CN103220601B - Method for reducing and streamlining three-dimensional multiple sound channel audio system speaker group by half - Google Patents

Abstract

The invention discloses a method for reducing and streamlining a three-dimensional multiple sound channel audio system speaker group by half. Mirror images are arranged to be symmetrical according to original speakers, and n speakers in a three-dimensional n sound channel audio system are streamlined into m speakers in a three-dimensional m sound channel audio system by means of half-reducing method. The method for reducing and streamlining the three-dimensional multiple sound channel audio system speaker group by half comprises the following steps: obtaining spatial location information of each speaker in the three-dimensional n sound channel audio system before half reduction and streamlining; reducing the speakers in the three-dimensional n sound channel audio system by half before the streamlining by means of the symmetrical surface, and obtaining original objects to be streamlined; conducting mirror image allocation on the speakers; analyzing all combinations of a triangular speaker group in objects to be streamlined, and analyzing speakers, obtaining speakers and rejecting speakers which should be streamlined; and rejecting mirror image points of the rejected streamlined speakers, judging whether the sum of the current speakers to be streamlined is larger than m, wherein a simplification process is continuously executed if the sum of the current speakers to be streamlined is larger than an-m, otherwise, iteration is finished, and obtaining optimal spatial location distribution of the m sound channel streamlined system speaker group.

Description

A kind of three-dimensional multi-channel audio system set of speakers is reduced by half compressing method

Technical field

The invention belongs to field of acoustics, particularly relate to a kind of three-dimensional multi-channel audio system set of speakers and to reduce by half compressing method.

Background technology

The three-dimensional movie " A Fanda " showed for the end of the year 2009 not only climbs up top box-office value in more than 30 country in the whole world, and at the beginning of 2010 9 months, global box office is accumulative more than 2,700,000,000 dollars.The gorgeous picture that " A Fanda " represents and sound effect true to nature have not only shaken spectators, also made industry have the asserting of " film enter three-dimensional epoch ".The upper data display obtained of International CES (CES) held in Las Vegas for 2013, within 2012, global 3D TV sales volume increases by 67% than previous year, wherein the sales volume in market, China's Mainland is 1,000 ten thousand, accounts for 25% of global 3D TV sales volume; The well-known market research agency iSuppli in the whole world predicts 2015, and the shipment amount of global 3D television set will reach 1.59 hundred million, account for the over half of global panel TV set shipment amount." 3D " has become the marking symbols of 21st century second 10 years Global Multi-media industry undoubtedly.But want to reach better audiovisual experience, need the three-dimensional sound field auditory effect synchronous with 3 d video content, could really reach hearing experience on the spot in person.Therefore, the scientific research institution of advanced country and main multimedia standardization body carry out correlative study one after another in the world: early stage three dimensional audio systems (as Ambisonics system) is due to its complex structure, require higher to collection and playback apparatus, be difficult to promote practicality; Doby company (Dolby) is proposed the ProLogic IIz multisound path three dimensional audio playback system of putting sound channel with height; 22.2 multichannel audio prototype systems have been developed in NHK (NHK) scientific and technical research laboratory in recent years, and its structure is simple, and the compatible 5.1 surround sound speaker configurations schemes of energy; Dynamic image expert group (Moving PicturesExperts Group, MPEG) great attention also started the formulation of 3D Audiotechnica standard in 2011, to wish while reaching certain code efficiency by fewer loud speaker or earphone to reduce three-dimensional sound field, so that can by this Technique Popularizing to ordinary family user; State natural sciences fund committee of China has issued " three-dimensional audio basic theory and key technology research " primary study project guide specially in 2012, and emphasis supports the research of 3D Audiotechnica.The three-dimensional audio frequency and video technology study hotspot having become multimedia technology field and the important directions further developed as can be seen here.Meanwhile, the thought of traditional sound field rebuilding technology (as WFS, Ambisonics etc.) is by a sound field formed as live concert hall music club at another space reconstruction, and its target reappears the original sound fields such as live concert hall.But be subject to the restriction of actual sound field acquisition method, the target of rebuilding original sound field is completely difficult to realize.But, the reconstruction again of carrying out the reconstruction sound field generated by multi-channel system in MIXING STUDIO in another indoor environment rebuilding sound field is then realized than being easier to, and this problem of again rebuilding sound field in other environment can be equivalent to looks for a kind of method and original weight is built multi-channel audio signal in sound field and be converted to and again rebuild multi-channel audio signal in sound field.For convenience of describing, generally the reconstruction sound field obtained by former multi-channel system being called " original sound field ", and being called " reconstruction sound field " by the sound field that the alternate audio system of different channel number is rebuild again.

