CN108376541A - A kind of domestic environment sound based on active noise reduction inhibits the location mode of signal - Google Patents

A kind of domestic environment sound based on active noise reduction inhibits the location mode of signal Download PDF

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CN108376541A
CN108376541A CN201810121985.1A CN201810121985A CN108376541A CN 108376541 A CN108376541 A CN 108376541A CN 201810121985 A CN201810121985 A CN 201810121985A CN 108376541 A CN108376541 A CN 108376541A
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sound
noise reduction
signal
inhibits
active noise
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唐智灵
姜静月
蓝如师
韦永成
罗笑南
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Guilin University of Electronic Technology
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Guilin University of Electronic Technology
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    • GPHYSICS
    • G10MUSICAL INSTRUMENTS; ACOUSTICS
    • G10KSOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1781Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions
    • G10K11/17821Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions characterised by the analysis of the input signals only
    • G10K11/17823Reference signals, e.g. ambient acoustic environment
    • GPHYSICS
    • G10MUSICAL INSTRUMENTS; ACOUSTICS
    • G10KSOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1781Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions
    • G10K11/17813Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions characterised by the analysis of the acoustic paths, e.g. estimating, calibrating or testing of transfer functions or cross-terms
    • GPHYSICS
    • G10MUSICAL INSTRUMENTS; ACOUSTICS
    • G10KSOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1781Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions
    • G10K11/17821Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions characterised by the analysis of the input signals only
    • G10K11/17825Error signals
    • GPHYSICS
    • G10MUSICAL INSTRUMENTS; ACOUSTICS
    • G10KSOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K2210/00Details of active noise control [ANC] covered by G10K11/178 but not provided for in any of its subgroups
    • G10K2210/10Applications
    • G10K2210/12Rooms, e.g. ANC inside a room, office, concert hall or automobile cabin
    • GPHYSICS
    • G10MUSICAL INSTRUMENTS; ACOUSTICS
    • G10KSOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K2210/00Details of active noise control [ANC] covered by G10K11/178 but not provided for in any of its subgroups
    • G10K2210/30Means
    • G10K2210/301Computational
    • G10K2210/3046Multiple acoustic inputs, multiple acoustic outputs

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Acoustics & Sound (AREA)
  • Multimedia (AREA)
  • Soundproofing, Sound Blocking, And Sound Damping (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

The invention discloses a kind of, and the domestic environment sound based on active noise reduction inhibits the location mode of signal, is modeled using the multichannel active noise reduction system frame structure based on Filtered x lms algorithms.Realize that a mute area, people can not be limited by fixed point in this region and avoid enjoying a kind of quiet atmosphere because of the discomfort of long periods of wear earplug in domestic environment.In the simulation model, it is proposed that seven path methods based on ray acoustics model acoustic path.Secondly, the three-dimensional sound field of the entire interior space is visualized;In addition, in order to weigh the noise reduction of analogue system, the signal data under sound suppression system is detected, it is clustered using FCM algorithms, the corresponding sound distributed areas of Delaunay Triangulation algorithm integration are introduced, the performance of emulation can directly be shown on three dimensions.

