm{ka}\right)-\frac{j_n^{\&prime;}\left(\mathrm{ka}\right)}{h_n^{\&prime;}\left(\mathrm{ka}\right)}{h}_n\left(\mathrm{ka}\right))}---\left(2\right)$

In following formula: (r, θ, φ) is the spherical coordinates of three dimensions any point in sound field; A is the radius of spherical microphone array, and k is wave number, and k=ω/c, ω are angular frequency, and c is the velocity of sound, ω=2 π f, and f is frequency.p _t(a, θ, φ) lists the holographic acoustic pressure data of collection for microphone array; p _t(r, θ, φ, ω) is the reconstruct acoustic pressure that three dimensions assigned address (r, θ, φ) is located;

For spheric harmonic function, j _n(kr) be the ball Bessel function, h _n(kr) be ball Hunk function; " * " represents conjugation, " ' " the expression derivative, N is spheric harmonic function expansion item number.The position of Reconstruction of Sound Field point in specifying whole three dimensions, the acoustic pressure that obtains whole sound field distributes.

3., according to the sound field information in the three dimensions that obtains in 2, calculate the distribution of the three dimensions objective parameter of each point sound quality (as loudness, sharpness, roughness etc.), and with the form of 3-D view, provide, realize the three-dimensional visualization of the objective parameter of sound quality.

In sound field, single-point sound quality loudness computation model is as follows:

$N_i^{\&prime;}=\left\{\begin{array}{cc}C[{(G{E}_i+2E_{\mathrm{THRQ}})}^{\mathrm{\&alpha;}}-{\left(2E_{\mathrm{THRQ}}\right)}^{\mathrm{\&alpha;}}]& E_{\mathrm{THRQ}}<E_i<{10}^{10}\\ C\left(\frac{2E_i}{E_i+E_{\mathrm{THRQ}}}\right)[{(G{E}_i+2E_{\mathrm{THRQ}})}^{\mathrm{\&alpha;}}-{\left(2E_{\mathrm{THRQ}}\right)}^{\mathrm{\&alpha;}}]& E_i<E_{\mathrm{THRQ}}\\ C{\left(\frac{E_i}{1.0707}\right)}^{0.2}& E_i>{10}^{10}\end{array}\right.---\left(3\right)$

N ' in following formula _iBe the characteristic loudness of i wave filter, E _THRQFor listening valve energy level, E _iFor the energy level of signal, unit is dB, and C is definite value 0.046871, works as f _iDuring 500Hz, E _THRQFor definite value 2.3067, cochlea low-frequency gain G is that 1, α is 0.2, and works as f _iDuring＜500Hz, E _THRQ, α all can obtain according to the discrete data interpolation calculation that ANSI provides.G is the cochlea low-frequency gain.Therefore total loudness formula is:

$N=0.2\underset{i=1}{\overset{372}{\mathrm{\&Sigma;}}}{N}_i^{\&prime;}---\left(4\right)$

According to the three-dimensional spatial distribution result of acoustic pressure in the sound field that calculates in 2, and in conjunction with the computation model of the objective parameter of single-point sound quality in space, set up the coupling three-dimensional matrice mapping model of sonic pressure field and loudness field in space, that is:

${[p_i(r,\mathrm{\&theta;},\mathrm{\&phi;},{\mathrm{\&omega;}}_1)\&CenterDot;\&CenterDot;p_i(r,\mathrm{\&theta;},\mathrm{\&phi;},{\mathrm{\&omega;}}_m)]}_{1\&times;m}{\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003409046400041.png,HDA00003409046400051.png"\; state="\{\{state\}\}">w</figure-callout>}}_1& \&CenterDot;\&CenterDot;& w_{372}\\ {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003409046400041.png,HDA00003409046400051.png"\; state="\{\{state\}\}">w</figure-callout>}}_1& \&CenterDot;\&CenterDot;& w_{372}\\ \&CenterDot;& \&CenterDot;\&CenterDot;& \&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003409046400041.png,HDA00003409046400051.png"\; state="\{\{state\}\}">w</figure-callout>}}_1& \&CenterDot;\&CenterDot;& w_{372}\end{array}\right]}_{m\&times;372}={[{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003409046400041.png,HDA00003409046400051.png"\; state="\{\{state\}\}">N</figure-callout>}}_1^{\&prime;}(r,\mathrm{\&theta;},\mathrm{\&phi;})\&CenterDot;\&CenterDot;N_{372}^{\&prime;}(r,\mathrm{\&theta;},\mathrm{\&phi;})]}_{1\&times;372}---\left(5\right)$

