CN110708647A - Spherical distribution guided data matching stereo field reconstruction method - Google Patents
Spherical distribution guided data matching stereo field reconstruction method Download PDFInfo
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Abstract
The invention provides a sphere distribution guided data matching stereo sound field reconstruction method, which adopts the principle that an omnidirectional microphone array accurately collects and reconstructs high-order spherical harmonic components of a sound field, provides a data matching stereo sound field reconstruction method based on sphere distribution, and is divided into a stereo sound field collection stage and a stereo sound field reconstruction stage. The comparative experiment with the grid allocation method shows that: when the signal frequency is 1kHz, the number of the spherical distribution matching points is reduced by 56.2%, the reconstruction average error is reduced by 44.3%, the reconstruction performance of the three-dimensional sound field is greatly improved by adopting the spherical distribution matching points, the number of the matching points is reduced, the problem of matrix irreversible in grid distribution is solved fundamentally, and a new and better matching point selection scheme is provided for reconstructing the three-dimensional sound field by using data matching.
Description
Technical Field
The invention relates to a data matching stereo field reconstruction method, in particular to a sphere distribution guided data matching stereo field reconstruction method, and belongs to the technical field of stereo field reconstruction methods.
Background
Stereo audio technology has received much attention in recent years, and is gradually moving from large screens to small viewing environments such as homes and personal mobile terminals. Stereo is sound with three-dimensional sense, and compared with single sound channel, stereo has the direction sense and the distribution sense of each sound source, improves the definition and the intelligibility of information, and improves the presence sense, the layering sense and the transparency of audio. The rapid development of the stereo audio and video technology cannot be separated from the rapid soaring of the economic society and the rapid improvement of the entertainment experience demand, and is a result of the rapid development of the scientific technology. If a user wants to provide high-quality three-dimensional experience, stereo audio and three-dimensional video must work and be displayed synchronously, equipment supporting three-dimensional video playing in the market is endless, such as red and blue three-dimensional, polarization three-dimensional, even naked eye 3D and the like, the development and application of the stereo audio technology are relatively backward, traditional low-quality audio still occupies most of audio markets, even home theaters and movie theaters.
The audio expert Senhaisel has introduced a breakthrough technology based on stereo scene immersive audio, realizes audio acquisition and playback, and converts the hearing experience of users into various applications from virtual reality games to audio recording and broadcasting. The stereo audio technology mainly comprises a plurality of basic steps of acquisition, encoding and reconstruction, the audio acquisition in the prior art has more technical schemes, but the stereo audio sound field reconstruction technology and the encoding compression technology have obvious shortages, the spatial parameter information contained in the stereo audio and multi-channel signals brought by the reconstruction technology based on a loudspeaker array can cause the sharp increase of the data volume of the stereo audio in the coding and decoding link, however, the coding and decoding link can not discard the spatial parameter information to achieve the purpose of reducing the data volume, so the sound field reconstruction link is the key for ensuring the immersive experience and the data volume control of multi-channel signals, and the prior art has various problems of obvious distortion, large reconstruction error, serious data redundancy, low running speed and the like in the stereo sound field reconstruction link.
The stereo sound field reconstruction based on the loudspeaker array takes an original sound field of a listening area as an ideal sound field, sound waves emitted by loudspeakers are overlapped through redistribution of loudspeaker signal weights, a stereo sound field identical to the original sound field is synthesized in a target listening area, and listeners can feel spatial stereo direction sense consistent with the original sound source in the reconstructed listening area. The signal weight of the loudspeaker changes with the change of the position of the listening area and the original sound source azimuth information, the prior art is limited by the sound field reconstruction technology, the position of the listening area can only be positioned at the center of the loudspeaker array, in order to enable more listeners to enjoy the fun brought by stereo audio, the main approach is to increase the number of the loudspeakers and reconstruct a larger stereo listening area, however, the loudspeaker arrays with excessive number and strict geometric distribution are not easy to realize in a general large-scale high-end film watching place, and the loudspeaker arrays are not applied in a small-scale common film watching environment such as a family. In the research of stereo field reconstruction based on loudspeaker arrays, how to adopt a smaller number of loudspeakers and how to reconstruct listening areas capable of accommodating multiple persons simultaneously is a practical and creative problem. The mainstream sound field reconstruction technology in the prior art is mainly aimed at simple reconstruction of a central area, for example, in sound field reconstruction based on an NHK22.2 multi-channel system of a japanese broadcasting company, when the number of speakers is 22, the radius of the reconstruction area is only 0.216 meter, and only the requirement of a single person can be met.
In summary, the plant identification and classification method in the prior art mainly has the following defects: firstly, the stereo audio sound field reconstruction technology and the coding compression technology in the prior art have obvious shortcuts, and spatial parameter information contained in stereo audio and multi-channel signals brought by the reconstruction technology based on a loudspeaker array can cause the data volume of the stereo audio to increase rapidly in the coding and decoding link, but the coding and decoding link can not discard the spatial parameter information to achieve the purpose of reducing the data volume, so that the sound field reconstruction link is the key for ensuring immersive experience and controlling the data volume of the multi-channel signals, and the prior art also has various problems of obvious distortion, large reconstruction error, serious data redundancy, low running speed and the like in the stereo sound field reconstruction link; secondly, in the prior art, because of the limitation of the sound field reconstruction technology, the listening area can only be positioned in the center of the loudspeaker array, in order to enable more listeners to enjoy the pleasure brought by stereo audio, the main approach is to increase the number of loudspeakers and reconstruct a larger stereo listening area, however, the loudspeaker arrays with excessive number and severe geometric distribution are not easy to realize in a general large-scale high-end film watching place, and not to say that the loudspeaker arrays are applied in small-scale common film watching environments such as a family, in the stereo sound field reconstruction research based on the loudspeaker arrays, how to adopt a smaller number of loudspeakers, and the reconstruction of the listening area capable of accommodating multiple persons simultaneously is a difficult problem with practicability and creativity; in the prior art, the data matching stereo field reconstruction method has the advantages that the matching points are uniformly distributed in a grid mode and are independent of the geometric arrangement of the loudspeakers, linear correlation equation sets can be constructed by the matching points on the same straight line and the same plane, the matrix is irreversible, the global optimal solution cannot be obtained, the spatial distribution of the matching points is unreasonable, the number of the matching points is too large, the reconstruction average error is high, the stereo field reconstruction performance is poor, the efficiency is low, the cost is high, errors are more, and the accuracy and the reliability of the stereo field reconstruction are not enough.
