阅读说明：本技术 具有分数阶的灵活差分麦克风阵列 (Flexible differential microphone array with fractional order ) 是由 陈景东 黄公平 于 2019-03-19 设计创作，主要内容包括：基于差分麦克风阵列(DMA)的指定目标方向性因子(DF)值为包括M个麦克风的DMA构建波束形成器。为DMA生成N阶波束图,其中N为整数,并且与N阶波束图相对应的第一DF值大于目标DF值。为DMA生成N-1阶波束图,其中与N-1阶波束图相对应的第二DF值大于目标DF值。为DMA生成分数阶波束图,其中与分数阶波束图相对应的第三DF值与目标DF值匹配,并且分数阶波束图包括来自N阶波束图的第一分数贡献和来自N-1阶波束图的第二分数贡献。(A beamformer is constructed for a Differential Microphone Array (DMA) including M microphones based on specified target Directivity Factor (DF) values of the DMA. An nth order beam pattern is generated for the DMA, where N is an integer and a first DF value corresponding to the nth order beam pattern is greater than a target DF value. An order-N-1 beam pattern is generated for the DMA, wherein a second DF value corresponding to the order-N-1 beam pattern is greater than the target DF value. A fractional order beam pattern is generated for the DMA, wherein a third DF value corresponding to the fractional order beam pattern matches the target DF value, and the fractional order beam pattern includes a first fractional contribution from the order-N beam pattern and a second fractional contribution from the order-N-1 beam pattern.)

1. A method for constructing a beamformer for a Differential Microphone Array (DMA) comprising M microphones, the method comprising:

assigning, by a processing device, a target Directivity Factor (DF) value of a beam pattern for the DMA;

generating, by the processing device, an N-order beam pattern for the DMA, where N is an integer and a first DF value corresponding to the N-order beam pattern is greater than the target DF value;

generating, by the processing device, an order-N-1 beam pattern for the DMA, wherein a second DF value corresponding to the order-N-1 beam pattern is less than the target DF value; and

generating, by the processing device, a fractional order beam pattern for the DMA, wherein a third DF value corresponding to the fractional order beam pattern matches the target DF value, and the fractional order beam pattern includes a first fractional contribution from the order-N beam pattern and a second fractional contribution from the order-N-1 beam pattern.

2. The method of claim 1, wherein the first, second and third DF values represent the ability of the respective nth order beamformer, nth-1 order beamformer and fractional order beamformer to suppress spatial noise from directions other than a specified look direction.

3. The method of claim 1, wherein the nth order, N-1 order, and fractional order beam patterns reflect sensitivity of the respective nth order, N-1 order, and fractional order beamformers to plane waves impinging on the DMA from a direction θ.

4. The method of any of claims 1 to 3, further comprising:

determining a value of the fractional order as (N-1+ α), where α is a real number between 0 and 1, α × (Nth order beam pattern) corresponding to the first fractional contribution and (1- α) × (N-1 order beam pattern) corresponding to the second fractional contribution.

5. The method of claim 4, wherein N is a maximum designable order of the beamformer based on a number M of microphones, the method further comprising:

receiving a plurality of electronic signals generated by the M microphones in response to a sound source;

determining, by an nth order beamformer, that a first estimate of the sound source includes more than a threshold amount of noise based on the signals;

performing an (N-1+ alpha) fractional order beamformer to compute a second estimate of the sound source based on the signals, where alpha is a maximum value for which the second estimate includes less than the threshold amount of noise.

6. The method of any one of claims 1 to 3, wherein the M microphones of the DMA are arranged as one of a linear array or a circular array.

7. The method of any of claims 1 to 3, further comprising:

generating a beamformer filter based on the fractional order beam pattern, wherein M > 2N + 1.