Conventional audio technology when gathering signal, encoding and playing by utilizing the apperceive characteristic of people's ear audition to promote simplification system: as when gathering sound, according to Nyquist's theorem, sample frequency should be more than the twice of auditory perceptual sound highest frequency could reduce to unaware distortion primary signal; When encoding to signal, the masking effect according to people ear eliminates the perception redundancy in sound channel, utilizes the perception sensitivity characteristic of people's ear to spatial parameter to eliminate parameter perception redundancy between sound channel; At playback end, more responsive to dead ahead contrast locating according to people's ear, to the more sensitive characteristic of ambient sound perception at rear, adopting at the main sound channel loud speaker of dead ahead placement for locating, placing the arrangement mode of ambient sound loud speaker in the wings.Because people's ear is symmetrical to the perception of left and right directions, therefore needs to design a kind of method and can simplify former multi-channel system set of speakers, can ensure again to rebuild sound field and original sound field error minimum, ensure symmetrical simultaneously.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, a kind of compressing method by half of being simplified by n loud speaker in three-dimensional n channel-audio system as m loud speaker in three-dimensional m channel-audio system is provided, obtains and simplify set of speakers optimal spatial positional information in rear symmetrical m sound channel system.

Technical scheme of the present invention is that a kind of three-dimensional multi-channel audio system set of speakers is reduced by half compressing method, for simplifying n loud speaker in three-dimensional n channel-audio system into m loud speaker in three-dimensional m channel-audio system by half, comprises following steps:

Step 1, obtains the luv space positional information of simplifying each loud speaker in front three-dimensional n channel-audio system;

Step 2, getting and simplifying the loud speaker being positioned at plane of symmetry side in front three-dimensional n channel-audio system and the loud speaker be positioned on the plane of symmetry is initial object to be simplified;

Step 3, makes mirror image to initial object to be simplified, and obtains corresponding mirror image loud speaker;

Step 4, analyzes all combinations of spherical triangle set of speakers in object current to be simplified, and forms spherical triangle set of speakers S set;

Step 5, according to step 4 gained spherical triangle set of speakers S set, therefrom selects the set of speakers only comprising single loud speaker, then gets the set of speakers (ξ that spherical triangle area is minimum ₁, ξ ₂, ξ ₃), redistribute set of speakers (ξ ₁, ξ ₂, ξ ₃) signal, by set of speakers (ξ ₁, ξ ₂, ξ ₃) the single loud speaker ζ that comprises rejects as by the loud speaker of simplifying;

Step 6, redistributes step 5 gained set of speakers (ξ ₁, ξ ₂, ξ ₃) mirror image set of speakers (ξ ' ₁, ξ ' ₂, ξ ' ₃) signal, reject and simplified the mirror image loud speaker ζ ' of loud speaker;

Step 7, judge whether loud speaker number sum current to be simplified is greater than default m value, if be greater than m, proceed to and perform step 4 and reanalyse all combinations of spherical triangle set of speakers in object current to be simplified and simplify, otherwise finishing iteration, according to remaining loud speaker, obtain the arrangement of m sound channel symmetrical simplified system set of speakers optimal spatial position.

And, redistribute set of speakers (ξ in step 5 ₁, ξ ₂, ξ ₃) signal, implementation is as follows,

According to loud speaker ζ and ξ ₁, ξ ₂, ξ ₃spatial positional information calculate weights distribution coefficient ω ₁, ω ₂, ω ₃it is as follows,

$w_1=\frac{{\tilde{D}}_1}{D},w_2=\frac{{\tilde{D}}_2}{D},w_3=\frac{{\tilde{D}}_3}{D}$

$D={\tilde{D}}_1+{\tilde{D}}_2+{\tilde{D}}_3$

By the frequency-region signal s of loud speaker ζ _ζ(ω) according to weights distribution coefficient ω ₁, ω ₂, ω ₃be assigned to loud speaker ξ ₁, ξ ₂, ξ ₃frequency-region signal on, obtain new frequency-region signal formula is as follows,

$q_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)+w_1{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)+w_2{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)+w_3{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

Finally make s _ζ(ω)=0.