Disclosure of Invention
Aiming at the defects of the prior art, the spherical distribution guided data matching stereo field reconstruction method provided by the invention adopts the principle that the omnidirectional microphone array accurately collects and reconstructs the high-order spherical harmonic component of the sound field, provides a data matching stereo field reconstruction method based on spherical distribution, and comprises a stereo field collection stage and a stereo field reconstruction stage, in the stereo field collection stage, based on the spherical harmonic analysis theory, a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface is used for developing a high-order spherical harmonic component collection system, spherical harmonic coefficients corresponding to a stereo field in a central reconstruction area are collected, in the stereo field reconstruction stage, the omnidirectional microphone array is used for collecting spherical harmonic coefficients, and the accurate reconstruction of the stereo field is realized based on the high-order environment stereo mixed sound stereo field reconstruction method to obtain complete spatial distribution of matching points. The comparative experiment with the grid allocation method shows that: when the signal frequency is 1kHz, the number of spherical distribution matching points is reduced by 56.2%, the reconstruction average error is reduced by 44.3%, the reconstruction performance of the stereo sound field is greatly improved by adopting the spherical distribution matching points, the number of the matching points is reduced, the problem of matrix irreversible in grid distribution is solved more fundamentally, a new and better matching point selection scheme is provided for reconstructing the stereo sound field by using data matching, the spatial distribution of the matching points is reasonable, the number of the matching points is scientifically set, the reconstruction performance of the stereo sound field is good, the efficiency is high, the cost is low, errors are few, and the reconstruction accuracy and reliability of the stereo sound field are high.
In order to achieve the technical effects, the technical scheme adopted by the invention is as follows:
a sphere distribution guided data matching stereo field reconstruction method is characterized in that high-order spherical harmonic component of a sound field is accurately collected and reconstructed based on an omnidirectional microphone array, the method is divided into a stereo field collection stage and a stereo field reconstruction stage, in the stereo field collection stage, a high-order spherical harmonic component collection system is developed by using a group of omnidirectional microphone arrays which are uniformly and axially distributed on a sphere based on a spherical harmonic function analysis theory, spherical harmonic coefficients corresponding to a stereo field in a central reconstruction area are collected, in the stereo field reconstruction stage, the spherical harmonic coefficients are collected by using the omnidirectional microphone arrays, and the accurate reconstruction of the stereo field is realized based on a high-order environment stereo mixed sound stereo field reconstruction method;
a sphere distribution guided data matching stereo field reconstruction method comprises four steps:
firstly, a stereo sound field is collected, and a high-order spherical harmonic component collecting system is developed by using a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface;
secondly, reconstructing a first stereo field, and obtaining a linear relation between the optimal sphere radius distributed by the matching points and the sphere radius of a reconstruction region according to a spherical distribution matching point configuration rule;
thirdly, reconstructing a stereo sound field, namely calculating the number of matching points distributed by the spherical surface according to a spherical surface distribution matching point selecting method;
and fourthly, reconstructing a three-dimensional sound field, and obtaining complete spatial distribution of the spherical distribution matching points according to the arrangement rule of the omnidirectional microphone array.
A sphere distribution guided data matching stereo field reconstruction method is further characterized in that a sphere distribution matching point selection method is used for selecting matching points, the principle of spherical harmonic orthogonal decomposition is followed, linear correlation does not exist in a constructed equation set, and a global optimal solution is obtained by directly solving;
in the method for selecting the spherical distribution matching points, a sound field is expressed and reconstructed by linear combination of a group of orthogonal spherical harmonic functions through environment stereo mixed sound, a high-order spherical harmonic component collecting system is developed by a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface on the basis of a spherical harmonic analysis theory, spherical harmonic coefficients corresponding to an ideal stereo field in a central reconstruction area are collected by the omnidirectional microphone arrays, the spherical harmonic coefficients are collected, and the accurate reconstruction of the stereo field is realized on the basis of a high-order environment stereo mixed sound stereo field reconstruction method.
A sphere distribution guided data matching stereo field reconstruction method is further characterized in that in a stereo field collection stage, based on a spherical harmonic analysis theory, a group of omnidirectional microphone arrays uniformly and axially distributed on a sphere are used for developing a high-order spherical harmonic component collection system, spherical harmonic coefficients corresponding to an ideal stereo field in a central reconstruction area are collected, and a sound field with a matching point x ═ theta, phi, x) epsilon omega is represented by a spherical harmonic function:
wherein f isnm(k) For spherical harmonic coefficients, n (0. ∞) and m (m ═ n.. times, n) are integers, n is the ambient stereo mix sound order, j is the ambient stereo mix sound order, andn(. is a spherical Bessel function of order n, Ynm(x) For spherical harmonics, the spherical harmonics expansion follows the following orthogonal decomposition behavior:
wherein the symbol "+" denotes conjugation, δnpThe method is characterized in that the method is a Kronek delta function, an integral domain is a unit sphere, and spherical harmonic coefficients are obtained through separation:
c (x; k) is the sound field of the sound source at the point x of reception in the reconstruction zone, when sufficientA plurality of sample points are distributed on the spherical surface with the radius of x, and when the sound pressure value corresponding to each sample point is known, the spherical harmonic coefficient f can be accurately calculatednm(k) If the microphone is a high-order sound field, the spherical harmonic coefficient f corresponding to the sound field surrounding the microphone can be collectednm(k)；
The invention utilizes a group of omnidirectional microphone group arrays distributed in different axial directions of a three-dimensional spherical surface in space according to proper positions to realize the accurate collection of high-order spherical harmonic coefficients, changes unit spherical integral into discrete summation, sets the number of omnidirectional microphones distributed on the spherical surface with the radius of R as A, and represents the sound field corresponding to each microphone as C (x)a(ii) a k) 1, a, formula:
the approximation is written as:
wherein a 1., a, ωaDeriving, for a set of appropriate weights, a relationship between the number of omni-directional microphones and the order N that satisfies:
A≥(N+1)2，
the omnidirectional microphones are arranged in a spherical surface mode that a ball is divided into grids according to an altitude angle and a horizontal angle, each omnidirectional microphone comprises information of the altitude angle and the horizontal angle, and the number of the omnidirectional microphones is at least (2N-1)2And the spherical surfaces are uniformly distributed at equal intervals.