Or be abbreviated as:

P _iW=N′ (6)

In formula: (r, θ, φ) is the spherical coordinates that three dimensions i is ordered, ω _mFor angular frequency, ω _m=2 π f _m, f _mFor frequency, m=1,2 ... M, M are that frequency corresponding to different sound sources forms number.p _iFor the acoustic pressure under the arbitrary frequency in i point place in sound field, P _iFor the vector that the acoustic pressure reconstruction value under each frequency of i point place in sound field forms, W is the auditory filter matrix that is comprised of 372 wave filter w, the response of expression people ear to all frequencies in audio-band, and N ' is the characteristic loudness vector.Just can obtain the loudness of sound field specified point by formula (4) to the every summation in characteristic loudness vector N ', and sound field three dimensions node is repeated this computation process, just can obtain sound field loudness distributed in three dimensions result.The objective amount distributed in three dimensions of other sound quality result also can adopt with loudness and calculate similar analysis process acquisition, sees accompanying drawing 1.

In the present embodiment, all use ball array as measuring battle array, as shown in Figure 2, on sphere, non-uniform Distribution 36 microphones, and the spacing between microphone does not wait.

1. as shown in Figure 3, arrange two pulsation ball sources in space: the parameter of sound source 1 is set to 1kHz, 75dB, is placed on 0.3m place (0.3m, 0,0) on the x positive axis of rectangular coordinate system in space; The parameter of sound source 2 is set to 3.5kHz, 69dB, and the x that is placed on rectangular coordinate system in space bears 0.3m place (0.3m, 0,0) on semiaxis, and namely the angle theta between two sound sources is 180 °, and the radius a of spherical microphone array (as Fig. 2) is 0.1m.The computing method reconstruct radius that adopts the present invention to provide is the three-dimensional spatial distribution figure of acoustic pressure, loudness and the sharpness at 0.2m place.Fig. 4 (a) is the acoustic pressure of 2 liang of sound sources of sound source of the sound source 1 of 1kHz, 75dB and 3.5kHz, 69dB while existing simultaneously and the comparison diagram of the three-dimensional spatial distribution result of calculation of loudness.Fig. 4 (b) is the acoustic pressure of 2 liang of sound sources of sound source of the sound source 1 of 1kHz, 75dB and 3.5kHz, 69dB while existing simultaneously and the comparison diagram of the three-dimensional spatial distribution result of calculation of sharpness.

2. adopt equally 1 described double sound source sound-field model, but the parameter of sound source 1 is set to 7kHz, 70dB, is placed on 0.3m place (0.3m, 0,0) on the x positive axis of rectangular coordinate system in space; The parameter of sound source 2 is set to 3.5kHz, 76dB, and the x that is placed on rectangular coordinate system in space bears 0.3m place (0.3m, 0,0) on semiaxis, and the angle theta between two sound sources is still 180 °.Fig. 4 (c) and Fig. 4 (d) are respectively that to adopt this method reconstruct radiuses be the comparison diagram of three-dimensional spatial distribution result of calculation of acoustic pressure, loudness and the sharpness of the sphere at 0.2m place to 2 liang of sound sources of sound source of the sound source 1 of 7kHz, 70B and 3.5kHz, 76dB.