And, redistribute in step 6 mirror image set of speakers (ξ ' ₁, ξ ' ₂, ξ ' ₃) signal, implementation is as follows,

By the frequency-region signal s of mirror image loud speaker ζ ' _{ζ '}(ω) according to weights distribution coefficient ω ₁, ω ₂, ω ₃be assigned to loud speaker ξ ' ₁, ξ ' ₂with ξ ' ₃frequency-region signal on, obtain new frequency-region signal formula is as follows,

$q_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)+w_1{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)+w_2{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)+w_3{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

Finally make s _{ζ '}(ω)=0.

Split provided by the invention is adopted to simplify three-dimensional multi-channel audio system loud speaker, gather the spatial positional information of waiting to simplify loud speaker in three-dimensional multi-channel audio system, because loud speaker is left and right specular, simplify in process, find in demifacet and should reject loud speaker, and it and it mirror point is together rejected.Simplify after iterative algorithm through set of speakers and can obtain the configuration of simplified system set of speakers optimal spatial, final realization simplifies the arrangement of loud speaker optimal spatial to three-dimensional multi-channel audio system.Set of speakers simplifies iterative algorithm can ensure that the process of simplifying does not affect the physical characteristic of the sound of audition central spot.Be compared to and wait to simplify loud speaker in three-dimensional multi-channel audio system and find to whole the way should rejecting loud speaker, the efficiency comparison of technical solution of the present invention is high, and work for the treatment of amount reduces, and saves system resource.

Accompanying drawing explanation

Fig. 1 is that the set of speakers of the embodiment of the present invention is reduced by half compressing method flow chart.

Fig. 2 is the loud speaker mirror image distribution map before the set of speakers of the embodiment of the present invention is simplified by half.

Embodiment

The invention provides and a kind of compressing method by half of being simplified by n loud speaker in three-dimensional n channel-audio system as m loud speaker in three-dimensional m channel-audio system is provided.During concrete enforcement, suitable weight calculation method and the best can be selected as required to be simplified loud speaker system of selection by those skilled in the art.

Technical solution of the present invention can adopt computer software technology to realize automatically running, and describe technical solution of the present invention in detail below in conjunction with drawings and Examples, those skilled in the art are not limited to this technical scheme when implementing.

As Fig. 1 gives the flow chart of the embodiment of the present invention, embodiment comprises following steps:

Step 1, gathers the spatial positional information of simplifying each loud speaker in front three-dimensional n channel-audio system;

Three-dimensional n channel-audio system is to there being n loud speaker, if with listening area central point O for summit structure three-dimensional system of coordinate XYZ, distance between loud speaker and central point is designated as ρ, and the angle of loud speaker and plane X OZ is designated as θ, and the angle of loud speaker and plane X OY is designated as speaker volume location parameter is labeled as being arranged in by n loud speaker with the spacing of central point is on the sphere of ρ, sets the value of ρ as 2 meters in embodiment.Because spacing and the loud speaker in original sound field of loud speaker and central point are with central point apart from equal in reconstruction sound field, simplify speaker volume location parameter in front audio system and simplify so gather in an embodiment and be labeled as make initial loud speaker number sum=n to be simplified.

Step 2, by half, obtains initial object to be simplified to simplifying loud speaker in front three-dimensional n channel-audio system;

The loud speaker of simplifying in front three-dimensional n channel-audio system is symmetrical.With XOZ face for the plane of symmetry, the loud speaker getting side (left side or right side) and the loud speaker be positioned on the plane of symmetry, form object to be simplified.

As Fig. 2, simplify the mirror image distribution of front 22 loud speakers.Horizontal shading face XOY is listening area, and vertical shading face XOZ is the plane of symmetry, and on the left of the desirable plane of symmetry, on black real point loud speaker (or the hollow loud speaker of right side black) and the plane of symmetry, black real point loud speaker is initial object to be simplified.