A sphere distribution guided data matching stereo field reconstruction method further comprises the steps of obtaining a linear relation between the optimal sphere radius distributed by a matching point and the sphere radius of a reconstruction area according to a sphere distribution matching point configuration rule in a stereo field reconstruction stage;
when the sound field is reconstructed by adopting the environment stereo mixed sound technology, the loudspeaker array strictly meets the geometrical characteristics of spherical distribution and is formed by the radius x of a reconstruction area0The relationship between the number of the stereo mixed sound and the number N of the environment is respectively obtained to obtain the reconstruction radius rmaxIs 0.272m and 0.326m, selecting enough sphere distribution matching points, setting the number of the sphere distribution matching points to be 144, setting the increase interval of the radius of the distribution sphere to be 0.02m, and respectively leading the radius r to be reconstructedmaxIncreasing the distance from 0.01m to 0.272m and 0.326m, calculating the average reconstruction error of the sample points distributed on the equatorial plane of the radius sphere once per cycle, and storing the current radius and the average error value for the corresponding radius when the observation error of the later drawing is minimum, namely the optimal distribution radius to be found;
according to the curve that the reconstruction average error of 36-and 49-loudspeaker arrays of environment stereo mixed sound changes along with the radius, the radius value corresponding to the minimum error is taken, the point distribution of 36-loudspeaker arrays corresponds to 0.16m, the point distribution of 49-loudspeaker arrays corresponds to 0.20m, the ratio of the optimal sample point distribution radius to the sphere radius of the reconstruction area is calculated,
u1＝0.16/0.272＝58.8％；u2＝0.20/0.326＝61.3％
taking the average value of the two, the proportionality coefficient is 0.60, and inducing the relation between the best distribution sphere radius of the matching point and the sphere radius of the reconstruction area:
rbest＝0.60rmax。
a sphere distribution guided data matching stereo field reconstruction method, further, in the stereo field reconstruction stage, according to the sphere distribution matching point selection method, calculate the sphere distribution matching point number;
finding the radius r from the known reconstruction regionmaxThe method of selecting matching point gridding includes that firstly, grid is divided on xoy plane, matching points are distributed on the intersection points of horizontal lines and vertical lines, enough discrete loudspeakers can approximately express kirchhoff's integral theorem formula, ideal wave field synthesis effect requires loudspeaker sets to be at least smaller than half wavelength of highest frequency, so that the interval w of adjacent horizontal lines or vertical lines is regulated to be smaller than the highest frequency z in signal max1/2 for the wavelength of the acoustic signal, the spacing w defining adjacent horizontal or vertical lines is selected to be the highest frequency z of the signal max1/4 for the wavelength of the acoustic signal, i.e. w ═ c/(4 z)max) And the number of the single-layer matching points can be well determined by setting the density of the matching points as follows:
c is the speed of sound, sign
Representing the smallest integer greater than or equal to a given expression, a z-axis division interval of 0.01, and a range of [0.1r ]max，0.1rmax]Obtaining the number of layers of longitudinal matching points Nportrait＝20rmax+1, the total number of points is Ngrid＝NportraitNxoyGiven the density of matching points, 1/2, i.e. N, is calculated for the number of matching points in the spherical distribution as the number of gridded matching points under the same conditionround＝NgridAnd/2, if the number of the grid distribution matching points is NgridIf 520, the number of the sphere distribution matching points is determined to be 260, and the number of the sphere distribution matching points is considered to be the square of one number, and finally set to be Nround＝162256 for same reason, if Ngrid175 according to the above rule Nround＝132＝169。
A sphere distribution guided data matching stereo field reconstruction method is further characterized in that point cloud contour dimension values of different plants are obviously different in plant classification based on point cloud fractal features, the dimension value corresponding to each tree can be found out through experiments or experiences, plant types are distinguished by the aid of the plant three-dimensional point cloud contour dimension values, and single plants are efficiently identified and classified.
Compared with the prior art, the invention has the advantages that:
1. the invention provides a sphere distribution guided data matching stereo field reconstruction method, which adopts the principle that an omnidirectional microphone array accurately collects and reconstructs high-order spherical harmonic component of a sound field, and provides a data matching stereo field reconstruction method based on sphere distribution. The comparative experiment with the grid allocation method shows that: when the signal frequency is 1kHz, the number of the spherical distribution matching points is reduced by 56.2%, the reconstruction average error is reduced by 44.3%, the reconstruction performance of the three-dimensional sound field is greatly improved by adopting the spherical distribution matching points, the number of the matching points is reduced, the problem of matrix irreversible in grid distribution is solved fundamentally, and a new and better matching point selection scheme is provided for reconstructing the three-dimensional sound field by using data matching.