Description

A kind of domestic environment sound based on active noise reduction inhibits the location mode of signal
Technical field
The present invention relates to field of Computer Graphics, and in particular to a kind of domestic environment sound inhibition based on active noise reduction The location mode of signal.
Background technology
Noise is inevitably sound pollution in modern humans' life, and Long Term Contact noise will generate people's health Harmful effect, the research for carrying out noise analysis and control are paid attention to by domestic and international researcher.What people faced is no longer From outdoor noise, it is also frequently subjected to the puzzlement of noise indoors.Wherein, high-power electric appliance noise, or exist together a Room other people The sound that activity (speak, sing, seeing TV etc.) is sent out, when people needs to rest or work, these, which can all become, interferes them Noise, and these environmental noises greatly reduce the acoustics comfort level of human body so that working efficiency is lower, it is bad to rest, long Phase influences that hearing impairment or the non-sense of hearing can even be caused to influence, such as agitation, sleep disturbance, angiocardiopathy etc..Therefore, how One No Tooting Area of structure is reduced into ear noise, and it is a project for being worth research to improve home environment.
With the continuous promotion of quality of life, various "smart" products and technology emerge one after another, domestic environment comfort at The primary demand lived and worked in peace and contentment for people.Important composition portion of the comfortable Journal of Sex Research of household sound as digital home's key technology Point, it is traditional essential step strided forward to intelligent home of living at home.By carrying out sound inhibition to the sound field in domestic environment With to inhibiting the distribution situation of signal to illustrate, promotes the comfortable Journal of Sex Research of household sound, can not only emulate entire home environment Sound-filed simulation, while may be that the research of other digital home appliances provides support.
In home environment, demand of the human body to environment is desirable to feel at home constantly comfortably, and Many times are more sought A kind of quiet atmosphere wears noise reduction earplug and meets such condition to a certain extent.However prolonged wear can also make People does not feel like oneself, and can not meet more people's demands simultaneously.
In order to keep indoor life more comfortable, actively dropped using the multichannel based on Filtered-x lms algorithms System frame structure of making an uproar is modeled.Its main target is one mute area of realization in domestic environment, and people can be at this It is not limited by fixed point in region and avoids enjoying a kind of quiet atmosphere because of the discomfort of long periods of wear earplug.In the emulation mould It in type, in order to describe the circulation way of sound in space, is analyzed for traditional image method, simplifies this method, proposed One seven path method based on ray acoustics model acoustic path, and improved method can not only reflect sound Circulation way, it is more simplified in computational methods.In addition, in order to weigh the noise reduction of analogue system, Delaunay tri- is introduced The corresponding sound distributed areas of angle subdivision algorithm integration, can directly show the performance in emulation on three dimensions.
Invention content
It is an object of the invention to overcome the deficiencies in the prior art, and provide a kind of domestic environment sound based on active noise reduction Sound inhibits the location mode of signal, and this method by the voice signal under suppression system by carrying out triangulation, after obtaining noise reduction Sound field, realize the visual representation in local noise reduction area, while Delaunay triangulation network is closest to regularization, three obtained Edged surface piece is stablized the most.
Realizing the technical solution of the object of the invention is:
A kind of domestic environment sound based on active noise reduction inhibits the location mode of signal, specifically comprises the following steps:
1) theoretical frame of sound suppression system is established;
2) with the propagation in seven path methods simulation sound sources of ray acoustics indoors space;
3) entire interior space three-dimensional sound field is visualized;
4) the voice signal point set under suppression system is detected;
5) utilize FCM algorithms to the signaling point clustering after inhibition;
6) cluster result is passed through into Delaunay subdivision Algorithm Demo noise reductions;
By above-mentioned step, the sound distribution situation after indoor suppression system is intuitively presented.
In step 1), the theoretical frame of the suppression system is mostly logical based on Filtered-x lms algorithms Road active noise reduction system frame structure, initial voice is overlapped mutually with antinoise in error microphone position, to reach noise reduction Effect.
In step 2), the propagation in space indoors of described seven path methods simulation sound sources, specifically includes following step Suddenly:
The discrete tone of microphone acquisition 2-1) is used to be normalized as sound source, and to sound source;
Seven path methods 2-2) are used, simplifies indoor propagation model, is only generally indicated by increasing a decay factor g All situations;
2-3) by all Signal averagings, the signal after final sound inhibits is obtained.
In step 3), the entire interior space three-dimensional sound field of visualization specifically comprises the following steps:
3-1) by the way of sparse sampling site, room is divided into the square junior unit of same size;
The method for 3-2) using step 1), calculates the sound vibrations situation of all receiving points under sound suppression system.
The magnitude of sound of receiving point is combined with colour code 3-3) and is exported;
3-4) position of setting point source of sound and number calculate in space all receiving points seven using the method for step 2) The acoustic vibrations situation of a path method obtains different sound visualization results.
In step 4), the sound wave amplitude information value range of the mute point under sound suppression system be [- 0.0001, 0.0001]。
In step 5), clustered to the mute point data collection under entire suppression system using clustering algorithm.
In step 6), the data set after cluster is specifically divided into K different subsets, using the calculation of Delaunay subdivisions Method carries out one-sided to the sound point set after inhibition, obtains the sound distribution situation after noise reduction.
Advantageous effect:A kind of domestic environment sound based on active noise reduction provided by the invention inhibits the distribution side of signal Method, this method uses the multichannel active noise reduction system frame structure based on Filtered-x lms algorithms, using seven The mode of a path method simplifies under interior space structural model and boundary condition, is only indicated by increasing a decay factor g All situations, emulate room sound field.And it introduces Delaunay subdivisions in acoustics simplation visualizing research indoors and calculates Method realizes the sound distribution situation under indoor sound inhibits.And by the clear and intuitive visual presentation of house indoor environment, Respective value is simulated and signature analysis, and power-assisted is in the research and improvement of house room acoustics environment;Interior may be implemented in this method The distribution situation of sound after the inhibition of sound, clearly sound distributed effect can promote people to the intuitive of indoor sound Solution, meets the application demand of sound field simplation visualizing in intelligent domestic system.
Description of the drawings
Fig. 1 is a kind of location mode stream of domestic environment sound inhibition signal based on active noise reduction in present example Cheng Tu;
Fig. 2 is multi-channel sound suppression system basic model;
Fig. 3 is a reflection path trajectory diagram in rectangular space;
Fig. 4 is simulation model figure of the voice signal in a paths;
Fig. 5 inhibits the visible process figure of sound.
Specific implementation mode
The present invention is further elaborated with reference to the accompanying drawings and examples, but is not limitation of the invention.
A kind of domestic environment sound based on active noise reduction inhibits the location mode of signal, the research based on HVSI and interior Acoustic simulation emulates data, visualization is whole using the algorithm based on Delaunay Triangulation in conjunction with the acoustics under home environment The mute region of a interior space;As shown in Figure 1, specifically comprising the following steps:
S1, the theoretical frame for establishing sound suppression system;
S2, inhibit with seven path methods simulations of ray acoustics after the sound source propagation in space indoors, obtain acoustics Emulate data;
S3, data are emulated according to the acoustics that S2 is obtained, visualizes entire interior space three-dimensional sound field;
Voice signal point set under S4, detection suppression system;
S5, using FCM algorithms to the signaling point clustering after inhibition;
S6, cluster result is passed through into Delaunay subdivision Algorithm Demo noise reductions.
In step S1, the theoretical frame of the suppression system is mostly logical based on Filtered-x lms algorithms Road active noise reduction system frame structure, initial voice is overlapped mutually with antinoise in error microphone position, to reach noise reduction Effect.
In step S2, seven path methods simulation sound sources with ray acoustics propagation in space indoors obtains Acoustics emulates data, specifically includes the following steps:
S2-1, the discrete tone acquired using microphone are normalized as sound source, and to sound source, obtain normalizing Original sound source numerical information after change;
S2-2, using seven path methods, simplify indoor propagation model, only by increasing a decay factor g come general table Show all situations;
S2-3, by all Signal averagings, obtain the signal after final sound inhibits, i.e., pinpoint acoustics in space and inhibit emulation As a result.
In step S3, the entire interior space three-dimensional sound field of visualization specifically comprises the following steps:
S3-1, by the way of sparse sampling site, room is divided into the square junior unit of same size;
S3-2, using the method for step S1, calculate the sound vibrations situation of all receiving points under sound suppression system;
S3-3, the magnitude of sound of receiving point is exported with colour code combination;
S3-4, the position that point source of sound is arranged and number calculate in space all receiving points on seven roads using the method for S2 The acoustic vibrations situation of shot obtains different sound visualization results.
In step S4, the sound wave amplitude information value range of the mute point under the sound suppression system be [- 0.0001, 0.0001]。
In step S5, clustered to the mute point data collection under entire suppression system using clustering algorithm.
In step S6, the data set after cluster is specifically divided into K different subsets, using the calculation of Delaunay subdivisions Method carries out one-sided to the sound point set after inhibition, obtains the sound distribution situation after noise reduction.