Step 3, makes mirror image to initial object to be simplified;

Each object to be simplified is the mirror image of this object to be simplified about the symmetric position place loud speaker in plane of symmetry XOZ face, loud speaker mirror image on the plane of symmetry is itself, with the first behavior object to be simplified, the mirror image of the second behavior object to be simplified accordingly, forms mirror image matrix A.That the θ of the two-loudspeaker of specular is added and be π odd-multiple, and elevation angle equal.

Such as, XOZ left side of face three loud speaker ξ ₁, ξ ₂and ξ ₃locus be xOZ right side of face three loud speaker ξ ' ₁, ξ ' ₂with ξ ' ₃locus be if θ ₁+ θ ' ₁=(2n+1) π, wherein n=0,1,2 ..., then ξ ₁with ξ ' ₁specular.If in like manner ξ ₂with ξ ' ₂, ξ ₃with ξ ' ₃meet similarity condition, then ξ ₂with ξ ' ₂, ξ ₃with ξ ' ₃also specular is.More the situation of multi-loudspeaker in like manner.

Then mirror image matrix $A=\left[\begin{array}{cccc}{\mathrm{\ξ}}_1& {\mathrm{\ξ}}_2& {\mathrm{\ξ}}_3& ...\\ {\mathrm{\ξ}}_1^{\′}& {\mathrm{\ξ}}_2^{\′}& {\mathrm{\ξ}}_3^{\′}& ...\end{array}\right]$

Step 4, analyzes all combinations of current object intermediate cam shape set of speakers to be simplified;

In the loud speaker of object to be simplified, in all combinations of optional three, analyze all speaker combination that can form spherical triangle, form spherical triangle set of speakers S set;

Such as, from the loud speaker in the left side of n loud speaker, select arbitrarily three form a speaker combination (ξ ₁, ξ ₂, ξ ₃), three loud speaker ξ can be obtained ₁, ξ ₂and ξ ₃locus be because locus point corresponding to these three loud speakers could be formed spherical triangle, if so wish speaker combination (ξ by camber line altogether when three speaker volume positions only in this speaker combination are different ₁, ξ ₂, ξ ₃) as a spherical triangle set of speakers, then can must meet θ ₁, θ ₂and θ ₃time different equal or with equal time different.

Step 5, obtains to be rejected by the loud speaker of simplifying according to the analysis result of step 4;

From above-mentioned S set, select the spherical triangle set of speakers only comprising single loud speaker, and sort by the spherical triangle size of its composition, composition set Q; Then set of speakers (the ξ that spherical triangle area is minimum is found ₁, ξ ₂, ξ ₃) the single loud speaker ζ that comprises, redistribute signal; Finally reject loud speaker ζ, i.e. distributing signal s _ζ(ω)=0, makes loud speaker number sum=sum-1 current to be simplified.The spherical triangle set of speakers element relevant with loud speaker ζ can be rejected from spherical triangle set of speakers S set.

Such as:

The set of speakers that in set Q, spherical triangle area is minimum is (ξ ₁, ξ ₂, ξ ₃), wherein comprised single loud speaker is ζ, locus coordinate spherical triangle intra-zone is being made up of or on three limits of spherical triangle three speaker volume.

By loud speaker ξ ₁, ξ ₂, ξ ₃corresponding frequency-region signal is obtained through Fourier transform with the time-domain signal of ζ and s _ζ(ω), when the spatial positional information of known loudspeaker: calculate weights according to formula 1 to distribute.

$w_1=\frac{{\tilde{D}}_1}{D},w_2=\frac{{\tilde{D}}_2}{D},w_3=\frac{{\tilde{D}}_3}{D}$ Formula (1)

Wherein: ω ₁, ω ₂, ω ₃for weights distribution coefficient, wherein parameter D, computing formula as follows:

$D={\tilde{D}}_1+{\tilde{D}}_2+{\tilde{D}}_3$

According to formula (2), the frequency-region signal of loud speaker ζ is assigned to loud speaker ξ according to corresponding weight value size ₁, ξ ₂, ξ ₃frequency-region signal on, obtain loud speaker ξ ₁, ξ ₂, ξ ₃new frequency-region signal ;

$q_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)+w_1{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)+w_2{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)+w_3{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$ Formula (2)

Finally make s _ζ(ω)=0

By loud speaker ξ ₁, ξ ₂, ξ ₃frequency-region signal be corresponding time-domain signal through inverse Fourier transform, from spherical triangle set of speakers S set, reject the spherical triangle set of speakers element relevant with loud speaker ζ.