2. According to the sphere distribution guided data matching stereo sound field reconstruction method, the sound field reconstruction technology can be used for knowing that the sound field reconstruction method based on data matching has the defects that the determination of the number of matching points is lack of guidance, the number of matching points and the distribution form directly influence the solution of an equation set, fewer matching points can cause under-fitting, the reconstruction error is larger, and the excessive matching points can directly cause overlarge calculated amount. The method is based on the principle that the omnidirectional microphone array can accurately collect the spherical harmonic component of an ideal stereo field, provides the data matching stereo field reconstruction based on spherical distribution, and directly avoids the construction of a linear correlation equation set by matching points following the spherical axial distribution principle of the omnidirectional microphone array, thereby ensuring the reversibility of a matrix without redundancy and obtaining the global optimal solution. The spatial distribution of the matching points is reasonable, the number of the matching points is scientifically set, the reconstruction performance of the stereo field is good, the efficiency is high, the cost is low, the error is few, and the reconstruction accuracy and reliability of the stereo field are high.
3. The sphere distribution guided data matching stereo field reconstruction method solves the problem that the stereo audio and sound field reconstruction technology and the coding compression technology in the prior art are obviously short, the spatial parameter information contained in stereo audio and multi-channel signals brought by the reconstruction technology based on a loudspeaker array can cause the sharp increase of the data volume of the stereo audio in the coding and decoding link, however, the coding and decoding link can not discard the spatial parameter information to achieve the purpose of reducing the data volume, so the sound field reconstruction link is the key for ensuring immersive experience and multi-channel signal data volume control.
4. The invention provides a sphere distribution guided data matching stereo field reconstruction method, which solves the problems that in the prior art, due to the limitation of a sound field reconstruction technology, the position of a listening area can only be positioned in the center of a loudspeaker array, and in order to enable more listeners to enjoy the pleasure brought by stereo audio, the main approach is to increase the number of loudspeakers and reconstruct a larger stereo listening area, but the loudspeaker arrays with excessive number and severe geometric distribution are not easy to realize in a general large-scale high-end video watching place, and the reconstruction method is not applied to small-scale common video watching environments such as families.
Drawings
Fig. 1 is a step diagram of a sphere distribution guided data matching stereo field reconstruction method according to the present invention.
Fig. 2 is a schematic diagram of the omnidirectional microphone array spherical axial distribution of the present invention.
Fig. 3 is a comparison graph of the third order stereo field collected by the real and high order microphones of the present invention.
Fig. 4 is a schematic diagram of the mesh matching point assignment and the spherical matching point assignment of the present invention.
Detailed Description
The following describes a technical solution of the sphere distribution guided data matching stereo field reconstruction method provided by the present invention with reference to the accompanying drawings, so that those skilled in the art can better understand the present invention and can implement the method.
Referring to fig. 1 to 4, the sphere distribution guided data matching stereo field reconstruction method provided by the present invention is based on the accurate collection and reconstruction of high-order spherical harmonic components of a sound field by an omnidirectional microphone array, and is divided into a stereo field collection stage and a stereo field reconstruction stage, wherein in the stereo field collection stage, based on a spherical harmonic function analysis theory, a set of omnidirectional microphone arrays uniformly and axially distributed on a sphere is used to develop a high-order spherical harmonic component collection system, and spherical harmonic coefficients corresponding to a stereo field in a central reconstruction region are collected, and in the stereo field reconstruction stage, the omnidirectional microphone arrays are used to collect spherical harmonic coefficients, and based on the high-order environment stereo mixed sound stereo field reconstruction method, the accurate reconstruction of the stereo field is realized, and the method comprises four steps:
firstly, a stereo sound field is collected, and a high-order spherical harmonic component collecting system is developed by using a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface;
secondly, reconstructing the stereo sound field, and obtaining a linear relation between the optimal sphere radius distributed by the matching points and the sphere radius of a reconstruction region according to the configuration rule of the spherical distribution matching points;
thirdly, reconstructing a stereo field, and calculating the number of matching points distributed by the spherical surface according to a spherical surface distribution matching point selecting method;
and fourthly, obtaining complete spatial distribution of the spherical distribution matching points according to the arrangement rule of the omnidirectional microphone array.
First, sphere distribution matching point selection method
The method aims at the problems that a large amount of redundancy of matching points is distributed to grids, a data matching matrix is irreversible, an optimal solution cannot be obtained, meanwhile, when the number of the matching points is selected to be too small, data is not fitted to obtain a global optimal solution, and when the number of the matching points is selected to be too large, the calculated amount is increased rapidly. The invention provides a matching point selection method for spherical distribution based on the principle that an omnidirectional microphone array accurately collects and reconstructs high-order spherical harmonic component of a sound field, matching points follow the spherical harmonic orthogonal decomposition principle, no matching point redundancy exists, no linear correlation exists in a constructed equation set, the problem of irreversible data matching matrix is solved, and the global optimal solution can be directly obtained by solving.
The environment stereo mixed sound (Ambisonics) can express and reconstruct a sound field by using a group of orthogonal linear combination of spherical harmonic functions, and in the sound field reconstruction technology of the high-order environment stereo mixed sound, accurately calculating the spherical harmonic coefficient corresponding to an ideal stereo sound field is an extremely important step, and directly influences the stereo sound field reconstruction effect. Therefore, gathering higher order spherical harmonic components of a given sound field is a key issue in stereo field reconstruction. By utilizing the characteristic that the collecting and reconstructing processes of a high-order environment stereo mixed sound system are mutually independent, in the stereo field collecting stage, based on a spherical harmonic function analysis theory, a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface is used for researching and developing a high-order spherical harmonic component collecting system, the spherical harmonic coefficients corresponding to an ideal stereo field in a central reconstruction area are successfully collected, and the more the number of the microphones is, the more the collected spherical harmonic coefficients are accurate. In the stereo field reconstruction stage, the omnidirectional microphone array is used for collecting spherical harmonic coefficients, and then the accurate reconstruction of the stereo field is realized based on the stereo mixed sound stereo field reconstruction method in the high-order environment.