In the present embodiment:
The system as shown in Figure 2 is mainly made of four parts:
(1) reference microphone array, the microphone array are mainly the sound that acquisition noise source is sent out, collected sound Signal is reference signal, and the reference signal that J reference microphone acquires at a certain moment is expressed as x1(n), x2(n) ..., xJ (n), the broad arrow in figure represents multichannel, and multiple signals are transmitted and handled in the matrix form, therefore reference signal Matrix indicates X (n)=[x1(n), x2(n) ..., xJ(n)]T, it is inputted as one of active noise reduction controller, due to System is that all pleasant sound to be directed in mute area be inhibited, therefore herein will be including all sounding such as people, household electrical appliances Sound source is defined as noise source;
(2) antinoise loudspeaker array, major function are the antinoises after playback process, it is therefore an objective to make to reach simultaneously quiet Antinoise at sound area space multiple spot is overlapped mutually with original sound, realizes that a degree of weakening of sound is even completely counterbalanced by. The anti-noise signal that K loud speaker of some time plays is expressed as y1(n),y2(n),...,yK(n), signal matrix is Y (n)=[y1 (n),y2(n),...,yK(n)]T
(3) error microphone array, major function are to acquire remaining sound as error signal, and M error microphone is adopted The signal of collection is respectively e1(n), e2(n) ..., eM(n), corresponding signal matrix E (n)=[e1(n),e2(n),...,eM(n)]T, The error signal also carrys out the coefficient of constantly regulate controller median filter as the input of active noise reduction controller;
(4) active noise reduction controller, major function are to be filtered generation anti-noise signal to reference signal, adaptive to calculate Method (such as LMS, FxLMS, FxNLMS etc.) calculates constantly regulate filter using reference signal and error signal as input Coefficient.
Seven path methods are that we are directed to a proposed simple model of acoustic path modeling in the course of the research, at present The model is directed to the rectangular space suitable for home environment, i.e. room is a cuboid.First, a space coordinate is defined System, the length in room are respectively X, Y, Z, and the point source of sound coordinate representation of any one position is (x in room1,y1,z1), and The coordinate of receiving point is (x2,y2,z2), and in the method only consider sound direct sound wave and through metope first reflection Sound, as title is contained, which contains only seven paths, i.e. a directapath and six difference The path reflected on six, space face (ceiling, floor, four sides wall), for the individual path of each, according to propagation Path length (li, i=1,2,3,4,5,6,7) and velocity of sound c calculate the propagation time for acquiring the path, you can learn that it reaches The delay of receiving point.
It is illustrated in figure 3 the paths that sound reaches receiving point by primary event.
When it is xoz coordinate sidewalls that sound (regarding a branch of sound ray as, that is, include a plurality of sound ray), which travels to coordinate, colliding At point p, a plurality of sound ray actually can be towards reflection from all directions, scattering, but the sound ray that can really return to receiving point only have Fig. 3 In this track.Shown in the flight distance calculation formula such as formula (1) in the path, reflected at the wall of xYz coordinate surfaces Shown in the distance calculation formula such as formula (2) that sound ray is propagated.
The distance of remaining four single reflection path and the distance of through acoustic path can be similarly found out, and then finds out seven The propagation time t of pathsi, ti=li/ c, i=1,2,3,4,5,6,7, and corresponding delay number of samples τi, τi=ti*fs, i= 1,2,3,4,5,6,7, wherein c, fsThe sample frequency of the velocity of sound and voice signal respectively in air.
It is the simulation modeling figure in one of path as shown in Figure 4.
The model that seven path methods establish sound is really a simplified model, and actual sound, which is propagated to also have, has biography A variety of situations such as the sound absorption of decaying, wall material during broadcasting and scattering, diffraction.These only pass through in the research of this paper Increase a decay factor g (0≤g≤1) generally to indicate all situations
X represents the voice signal of point source of sound, and x is after certain decaying reduction amplitude, with t (i.e. time delay) while as prolonging Slow module z-iInput, you can obtain a paths signal y at receiving point, similarly remaining six path be also use identical molds Type is simulated, and all Signal averagings finally can be obtained required voice signal.
As shown in figure 5, the present embodiment first simulates space, spatial model parameter is selected;Secondly, in space Each subelement carries out fixed point acoustics emulation, obtains the acoustics simulation numerical of each receiving point whithin a period of time;Secondly, then lead to The distance between calculating point source of sound and each receiving point are crossed, sound wave is obtained and travels to the propagation time of receiving point from sound source, then use The difference for showing visual time and propagation time obtains current time each receiving point in pinpointing acoustics simulation result Corresponding array index;Then, the information of acoustic wave of different amplitudes is shown visualization result by the color chart of different colours Come, finally uses the algorithm of Delaunay subdivisions to carry out one-sided to the sound point set after inhibition, obtain the sound after noise reduction point Cloth situation.