8. A method for constructing a fractional order beamformer for a Differential Microphone Array (DMA) comprising M microphones, the method comprising:

specifying, by a processing device, a target White Noise Gain (WNG) value for the DMA;

generating, by the processing device, an N +1 order beam pattern and an N +1 order beamformer for the DMA, wherein N is an integer value and a first WNG value corresponding to the N +1 order beamformer is less than the target WNG value;

generating, by the processing device, an N-order beam pattern and an N-order beamformer for the DMA, wherein a second WNG value corresponding to the N-order beamformer is greater than the target WNG value; and

generating, by the processing device, a fractional order beam pattern and the fractional order beamformer for the DMA, wherein a third WNG value corresponding to the fractional order beamformer matches the target WNG value and the fractional order beam pattern includes a first fractional contribution from the N +1 order beam pattern and a second fractional contribution from the N order beam pattern.

9. The method of claim 8, wherein the first, second, and third WNG values reflect sensitivity of the respective nth order beamformer, N-1 order beamformer, and fractional order beamformer to self-noise from M microphones of the DMA within a specified frequency range.

10. A system, comprising:

a data storage device; and

a processing device communicatively coupled to the data storage device and M microphones of a Differential Microphone Array (DMA) to:

specifying a target Directivity Factor (DF) value for the DMA;

generating an N-order beam pattern for the DMA, wherein N is an integer and a first DF value corresponding to the N-order beam pattern is greater than the target DF value;

generating an order-N-1 beam pattern for the DMA, wherein a second DF value corresponding to the order-N-1 beam pattern is less than the target DF value; and

generating a fractional order beam pattern for the DMA, wherein a third DF value corresponding to the fractional order beam pattern matches the target DF value and the fractional order beam pattern includes a first fractional contribution from the order-N beam pattern and a second fractional contribution from the order-N-1 beam pattern.

11. The system of claim 10, wherein the processing device generates a beamformer filter based on the fractional order beam pattern, where M >2 x N + 1.

12. The system of any one of claim 10 or claim 11, wherein the M microphones of the DMA are arranged as one of a linear array or a circular array

13. A Differential Microphone Array (DMA), comprising:

m microphones located on a substantially flat platform;

a processing device communicatively coupled to the M microphones to:

specifying a target Directivity Factor (DF) value for the DMA;

generating an N-order beam pattern for the DMA, wherein N is an integer and a first DF value corresponding to the N-order beam pattern is greater than the target DF value;

generating an order-N-1 beam pattern for the DMA, wherein a second DF value corresponding to the order-N-1 beam pattern is less than the target DF value; and

generating a fractional order beam pattern for the DMA, wherein a third DF value corresponding to the fractional order beam pattern matches the target DF value and the fractional order beam pattern includes a first fractional contribution from the order-N beam pattern and a second fractional contribution from the order-N-1 beam pattern.

14. The differential microphone array of claim 13, wherein the processing device:

determining a value of the fractional order as (N-1+ α), where α is a real number between 0 and 1, α × (Nth order beam pattern) corresponding to the first fractional contribution and (1- α) × (N-1 order beam pattern) corresponding to the second fractional contribution.

15. A differential microphone array according to any of claims 13 or 14, wherein N is the maximum designable order of the beamformer based on the number M of microphones and the processing means:

receiving a plurality of electronic signals generated by the M microphones in response to a sound source;

determining, by an nth order beamformer, that a first estimate of the sound source includes more than a threshold amount of noise based on the signals;

performing an (N-1+ alpha) fractional order beamformer to compute a second estimate of the sound source based on the signals, where alpha is a maximum value for which the second estimate includes less than the threshold amount of noise.

16. The differential microphone array of claim 13, wherein the M microphones of the DMA are arranged in one of a linear array or a circular array.

17. The differential microphone array of claim 13, wherein the processing device:

generating a beamformer filter based on the fractional order beam pattern, wherein M > 2N + 1.