the result that the above-mentioned figure of comparative analysis provides, the acoustical holography method of identifying localization of sound source according to acoustic pressure from tradition is different, method provided by the invention can obtain the three-dimensional spatial distribution information of the objective parameter of sound quality of sound field, and identify and the closely-related sound source position information of the subjective sense of hearing of people, Fig. 4 has provided the three-dimensional spatial distribution figure of the objective parameters of sound quality such as loudness and sharpness, realized the auditory localization according to people's subjective auditory perception, comparison diagram 4 (a) and Fig. 4 (b), Fig. 4 (c) and Fig. 4 (d), the locus that can find the acoustic pressure maximum is not identical with the locus of loudness maximum, and the locus of loudness maximum is not identical with the locus of sharpness maximum yet.Therefore, locator key sound source that auditory perception subjective according to the people also takes appropriate measures and could really realize the purpose of sound field noise reduction harmony quality improving.

Claims (1)

1. the objective parameter three-dimensional spatial distribution of sound quality digital image generation method, carry out as follows:

Step 1. is utilized microphone array, and microphone array can be the spherical microphone array, hollow ball array of rigid surface, microphone array or the planar array conformal with the sound source structure, the holographic acoustic pressure data on recording holographic measurement face.

Sound field is arranged spherical microphone array in sealing, measures and record the acoustics amount information such as the holographic acoustic pressure of sound field.Can obtain holographic acoustic pressure data with plane microphone array and the conformal microphone array of other arbitrary shape in open and semi-open sound field.

The reconstruct of step 2. three-dimensional sound field acoustics amount

, according to the holographic acoustic pressure data that measure, obtain the distributed intelligence (acoustic pressure, normal direction particle rapidity and the normal direction sound intensity etc.) of Enclosed Sound Field acoustics amount by the near field acoustic holography method, and with the form of 3-D view, provide;

As adopt the holographic acoustic pressure that spherical microphone array is measured to come the three-dimensional acoustics amount of reconstruct to distribute, the sound field transformation for mula is as follows:

$p_t(r,\mathrm{\&theta;},\mathrm{\&phi;},\mathrm{\&omega;})\&ap;\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}(j_n\left(\mathrm{kr}\right)-\frac{j_n^{\&prime;}\left(\mathrm{ka}\right)}{h_n^{\&prime;}\left(\mathrm{ka}\right)}{j}_n\left(\mathrm{kr}\right))\underset{m=-n}{\overset{n}{\mathrm{\&Sigma;}}}{A}_{\mathrm{mn}}{Y}_n^m(\mathrm{\&theta;},\mathrm{\&phi;})---\left(1\right)$

A in formula _mnBy being arranged, following formula determines:

$A_{\mathrm{mn}}=\frac{{\&Integral;}_0^{2\mathrm{\&pi;}}{\&Integral;}_0^{\mathrm{\&pi;}}{p}_t(a,\mathrm{\&theta;},\mathrm{\&phi;})Y_n^m{(\mathrm{\&theta;},\&phi;)}^{*}\sin \mathrm{\&theta;d\&theta;d\&phi;}}{(j_n\left(\mathrm{ka}\right)-\frac{j_n^{\&prime;}\left(\mathrm{ka}\right)}{h_n^{\&prime;}\left(\mathrm{ka}\right)}{h}_n\left(\mathrm{ka}\right))}---\left(2\right)$

In following formula: (r, θ, φ) is the spherical coordinates of three dimensions any point in sound field; A is the radius of spherical microphone array, and k is wave number, and k=ω/c, ω are angular frequency, and c is the velocity of sound, ω=2 π f, and f is frequency.p _t(a, θ, φ) lists the holographic acoustic pressure data of collection for microphone array; p _t(r, θ, φ, ω) is the reconstruct acoustic pressure that three dimensions assigned address (r, θ, φ) is located;

For spheric harmonic function, j _n(kr) be the ball Bessel function, h _n(kr) be ball Hunk function; " * " represents conjugation, " ' " the expression derivative, N is spheric harmonic function expansion item number.The position of Reconstruction of Sound Field point in specifying whole three dimensions, the acoustic pressure that obtains whole sound field distributes;