Two, three-dimensional sound field collecting stage
In the stereo field collection stage, based on a spherical harmonic analysis theory, a high-order spherical harmonic component collection system is developed by using a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface, so that spherical harmonic coefficients corresponding to an ideal stereo field in a central reconstruction area are successfully collected, and the more the number of the microphones is, the more accurate the collected spherical harmonic coefficients are;
the sound field at the matching point x ═ θ, Φ, x ∈ Ω is expressed by a spherical harmonic function as:
wherein f isnm(k) For spherical harmonic coefficients, n (0. ∞) and m (m ═ n.. times, n) are integers, n is the ambient stereo mix sound order, j is the ambient stereo mix sound order, andn(. is a spherical Bessel function of order n, Ynm(x) For spherical harmonics, the spherical harmonics expansion follows the following orthogonal decomposition behavior:
wherein the symbol "+" denotesYoke, deltanpThe method is characterized in that the method is a Kronek delta function, an integral domain is a unit sphere, and spherical harmonic coefficients are obtained through separation:
c (x; k) is the sound field of the sound source at the receiving point x in the reconstruction region, when enough sample points are distributed on the spherical surface with the radius of x and the sound pressure value corresponding to each sample point is known, the spherical harmonic coefficient f can be accurately calculatednm(k) If the microphone is a high-order sound field, the spherical harmonic coefficient f corresponding to the sound field surrounding the microphone can be collectednm(k) An omnidirectional microphone can only collect 0 order spherical harmonic coefficient f00(k) The collection of the high-order spherical harmonic coefficients corresponding to a given sound field is a practical and creative problem.
The invention utilizes a group of omnidirectional microphone group arrays distributed in different axial directions of a three-dimensional spherical surface in space according to proper positions to realize the accurate collection of high-order spherical harmonic coefficients, and for realizing convenience, the unit spherical integral is changed into discrete summation, and assuming that the number of omnidirectional microphones distributed on the spherical surface with the radius of R is A, the sound field corresponding to each microphone can be represented as C (x)a(ii) a k) 1, a, formula:
the approximation is written as:
wherein a 1., a, ωaThe above equation provides a new method for collecting higher order spherical harmonic coefficients for a set of appropriate weights for an array of spherically distributed omnidirectional microphones, and in order to prevent the missing of higher order spherical harmonic components, it is derived that the relationship between the number of omnidirectional microphones and the order number N satisfies:
A≥(N+1)2，
the spherical surface of the omnidirectional microphone is arranged in a mode that the ball is scratched according to the altitude angle and the horizontal angleDivided into grids (N +1)2The omnidirectional microphone has the condition that two poles of a sphere are relatively dense and the middle of the sphere is relatively sparse, so that the high-order spherical harmonic component of a sound field is missed, and the distortion of a reconstructed sound field is serious. For this purpose, the adjacent omnidirectional microphones are equally spaced, as shown in FIG. 2, and each omnidirectional microphone contains information on the elevation angle and the horizontal angle except for the same radius of the distribution sphere, so that the number of omnidirectional microphones is at least (2N-1)2So as to realize the even distribution of the spherical surfaces at equal intervals.
Fig. 2 is a schematic diagram of axial distribution of spherical surfaces of an omnidirectional microphone array, which is called an omnidirectional microphone array, and according to the principle that the omnidirectional microphone array can accurately collect spherical harmonic component of an ideal sound field, in a data-matching stereo field reconstruction method, sufficient sound pressure data is acquired by using the spherical surface distribution position of the omnidirectional microphone array as the position of a matching point.
In a three-dimensional sound field collection feasibility experiment, a spherical harmonic coefficient v obtained by deducing a spherical harmonic analysis formulanm(k) Spherical harmonic coefficient f acquired by omnidirectional microphone arraynm(k) Comparing numerical values, verifying accuracy of searching and collecting spherical harmonic component of high-order loudspeaker, and calculating sound field C of two methodsv(x; k) and CfAnd (x; k), observing the similarity of sound fields, and verifying the feasibility of collecting high-order spherical harmonic component by the spherical distribution omnidirectional microphone array.
Taking a three-order 1000Hz spherical wave generated sound field as an example, the spherical harmonic coefficients are 16 in total, and given sound source directions y [ pi/3, 1]Calculating vnm(k) And sound field Cv(x; k) using 26 omnidirectional microphones distributed on a spherical surface with a radius of 0.04m to collect fnm(k) And calculate Cf(x；k)。
The experimental result is that vnm(k) And fnm(k) The corresponding numerical values of all orders are similar, and C is calculated respectivelyv(x; k) and Cf(x; k) and plots the sound field as shown in FIG. 3, f at a spherical wave frequency of 1000Hznm(k) The corresponding collected third-order sound field is almost the same as the real third-order sound field, the fact that the omnidirectional microphone system with spherical distribution can collect high-order spherical harmonic component with high fidelity is verified, and the spherical harmonic component passes through the omnidirectional microphone system according to the obtained spherical harmonic coefficientThe high-order environment stereo mixed sound technology can realize accurate reconstruction of a sound field.
Fig. 3 shows a real third-order sound field corresponding to 1kHz spherical waves and a third-order sound field collected by the omnidirectional microphone array, which are basically consistent, and verifies that the omnidirectional microphone array can accurately collect spherical harmonic components of an ideal stereo sound field, and the matching point of spherical distribution has a good retaining effect on the whole three-dimensional reconstruction sound field.
From the results of the stereo field gathering stage, it can be deduced: the method has the advantages that firstly, matching points at corresponding positions of the omni-directional microphones distributed in a spherical surface are distributed in an axial orthogonal mode, no redundancy exists, a linear correlation-free equation set can be constructed when the method is applied to a data matching stereo field reconstruction method, matrix inversion can be solved, and a global optimal solution can be obtained; secondly, based on the accurate collection of the omnidirectional microphone distributed by the spherical surface to an ideal stereo field and the mathematical principle of the reconstruction method of the data matching stereo field, the matching points uniformly distributed by the spherical surface can well keep the sound pressure data of the reconstruction region. And in the stereo field reconstruction stage, comparing and analyzing the performance of the data matching stereo field reconstruction method based on spherical distribution and the data matching stereo field reconstruction method based on grid distribution according to an experimental result, and verifying the above steps.