18. A non-transitory machine-readable storage medium storing instructions that, when executed, cause a processing device to:

assigning a target Directivity Factor (DF) value to a Differential Microphone Array (DMA) having M microphones;

generating an N-order beam pattern for the DMA, wherein N is an integer and a first DF value corresponding to the N-order beam pattern is greater than the target DF value;

generating an order-N-1 beam pattern for the DMA, wherein a second DF value corresponding to the order-N-1 beam pattern is less than the target DF value; and

generating a fractional order beam pattern for the DMA, wherein a third DF value corresponding to the fractional order beam pattern matches the target DF value and the fractional order beam pattern includes a first fractional contribution from the order-N beam pattern and a second fractional contribution from the order-N-1 beam pattern.

19. The non-transitory machine-readable storage medium of claim 18, further comprising instructions that when executed cause the processing device to generate a beamformer filter based on the fractional order beampattern, wherein M >2 x N + 1.

20. The non-transitory machine-readable storage medium of any one of claim 18 or claim 19, wherein the M microphones of the DMA are arranged as one of a linear array or a circular array.

Technical Field

The present disclosure relates to microphone arrays, and more particularly, to Flexible Differential Microphone Arrays (FDMA) having fractional order beamformers.

Background

In voice communications between humans and human-machine voice interfaces, the signal of interest picked up by a microphone sensor is often contaminated by unwanted elements such as additive noise, reverberation and interference, which may impair the fidelity and quality of the signal of interest and also affect the performance of subsequent operations, such as signal-based Automatic Speech Recognition (ASR). To address these adverse effects and recover the signal of interest, directional signal transmission or reception may be performed using a microphone array with spatial filters called beamformers. A microphone array may contain a plurality of microphones arranged according to a geometric relationship (e.g., in a line, on a plane, on a three-dimensional surface, or in three-dimensional space). Each microphone of the array of microphones may capture a version of a sound signal originating from the sound source and convert the captured signal into an electronic signal. Each version of the signal may represent a sound source captured at a particular angle of incidence relative to a reference point (e.g., a reference microphone position in the array) at a particular time. The time may be recorded to determine the time delay of each microphone relative to a reference point.

A Differential Microphone Array (DMA) uses signal processing techniques to obtain a directional response to a source signal based on the difference of pairs of source signals. The difference can be obtained by combining the electronic signals from the microphones of the DMA.

Drawings

The present disclosure is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings.

Fig. 1 is a flowchart illustrating a method for constructing a beamformer with a fractional order beam pattern based on a target Directivity Factor (DF) value of FDMA according to an embodiment of the present disclosure.

Fig. 2 is a flowchart illustrating a method for FDMA-based target White Noise Gain (WNG) construction of a beamformer with a fractional order beam pattern according to an embodiment of the present disclosure.

Fig. 3 illustrates an FDMA and beamformer system according to an embodiment of the present disclosure.

Fig. 4 is a data flow diagram illustrating the data flow of an FDMA and beamformer system according to an embodiment of the present disclosure.

Figures 5A-5C illustrate a graph of beam patterns of integer order and their corresponding DF and WNG values as a function of frequency, according to an embodiment of the present disclosure.

Figures 6A-6C illustrate integer and fractional order beam patterns, and their corresponding DF and WNG values, as a function of frequency, according to embodiments of the present disclosure.

Figures 7A-7B illustrate graphs of DF and WNG values as a function of fractional order according to embodiments of the present disclosure.

Fig. 8 is a block diagram illustrating an exemplary computer system in accordance with an embodiment of the present disclosure.

Detailed Description

Compared to a single microphone, sound signals received at different microphones in a microphone array include redundancy that can be used to compute an estimate of the sound source to achieve certain goals, such as noise reduction/speech enhancement, Automatic Speech Recognition (ASR), sound source separation, dereverberation, spatial recording, and sound source localization and tracking. The microphone array may be communicatively coupled to a processing device (e.g., a Digital Signal Processor (DSP) or Central Processing Unit (CPU)) that includes circuitry programmed to implement a beamformer to compute an estimate of a sound source.