Step 6, rejects and is simplified the mirror image loud speaker of loud speaker;

According to mirror image matrix A, find the mirror image loud speaker ζ ' of disallowable loud speaker ζ in step 5, and press the same method distributing signal of step 5, reject mirror image loud speaker ζ '.Make loud speaker number sum=sum-1 current to be simplified.The spherical triangle set of speakers element relevant with loud speaker ζ ' can be rejected from spherical triangle set of speakers S set, obtain remaining loud speaker number, namely new loud speaker number sum current to be simplified.

Such as, loud speaker disallowable in step 5 is ζ, and step 6 is item according to matrix A, and obtaining its mirror image loud speaker is ζ ', and the element of corresponding smallest triangle set of speakers is ξ ' ₁, ξ ' ₂with ξ ' ₃, by loud speaker ξ ' ₁, ξ ' ₂with ξ ' ₃corresponding frequency-region signal is obtained through Fourier transform with the time-domain signal of ζ ' and s _{ζ '}(ω), loud speaker ξ ' is obtained by formula (3) distribution ₁, ξ ' ₂with ξ ' ₃new frequency-region signal

$q_{{\mathrm{\ξ}}_1^{\′}}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_1^{\′}}\left(\mathrm{\ω}\right)+w_1{s}_{{\mathrm{\ζ}}^{\′}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_2^{\′}}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_2^{\′}}\left(\mathrm{\ω}\right)+w_2{s}_{{\mathrm{\ζ}}^{\′}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_3^{\′}}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_3^{\′}}\left(\mathrm{\ω}\right)+w_3{s}_{{\mathrm{\ζ}}^{\′}}\left(\mathrm{\ω}\right)$ Formula (3)

Finally make s _{ζ '}(ω)=0, rejects mirror image loud speaker ζ '.

Wherein, weights distribution coefficient ω ₁, ω ₂, ω ₃direct employing step 5 acquired results.

Step 7, iterated conditional judges;

Judge whether loud speaker number sum current to be simplified is greater than m,

If be greater than m, proceed to and perform all combinations that step 4 reanalyses the current object intermediate cam shape set of speakers to be simplified of analysis, continue to simplify based on new spherical triangle set of speakers S set;

Otherwise finishing iteration, take out the loud speaker in spherical triangle set of speakers S set corresponding to each spherical triangle set of speakers element and the spatial positional information of its corresponding mirror image loud speaker, obtain the arrangement of m sound channel symmetrical simplified system set of speakers optimal spatial position.

During concrete enforcement, the value of m can be pre-set according to the distribution situation of n loud speaker in three-dimensional n channel-audio system by those skilled in the art.

Be compared to and wait to simplify loud speaker in three-dimensional multi-channel audio system and find to whole the way should rejecting loud speaker, the efficiency comparison of technical solution of the present invention is high, and work for the treatment of amount reduces, and saves system resource.

Such as, 22 sound channels are simplified when being 8 sound channel, waiting to simplify loud speaker in three-dimensional multi-channel audio system find the way data processing time t that should reject loud speaker to whole before ₁be approximately 79.354936, and the data processing time t of technical solution of the present invention ₂be about 18.925047.

(t ₁-t ₂)÷t ₁＝(79.354936-18.925047)÷79.354936≈0.76

Therefore be compared to and wait to simplify loud speaker in three-dimensional multi-channel audio system and find to whole the way should rejecting loud speaker, the efficiency of technical solution of the present invention improves about 0.6 times.

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various amendment or supplement or adopt similar mode to substitute to described specific embodiment, but can't depart from spirit of the present invention or surmount the scope that appended claims defines.