Three, stereo sound field reconstruction stage
The main purpose of the stereo field reconstruction stage is:
the method comprises the steps of obtaining the radius of a known reconstruction area, exploring the relation between the optimal sphere radius of matching point distribution and the sphere radius of the reconstruction area, and determining the number of the spherical surface distribution matching points according to the given matching point distribution density.
And secondly, the feasibility of the data matching stereo field reconstruction method based on spherical distribution is verified through experiments, the data matching stereo field reconstruction method based on grid distribution is compared with the reconstruction effect of the data matching stereo field reconstruction method, a reconstruction error curve is analyzed, and the approximation degree of a reconstructed sound field and an ideal stereo field is analyzed.
Spherical surface distribution matching point configuration rule:
in the data matching stereo sound field reconstruction method based on grid distribution, the matching point selection has high blindness, and in order to ensure the sound field reconstruction effect, if the matching point is filled in the reconstruction area as much as possible, the calculation amount is increased undoubtedly. In the sphere distribution sample point selection, there is also no clear rule for the number of matching points and the distribution of sphere radii. Therefore, the invention firstly finds the relation between the optimal sphere radius of the matching point distribution and the radius of the reconstruction area, and then determines the number of the matching points according to the distribution density of the matching points.
(1) The optimal spherical radius of the matching point assignment is related to the spherical radius of the reconstruction region.
In order to better observe the influence of the relationship between the sphere radius of a reconstruction area and the sphere radius of matching point distribution on sound field reconstruction errors, 36-and 49-loudspeaker arrays of environment stereo mixed sound are selected, because the loudspeaker arrays strictly meet the geometrical characteristics of spherical distribution when the sound field is reconstructed by adopting the environment stereo mixed sound technology, the radius x of the reconstruction area is used0The relationship between the number of the stereo mixed sound and the number N of the environment is respectively obtained to obtain the reconstruction radius rmaxSelecting enough sphere distribution matching points for 0.272m and 0.326m, setting the number of the sphere distribution matching points to be 144, setting the radius increment interval of the distribution sphere to be 0.02m, and respectively leading the radius r to be reconstructedmaxAnd increasing the radius from 0.01m to 0.272m and 0.326m, calculating the average reconstruction error of the sample points distributed on the equatorial plane of the radius sphere once per cycle, and storing the current radius and the average error value for the corresponding radius when the observation error of the later drawing is minimum, namely the optimal distribution radius to be found.
According to the curve that the reconstruction average error of 36-and 49-loudspeaker arrays of environment stereo mixed sound changes along with the radius, the radius value corresponding to the minimum error is taken, the point distribution of the 36-loudspeaker array corresponds to 0.16m, the point distribution of the 49-loudspeaker array corresponds to 0.20m, and the ratio of the optimal sample point distribution radius to the sphere radius of the reconstruction area is calculated.
u1＝0.16/0.272＝58.8％；u2＝0.20/0.326＝61.3％
Taking the average value of the two, the proportionality coefficient is 0.60, inducing the relation between the best distribution sphere radius of the matching point and the sphere radius of the reconstruction area
rbest＝0.60rmax。
(2) Method for calculating number of spherical distribution matching points
And giving the sphere radius of the reconstruction region, and determining the optimal sphere radius assigned by the matching point according to the relationship between the optimal sphere radius assigned by the matching point and the sphere radius of the reconstruction region. However, the determination of the number of the spherical distribution matching points only depends on the density of the matching points in the reconstruction region, the reconstruction error tends to be stable as the number of the matching points increases, and the appropriate number of the matching points needs to be determined in order to avoid overlarge calculation amount.
Finding the radius r from the known reconstruction regionmaxThe method for selecting the scheme for meshing the matching points comprises the steps of firstly dividing a mesh on the xoy plane and distributing the matching points on intersection points of horizontal lines and vertical lines. In the WFS reconstruction technique, according to the huygens principle, sufficiently discrete speakers can approximately express kirchhoff's integral theorem formula, and the ideal wave field synthesis effect requires that the speaker group is at least less than half wavelength of the highest frequency, for example, 20KHz corresponds to 8.5mm, so that it is specified that the interval w between adjacent horizontal lines or vertical lines is less than the highest frequency z in the signal max1/2 wavelength of sound wave signal, selecting more dense matching points to ensure reconstruction error stability, and selecting interval w of adjacent horizontal lines or vertical lines as highest frequency z in signal max1/4 for the wavelength of the acoustic signal, i.e. w ═ c/(4 z)max) And the number of the single-layer matching points can be well determined by setting the density of the matching points as follows:
c is the speed of sound, sign
Representing the smallest integer greater than or equal to a given expression, a z-axis division interval of 0.01, and a range of [0.1r ]max，0.1rmax]Obtaining the number of layers of longitudinal matching points Nportrait＝20rmax+1, the total number of points is Ngrid＝NportraitNxoySince the optimum assigned sphere radius of the matching points is only that of the reconstruction region0.60, if the matching points of the grid distribution are directly applied to the spherical distribution, the spherical matching points are too dense, the number of the matching points needs to be reduced to reduce the distribution density of the matching points, and 1/2, namely N, is calculated according to the given density of the matching points, wherein the number of the matching points of the spherical distribution is the number of the gridded matching points under the same conditionround＝NgridAnd/2, if the number of the grid distribution matching points is NgridIf 520, the number of sphere distribution matching points is determined to be 260, and finally N is set in consideration of the square of one sphere distribution matching point numberround＝162256 for same reason, if Ngrid175 according to the above rule Nround＝132＝169。
(3) Comparison of Experimental results
According to the spherical surface distribution matching point configuration rule, an NHK22.2 multi-channel stereo system distributed on a spherical surface with the radius of 2 meters is used as a loudspeaker configuration environment, the position y of a 1000Hz spherical wave sound source is [ pi/3, 2], a reconstruction area is selected as a spherical area with the origin of coordinates as the sphere center and the radius of 0.3 meter, matching points are distributed on a grid, the number of the selected points is 448, and the number of the distributed points of xoy plane sample points is 64, as shown in fig. 4(a), under the condition, the reconstruction distortion of a stereo sound field can be kept small and the trend is stable. According to the sphere distribution matching point configuration rule of the present invention, the number of the selected sample points is 225, which are distributed at 1/2 (i.e. 0.15 m) where the sphere radius is the sphere radius of the reconstruction region, as shown in fig. 4 (b).