A beamformer is a spatial filter that uses multiple versions of a sound signal captured by microphones in an array of microphones to identify sound sources according to certain optimization rules. Some embodiments of the beamformer do not work well when dealing with low frequency noise components because the beamwidth (i.e., the width of the main lobe in the frequency domain) associated with the beamformer is inversely proportional to frequency. To combat the non-uniform frequency response of the beamformer, Differential Microphone Arrays (DMAs) have been used to implement fundamental frequency invariant beam patterns. The beam pattern (also called a directivity pattern) reflects the sensitivity of the beamformer to plane waves striking the DMA from a particular angular direction. The DMA may contain an array of microphone sensors that are responsive to the spatial derivative of the sound pressure field generated by the sound source. FDMA may include flexibly distributed microphones (e.g., linear, circular, or other array structures) arranged on a common corporate platform.

The DMA may measure the derivatives (derivatives in different orders) of sound signals captured by the microphones, where the collection of sound signals forms the sound field associated with the microphone array. For example, a first order DMA beamformer formed using the difference between a pair of two microphones (adjacent or non-adjacent) may measure the first derivative of the sound pressure field, and a second order DMA beamformer formed using the difference between a pair of two first order differences of the first order DMA may measure the second derivative of the sound pressure field, where the first order DMA includes at least two microphones and the second order DMA includes at least three microphones. Thus, an nth order DMA beamformer may measure the nth order derivative of the sound pressure field, where the nth order DMA comprises at least N +1 microphones. An aspect of the beam pattern of a microphone array may be quantified by a directivity factor (or directivity), which is the ability of the beam pattern to maximize the ratio of its sensitivity in the look direction to its average sensitivity in all directions. The viewing direction is the angle of incidence of the sound signal with the greatest sensitivity. The DF of the DMA beam pattern may increase with the order of the DMA. However, higher order DMAs may be very sensitive to noise generated by the hardware elements of each microphone of the DMA itself, referred to as White Noise Gain (WNG).

One way to reduce WNG is to increase the number of microphones without increasing the order of the DMA beamformer. However, with a fixed array structure and number of microphones for the DMA, the order of the DMA beamformer may need to be reduced from the current order to a lower positive integer order if the WNG of the DMA beamformer cannot meet the robustness requirement (e.g., a minimum tolerable WNG). A lower order would have a detrimental effect on DF and therefore in DMA applications where the number of microphones is fixed, it would be beneficial to be able to reduce the order of the DMA beamformer to a certain level. To address these technical issues, embodiments of the present disclosure provide a microphone array that may be associated with a beamformer that may have an integer or fractional order of beampatterns to meet robustness requirements while maintaining a desired (or target) DF.

According to these embodiments, a DMA beamformer with fractional order may achieve a continuous tradeoff between performance (e.g., DF versus WNG) of the maximum designable order (e.g., order N) and the omni-directional order (e.g., order 0). Fractional order beam patterns are generated to achieve a continuous tradeoff of performance between order N and 0. To construct the DMA beamformer, the beamformer's beam pattern (e.g., directivity pattern) is approximated using Jacobi-Anger expansion, and then appropriate beamforming filters are determined so that their beam patterns are as close as possible to the desired frequency-invariant beam pattern. Further, a value representing the fractional order of the constructed beamformer may be determined based on the specified DF or WNG value for the fractional order DMA beamformer as explained below with respect to fig. 1 and 2.

Fig. 1 is a flow diagram illustrating a method 100 for constructing a beamformer with a fractional order beam pattern based on a target DF value of FDMA according to an embodiment of the present disclosure. The method 100 may be performed by processing logic that comprises hardware (e.g., circuitry, dedicated logic, programmable logic, microcode, etc.), software (e.g., instructions run on a processing device to perform hardware simulation), or a combination thereof.