Claims (7)

1. a kind of domestic environment sound based on active noise reduction inhibits the location mode of signal, which is characterized in that specifically include as Lower step:
1)Establish the theoretical frame of sound suppression system;
2)With seven path methods simulation sound sources propagation in space indoors of ray acoustics;
3)Visualize entire interior space three-dimensional sound field;
4)Detect the voice signal point set under suppression system;
5)Using FCM algorithms to the signaling point clustering after inhibition;
6)Cluster result is passed through into Delaunay subdivision Algorithm Demo noise reductions;
By above-mentioned step, the distribution in indoor mute region is intuitively presented.
2. a kind of domestic environment sound based on active noise reduction according to claim 1, inhibits the location mode of signal, It is characterized in that, step 1)In, the theoretical frame of the suppression system is based on the more of Filtered-x lms algorithms Channel active noise reduction system frame structure, initial voice are overlapped mutually with antinoise in error microphone position, to reach drop The effect made an uproar.
3. a kind of domestic environment sound based on active noise reduction according to claim 1, inhibits the location mode of signal, It is characterized in that, step 2)In, seven path methods simulation sound sources with ray acoustics propagation in space indoors obtains Data are emulated to acoustics, are specifically included the following steps:
2-1)The discrete tone acquired using microphone is normalized as sound source, and to sound source, after obtaining normalization Original sound source numerical information;
2-2)Using seven path methods, simplifies indoor propagation model, only generally indicate all by increasing a decay factor g The case where;
2-3)By all Signal averagings, the signal after final sound inhibits is obtained, i.e., pinpoints acoustics in space and inhibits simulation result.
4. a kind of domestic environment sound based on active noise reduction according to claim 1, inhibits the location mode of signal, It is characterized in that, step 3)In, the entire interior space three-dimensional sound field of visualization specifically comprises the following steps:
3-1)By the way of sparse sampling site, room is divided into the square junior unit of same size;
3-2)Using step 1)Method, calculate sound suppression system under all receiving points sound vibrations situation;
3-3)The magnitude of sound of receiving point is combined with colour code and is exported;
3-4)Position and the number of point source of sound are set, using step 2)Method, calculate space in all receiving points on seven roads The acoustic vibrations situation of shot obtains different sound visualization results.
5. a kind of domestic environment sound based on active noise reduction according to claim 1, inhibits the location mode of signal, It is characterized in that, step 4)In, the sound wave amplitude information value range of the mute point under the sound suppression system be [- 0.0001, 0.0001]。
6. a kind of domestic environment sound based on active noise reduction according to claim 1, inhibits the location mode of signal, It is characterized in that, step 5)In, it is to be clustered to the mute point data collection under entire suppression system using clustering algorithm.
7. a kind of domestic environment sound based on active noise reduction according to claim 1, inhibits the location mode of signal, It is characterized in that, step 6)In, the data set after cluster is specifically divided into K different subsets, using Delaunay subdivisions Algorithm to after inhibition sound point set carry out one-sided, obtain the sound distribution situation after noise reduction.
CN201810121985.1A 2018-02-07 2018-02-07 A kind of domestic environment sound based on active noise reduction inhibits the location mode of signal Pending CN108376541A (en)

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Publication number Priority date Publication date Assignee Title
CN109036368A (en) * 2018-10-17 2018-12-18 广州市纳能环保技术开发有限公司 A kind of external device for actively eliminating noise
CN109994099A (en) * 2019-03-18 2019-07-09 佛山市云米电器科技有限公司 A kind of bedroom active noise reducing device and the bedroom with the active noise reducing device
CN116975528A (en) * 2023-07-17 2023-10-31 哈尔滨工程大学 Polar region sound signal characteristic extraction method and device based on Deltay internal triangulation
CN116975528B (en) * 2023-07-17 2024-03-15 哈尔滨工程大学 Polar region sound signal characteristic extraction method and device based on Deltay internal triangulation

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Application publication date: 20180807