Fig. 4 is a grid matching point distribution diagram and a sphere matching point distribution diagram, and the areal density of 225 point sphere distribution is equivalent to the bulk density of 448 point grid distribution.
Based on the experimental configuration, sound field diagrams of equatorial planes of a grid distribution method and a spherical distribution method are respectively drawn, and the comparison shows that the two methods can well restore an ideal stereo field, and the stereo field obtained by spherical distribution reconstruction is more uniform and clear and is closer to the ideal stereo field.
According to the reconstruction error curves corresponding to the sample points distributed by the grids with different numbers by the grid matching method, when the total number of the matching points is 180, the change range of the reconstruction error is large along with the increase of the radius of a reconstruction area, which fully indicates that when the number of the matching points is small, data under-fitting is serious, a global optimal solution cannot be obtained at all, and the change trend of the reconstruction error is consistent and gradually tends to be stable along with the increase of the number of the matching points. The sound field reconstruction of data matching must be based on a large amount of matching point sound pressure data, but the selection of the number of matching points of the xoy plane does not have a reliable guiding standard, when the number of the matching points is large enough, the reconstruction error tends to be stable, and in order to avoid the problem that the global optimal solution cannot be obtained due to the small number of the matching points, the prior art selects enough matching points according to experience, which undoubtedly causes the great increase of the calculation amount and the calculation complexity, and the requirement on the calculation capacity of hardware equipment in practical application is too high, and the speed is too low.
And then the effects of the two methods are further analyzed from the reconstruction error curve, the error curves with the heights of-0.03 meter, 0 meter and 0.03 meter slices respectively show that the reconstruction errors of the stereo sound field corresponding to the spherical distribution method keep lower distortion in a reconstruction area, particularly the error in the area with the radius of 0.25 meter is less than 4.5 percent of the expected maintenance error, and the spherical distribution matching points are applied to the stereo sound field reconstruction technology of data matching, so that a satisfactory reconstruction effect can be obtained: the number of the matching points is reduced by 56.2 percent compared with the gridding division method, and the reconstruction average error is reduced by 44.3 percent.
The distribution of the matching points of the grid distribution method on the z axis is only in the range of-0.03 m to 0.03 m, the distortion is very obvious once the longitudinal range exceeds 0.03 m according to the fitting principle of minimum square data, the reconstruction errors are more than 4.5% and maximally reach 7.8% along with the increase of the radius of a reconstruction area, a human ear system can obviously sense the distortion of a stereo field, the spherical distribution method can keep the error less than 4.5% in a spatial area of +/-0.055 m on the z axis, the accurate reconstruction of the stereo field in a large area range is proved to be kept by the spherical distribution method, the listening effect cannot be greatly influenced even if a listener rotates a head locally and quickly, the matching points of the spherical distribution method are distributed on a spherical surface with the radius of 0.16m, the spherical area with the radius of 0.32 m can be accurately reconstructed, not only the area stereo field surrounded by the accurately reconstructed matching points, but also the stereo field can be well kept beyond the distribution of the sphere of the matching points, the method fully shows that the method for reconstructing the stereo sound field by applying the matching points obtained based on the spherical harmonic orthogonal theory to data matching is completely feasible and efficient.
Claims (5)
1. A sphere distribution guided data matching stereo field reconstruction method is characterized in that: the method comprises the steps that high-order spherical harmonic component of a sound field is accurately collected and reconstructed on the basis of an omnidirectional microphone array, the sound field is divided into a stereo sound field collection stage and a stereo sound field reconstruction stage, in the stereo sound field collection stage, a high-order spherical harmonic component collection system is developed by using a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface on the basis of a spherical harmonic analysis theory, spherical harmonic coefficients corresponding to a stereo sound field in a central reconstruction area are collected, in the stereo sound field reconstruction stage, the spherical harmonic coefficients are collected by using the omnidirectional microphone arrays, and the stereo sound field is accurately reconstructed on the basis of a high-order environment stereo mixed sound stereo sound field;
a sphere distribution guided data matching stereo field reconstruction method comprises four steps:
firstly, a stereo sound field is collected, and a high-order spherical harmonic component collecting system is developed by using a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface;
secondly, reconstructing a first stereo field, and obtaining a linear relation between the optimal sphere radius distributed by the matching points and the sphere radius of a reconstruction region according to a spherical distribution matching point configuration rule;
thirdly, reconstructing a stereo sound field, namely calculating the number of matching points distributed by the spherical surface according to a spherical surface distribution matching point selecting method;
and fourthly, reconstructing a three-dimensional sound field, and obtaining complete spatial distribution of the spherical distribution matching points according to the arrangement rule of the omnidirectional microphone array.
2. The sphere distribution guided data matching stereo field reconstruction method according to claim 1, wherein: the matching points of the spherical distribution matching point selection method follow the spherical harmonic orthogonal decomposition principle, the established equation set has no linear correlation, and the global optimal solution is obtained by directly solving;
in the method for selecting the spherical distribution matching points, a sound field is expressed and reconstructed by linear combination of a group of orthogonal spherical harmonic functions through environment stereo mixed sound, a high-order spherical harmonic component collecting system is developed by a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface on the basis of a spherical harmonic analysis theory, spherical harmonic coefficients corresponding to an ideal stereo field in a central reconstruction area are collected by the omnidirectional microphone arrays, the spherical harmonic coefficients are collected, and the accurate reconstruction of the stereo field is realized on the basis of a high-order environment stereo mixed sound stereo field reconstruction method.