For purposes of explanation, the methodologies are depicted and described as a series of acts. However, acts in accordance with this disclosure may occur in various orders and/or concurrently with other acts not presented and described herein. Moreover, not all illustrated acts may be required to implement a methodology in accordance with the disclosed subject matter. Further, the methodologies may alternatively be represented as a series of interrelated states via a state diagram or events. Moreover, it should be appreciated that the methodologies disclosed herein are capable of being stored on an article of manufacture to facilitate transporting and transferring such methodologies to computing devices. The term article of manufacture, as used herein, is intended to encompass a computer program accessible from any computer-readable device or storage media. In one embodiment, these methods may be performed by a fractional beamformer 310 executing on the processing device 306 as shown in fig. 3.

Referring to fig. 1, at 102, a processing device may begin performing operations to construct a beamformer for DMA with M microphones flexibly distributed over a plane, such as FDMA302 of fig. 3. Without limitation, it may be assumed that the center of the DMA coincides with the origin of a two-dimensional Cartesian coordinate system, whichThe neutral azimuth angle is measured counterclockwise from the x-axis. In this case, the mth array element (e.g., mth microphone in FDMA 302) may have a radius r_mAnd angular position psi_mAnd the direction of the source signal to the DMA may be determined by an azimuth angle θ_sAnd (4) parameterizing. The steering vector may represent the relative phase shift of the incident far-field waveform of the microphone across the DMA. As described above, using the characteristics of a DMA, the steering vector of the DMA may be defined as:

where superscript T is the transpose operator, j is the imaginary unit, j²-1, ω -2 pi f is the angular frequency, and f>0 is the time frequency.

At 104, the processing device may specify a target DF value for the DMA. As described above, DF represents the ability of the beamformer to suppress spatial noise from directions other than the look direction. As described above, the DF associated with a DMA can be written as:

wherein H (ω) ═ H₁(ω)H₂(ω)...H_m(ω)]^TIs the global filter of the beamformer associated with the DMA, the superscript H denotes the conjugate transpose operator, [ H₁(ω)H₁(ω)...H_M(ω)]^TSpatial filters, Γ, for M microphones_d(ω) is the pseudo-coherence matrix of the noise signal in a diffuse (spherical isotropic) noise field, and Γ_dThe (i, j) th element of (ω) isWherein delta_ijIs the distance between microphone elements i and j, and c is a constant of the speed of sound.

At 106, the processing device may generate an nth order beampattern for the DMA, where N is an integer and a first DF value corresponding to the nth order beampattern is greater than a target DF value. In this case, the nth order beam pattern exceeds the target DF value, and thus negatively affects the WNG value more than necessary, e.g., there is more spatial white noise than needed to achieve the target DF value.

As described above, the DMAs may be associated with beam patterns that reflect the sensitivity of the respective beamformer to plane waves that strike the DMA from a particular angular direction θ. The beam pattern of a plane wave impinging on the above described DMA from the angle θ can be defined as:

therefore, for such DMA, the angle θ_sThe corresponding target frequency invariant beam pattern, i.e. the angle of incidence of the sound signal, can be written asWherein a is_N,nAre real coefficients that determine the shape of the different beam patterns of the N-th order DMA. B (a)_N,θ-θ_s) Can be rewritten as:

wherein b is_N,0＝a_N,0,

Is a (2N +1) X (2N +1) diagonal matrix, and

b_N＝[b_N,-N...b_N,0...b_N,N]^Tand an

P_e(θ)＝[e^-jNθ...1...e^jNθ]^T,

Respectively, vectors of length 2N + 1. Using beam formingWave beam pattern (Vb [ h (omega) ]), theta) after filter h (omega)]Should correspond to the target beam pattern B (B)_N,θ-θ_s) And (6) matching. For example, the target (or desired) beam pattern may be a second order hypercardioid with coefficients:

and

at 108, the processing device may generate an order N-1 beam pattern for the DMA, where a second DF value corresponding to the order N-1 beam pattern is less than the target DF value. In this case, the order N-1 does not reach the target DF value, so there is more diffuse noise (e.g., from the unfocused direction) than is required for the target DF value, e.g., there is more noise from a direction other than the viewing direction than is desired (e.g., of the target).