Claims (1)

1. three-dimensional multi-channel audio system set of speakers is reduced by half a compressing method, for simplifying n loud speaker in three-dimensional n channel-audio system into m loud speaker in three-dimensional m channel-audio system by half, it is characterized in that, comprise following steps:

Step 1, obtains the luv space positional information of simplifying each loud speaker in front three-dimensional n channel-audio system;

Step 2, getting and simplifying the loud speaker being positioned at plane of symmetry side in front three-dimensional n channel-audio system and the loud speaker be positioned on the plane of symmetry is initial object to be simplified;

Step 3, makes mirror image to initial object to be simplified, and obtains corresponding mirror image loud speaker;

Step 4, analyzes all combinations of spherical triangle set of speakers in object current to be simplified, and forms spherical triangle set of speakers S set;

Step 5, according to step 4 gained spherical triangle set of speakers S set, therefrom selects the set of speakers only comprising single loud speaker, then gets the set of speakers (ξ that spherical triangle area is minimum ₁, ξ ₂, ξ ₃), redistribute set of speakers (ξ ₁, ξ ₂, ξ ₃) signal, by set of speakers (ξ ₁, ξ ₂, ξ ₃) the single loud speaker ζ that comprises rejects as by the loud speaker of simplifying;

Describedly redistribute set of speakers (ξ ₁, ξ ₂, ξ ₃) signal, implementation is as follows,

According to loud speaker ζ and ξ ₁, ξ ₂, ξ ₃spatial positional information calculate weights distribution coefficient ω ₁, ω ₂, ω ₃it is as follows,

$w_1=\frac{{\tilde{D}}_1}{D},w_2=\frac{{\tilde{D}}_2}{D},w_3=\frac{{\tilde{D}}_3}{D}$

$D={\tilde{D}}_1+{\tilde{D}}_2+{\tilde{D}}_3$

By the frequency-region signal s of loud speaker ζ _ζ(ω) according to weights distribution coefficient ω ₁, ω ₂, ω ₃be assigned to loud speaker ξ ₁, ξ ₂, ξ ₃frequency-region signal on, obtain new frequency-region signal formula is as follows,

$q_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_1}\left(\mathrm{\ω}\right)+w_1{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_2}\left(\mathrm{\ω}\right)+w_2{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_3}\left(\mathrm{\ω}\right)+w_3{s}_{\mathrm{\ζ}}\left(\mathrm{\ω}\right)$

Finally make s _ζ(ω)=0;

Step 6, redistributes step 5 gained set of speakers (ξ ₁, ξ ₂, ξ ₃) mirror image set of speakers (ξ ₁', ξ ₂', ξ ₃') signal, reject and simplified the mirror image loud speaker ζ ' of loud speaker;

Described redistribute mirror image set of speakers (ξ ' ₁, ξ ' ₂, ξ ' ₃) signal, implementation is as follows,

By the frequency-region signal s of mirror image loud speaker ζ ' _{ζ '}(ω) according to weights distribution coefficient ω ₁, ω ₂, ω ₃be assigned to loud speaker ξ ' ₁, ξ ' ₂with ξ ' ₃frequency-region signal on, obtain new frequency-region signal formula is as follows,

$q_{{\mathrm{\ξ}}_1^{\′}}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_1^{\′}}\left(\mathrm{\ω}\right)+w_1{s}_{{\mathrm{\ζ}}^{\′}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_2^{\′}}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_2^{\′}}\left(\mathrm{\ω}\right)+w_2{s}_{{\mathrm{\ζ}}^{\′}}\left(\mathrm{\ω}\right)$

$q_{{\mathrm{\ξ}}_3^{\′}}\left(\mathrm{\ω}\right)=s_{{\mathrm{\ξ}}_3^{\′}}\left(\mathrm{\ω}\right)+w_3{s}_{{\mathrm{\ζ}}^{\′}}\left(\mathrm{\ω}\right)$

Finally make s _{ζ '}(ω)=0;

Step 7, judge whether loud speaker number sum current to be simplified is greater than default m value, if be greater than m, proceed to and perform step 4 and reanalyse all combinations of spherical triangle set of speakers in object current to be simplified and simplify, otherwise finishing iteration, according to remaining loud speaker, obtain the arrangement of m sound channel symmetrical simplified system set of speakers optimal spatial position.