3. The sphere distribution guided data matching stereo field reconstruction method according to claim 1, wherein: in the stereo field collection stage, based on a spherical harmonic analysis theory, a group of omnidirectional microphone arrays which are uniformly and axially distributed on a spherical surface is used for developing a high-order spherical harmonic component collection system, a spherical harmonic coefficient corresponding to an ideal stereo field in a central reconstruction region is collected, and a sound field with a matching point x ═ theta, phi, x ∈ omega is expressed by a spherical harmonic function as follows:
wherein f isnm(k) For spherical harmonic coefficients, n (0. ∞) and m (m ═ n.. times, n) are integers, n is the ambient stereo mix sound order, j is the ambient stereo mix sound order, andn(. is a spherical Bessel function of order n, Ynm(x) For spherical harmonics, the spherical harmonics expansion follows the following orthogonal decomposition behavior:
wherein the symbol "+" denotes conjugation, δnpThe method is characterized in that the method is a Kronek delta function, an integral domain is a unit sphere, and spherical harmonic coefficients are obtained through separation:
c (x; k) is the point x where the sound source is received in the reconstruction regionWhen enough sample points are distributed on the spherical surface with the radius of x and the sound pressure value corresponding to each sample point is known, the spherical harmonic coefficient f can be accurately calculatednm(k) If the microphone is a high-order sound field, the spherical harmonic coefficient f corresponding to the sound field surrounding the microphone can be collectednm(k)；
The invention utilizes a group of omnidirectional microphone group arrays distributed in different axial directions of a three-dimensional spherical surface in space according to proper positions to realize the accurate collection of high-order spherical harmonic coefficients, changes unit spherical integral into discrete summation, sets the number of omnidirectional microphones distributed on the spherical surface with the radius of R as A, and represents the sound field corresponding to each microphone as C (x)a(ii) a k) 1, a, formula:
the approximation is written as:
wherein a 1., a, ωaDeriving, for a set of appropriate weights, a relationship between the number of omni-directional microphones and the order N that satisfies:
A≥(N+1)2，
the omnidirectional microphones are arranged in a spherical surface mode that a ball is divided into grids according to an altitude angle and a horizontal angle, each omnidirectional microphone comprises information of the altitude angle and the horizontal angle, and the number of the omnidirectional microphones is at least (2N-1)2And the spherical surfaces are uniformly distributed at equal intervals.
4. The sphere distribution guided data matching stereo field reconstruction method according to claim 1, wherein: in the stereo field reconstruction stage, obtaining a linear relation between the optimal sphere radius distributed by the matching points and the sphere radius of the reconstruction region according to the spherical distribution matching point configuration rule;
when the sound field is reconstructed by adopting the environment stereo mixed sound technology, the loudspeaker array strictly meets the geometrical characteristics of spherical distribution, and the reconstruction is carried outRadius of area x0The relationship between the number of the stereo mixed sound and the number N of the environment is respectively obtained to obtain the reconstruction radius rmaxSelecting enough sphere distribution matching points for 0.272m and 0.326m, setting the number of the sphere distribution matching points to be 144, setting the radius increment interval of the distribution sphere to be 0.02m, and respectively leading the radius r to be reconstructedmaxIncreasing the distance from 0.01m to 0.272m and 0.326m, calculating the average reconstruction error of the sample points distributed on the equatorial plane of the radius sphere once per cycle, and storing the current radius and the average error value for the corresponding radius when the observation error of the later drawing is minimum, namely the optimal distribution radius to be found;
according to the curve that the reconstruction average error of 36-and 49-loudspeaker arrays of environment stereo mixed sound changes along with the radius, the radius value corresponding to the minimum error is taken, the point distribution of 36-loudspeaker arrays corresponds to 0.16m, the point distribution of 49-loudspeaker arrays corresponds to 0.20m, the ratio of the optimal sample point distribution radius to the sphere radius of the reconstruction area is calculated,
u1＝0.16/0.272＝58.8％；u2＝0.20/0.326＝61.3％
taking the average value of the two, the proportionality coefficient is 0.60, and inducing the relation between the best distribution sphere radius of the matching point and the sphere radius of the reconstruction area:
rbest＝0.60rmax。
5. the sphere distribution guided data matching stereo field reconstruction method according to claim 1, wherein: in the stereo field reconstruction stage, calculating the number of matching points distributed by the spherical surface according to a spherical surface distribution matching point selection method;
finding the radius r from the known reconstruction regionmaxThe method of selecting matching point gridding includes that firstly, grid is divided on xoy plane, matching points are distributed on the intersection points of horizontal lines and vertical lines, enough discrete loudspeakers can approximately express kirchhoff's integral theorem formula, ideal wave field synthesis effect requires loudspeaker sets to be at least smaller than half wavelength of highest frequency, so that the interval w of adjacent horizontal lines or vertical lines is regulated to be smaller than the highest frequency z in signalmax1/2 of the wavelength of the acoustic wave signal will define the adjacent horizontal line or vertical lineThe spacing w of the lines is chosen to be the highest frequency z in the signalmax1/4 for the wavelength of the acoustic signal, i.e. w ═ c/(4 z)max) And the number of the single-layer matching points can be well determined by setting the density of the matching points as follows:
c is the speed of sound, sign
Representing the smallest integer greater than or equal to a given expression, a z-axis division interval of 0.01, and a range of [0.1r ]max，0.1rmax]Obtaining the number of layers of longitudinal matching points Nportrait＝20rmax+1, the total number of points is Ngrid＝NportraitNxoyGiven the density of matching points, 1/2, i.e. N, is calculated for the number of matching points in the spherical distribution as the number of gridded matching points under the same conditionround＝NgridAnd/2, if the number of the grid distribution matching points is NgridIf 520, the number of the sphere distribution matching points is determined to be 260, and the number of the sphere distribution matching points is considered to be the square of one number, and finally set to be Nround＝162256 for same reason, if Ngrid175 according to the above rule Nround＝132＝169。
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