Step 3. distributes according to the acoustic pressure in the three dimensions that obtains in step 2, calculates the distribution of the objective parameter of three dimensions each point sound quality, and with the form of 3-D view, provides, and realizes the three-dimensional visualization of the objective parameter of sound quality;

In sound field, single-point sound quality loudness computation model is as follows:

$N_i^{\&prime;}=\left\{\begin{array}{cc}C[{(G{E}_i+2E_{\mathrm{THRQ}})}^{\mathrm{\&alpha;}}-{\left(2E_{\mathrm{THRQ}}\right)}^{\mathrm{\&alpha;}}]& E_{\mathrm{THRQ}}<E_i<{10}^{10}\\ C\left(\frac{2E_i}{E_i+E_{\mathrm{THRQ}}}\right)[{(G{E}_i+2E_{\mathrm{THRQ}})}^{\mathrm{\&alpha;}}-{\left(2E_{\mathrm{THRQ}}\right)}^{\mathrm{\&alpha;}}]& E_i<E_{\mathrm{THRQ}}\\ C{\left(\frac{E_i}{1.0707}\right)}^{0.2}& E_i>{10}^{10}\end{array}\right.---\left(3\right)$

N ' in following formula _iBe the characteristic loudness of i wave filter, E _THRQFor listening valve energy level, E _iFor the energy level of signal, unit is dB, and C is definite value 0.046871, works as f _iDuring 500Hz, E _THRQFor definite value 2.3067, cochlea low-frequency gain G is that 1, α is 0.2, and works as f _iDuring＜500Hz, E _THRQ, α all can obtain according to the discrete data interpolation calculation that ANSI provides.G is the cochlea low-frequency gain.Therefore total loudness formula is:

$N=0.2\underset{i=1}{\overset{372}{\mathrm{\&Sigma;}}}{N}_i^{\&prime;}---\left(4\right)$

According to the three-dimensional spatial distribution result of acoustic pressure in the sound field that calculates in step 2, and in conjunction with the computation model of the objective parameter of single-point sound quality in space, set up the coupling of sonic pressure field and loudness field in space, the matrix mapping model is:

${[p_i(r,\mathrm{\&theta;},\mathrm{\&phi;},{\mathrm{\&omega;}}_1)\&CenterDot;\&CenterDot;p_i(r,\mathrm{\&theta;},\mathrm{\&phi;},{\mathrm{\&omega;}}_m)]}_{1\&times;m}{\left[\begin{array}{ccc}{w}_1& \&CenterDot;\&CenterDot;& w_{372}\\ w_1& \&CenterDot;\&CenterDot;& w_{372}\\ \&CenterDot;& \&CenterDot;\&CenterDot;& \&CenterDot;\\ w_1& \&CenterDot;\&CenterDot;& w_{372}\end{array}\right]}_{m\&times;372}={[N_1^{\&prime;}(r,\mathrm{\&theta;},\mathrm{\&phi;})\&CenterDot;\&CenterDot;N_{372}^{\&prime;}(r,\mathrm{\&theta;},\mathrm{\&phi;})]}_{1\&times;372}---\left(5\right)$

Or be abbreviated as:

P _iW=N′ (6)

In formula: (r, θ, φ) is the spherical coordinates that three dimensions i is ordered, ω _mFor angular frequency, ω _m=2 π f _m, f _mFor frequency, m=1,2 ... M, M are that frequency corresponding to different sound sources forms number.p _iFor the acoustic pressure under i point place assigned frequency in sound field, P _iFor the vector that the acoustic pressure reconstruction value under each frequency of i point place in sound field forms, W is the auditory filter matrix that is comprised of 372 wave filter w, the response of expression people ear to all frequencies in audio-band, and N ' is the characteristic loudness vector; Just can obtain the loudness of sound field specified point by formula (4) to the every summation in characteristic loudness vector N ', and sound field three dimensions node is repeated this computation process, just can obtain sound field loudness distributed in three dimensions result.

Images