At 110, the processing device may generate a fractional order beam pattern for the DMA, where a third DF value corresponding to the fractional order beam pattern matches the target DF value and the fractional order beam pattern includes a first fractional contribution from the order-N beam pattern and a second fractional contribution from the order-N-1 beam pattern.

A beam pattern that achieves a tradeoff (e.g., something in between) between the performance of the beam patterns of order N to 0 (e.g., DF and WNG) may be defined as:

wherein alpha is_N＝[α₀ α₁ … α_N]^TWherein 0 is>αN′<1, andthe compromise beam pattern can be written as:

wherein

Wherein N' is 0,1, N as a componentThe weighting coefficient of (2). In addition, in n>In case of N ', b'_N′,nThe value of (d) may default to 0.

Therefore, by appropriately selecting α_N′The above-described compromise beam pattern may achieve a continuous performance tradeoff between an nth order and a 0 (omni-) order beam pattern. The compromise beam pattern defined above has N +1 different parameters which can be determined in a multi-stage manner, i.e. a compromise can be established between the beam patterns of order N and (N-1), if not (N-1) and (N-2), and so on, up to omni-direction. First, the fraction (N-1+ alpha) [ hereinafter abbreviated as (N-1)_α]The order beam pattern achieves a trade-off between an order N beam pattern and an order (N-1) beam pattern, defined as:

where α ∈ [0,1] is the actual weight that determines the degree of compromise between order N and (N-1).

Fractional order beam patterns between the N order and (N-1) order beam patterns may also be rewritten as:

wherein

And

whereinIs a zero-padded coefficient vector of length 2N + 1.

Thus, a beam pattern that achieves a continuous tradeoff between the N-order and 0-order beam patterns is defined as

Wherein the content of the first and second substances,is the fractional order of the beam pattern, wherein Is an integer part, and α, (α ∈ [0,1]]) Is the fractional part. Fractional orderAnd corresponding vectorCan be defined in a multistage manner as:

wherein

Where N is 0,1, N, a zero-padding coefficient vector of length 2N + 1. Therefore, the temperature of the molten metal is controlled,

wherein

At 112, the processing device may end execution of the operations to build a fractional order beamformer for the DMA. For example, as a final step in constructing the beamformer, the processing means may generate a beamforming filter based on the generated fractional order beam pattern. The beamforming filter h (ω) may be derived, for example, by using a minimum norm method:

complianceThe solution may be:

as explained more fully below with respect to fig. 4. The wave beam pattern B [ h (omega), theta ] constructed after the wave beam forming filter h (omega) is applied]Should be aligned with the target beam pattern B (B)_N,θ-θ_s) Substantially matching.

Determining fractional order using target DF values

Given the target DF value of the DMA, fractional orderMay be based on θ_sDetermined at 0 ° because of θ_sThe value of (d) has no effect on DF. Thus, N_αThe frequency-independent plane DF of the order beam pattern (in the plane of the M microphones of the DMA) is defined as:

it can be written as:

thus, the frequency-independent DF of the nth order beam pattern can be defined as:

wherein

Therefore, the temperature of the molten metal is controlled,DF of beam pattern satisfiesSo that for a given value of DF,desired stepThe integer part of (1), i.e.Is obtained as

Thus, it is possible to provide

Wherein:

and

andis a vector that determines the real coefficients of the beam pattern. Thus, the solution to the fractional part α is determined by the following equation:

it can be equivalently converted to a quadratic equation, the solution of which is simply calculated as:

the fractional parameter a may be determined as a solution in the range of 0, 1.

In one embodiment, the fractional order beam pattern may be determined based on a target WNG value. Figure 2 is a flow diagram illustrating a method 200 for constructing a beamformer with a fractional order beam pattern based on FDMA target WNG values according to some embodiments of the present disclosure. Method 200 may be performed by processing logic that comprises hardware (e.g., circuitry, dedicated logic, programmable logic, microcode, etc.), software (e.g., instructions run on a processing device to perform hardware simulation), or a combination thereof.

Referring to fig. 2, at 202, a processing device may begin performing operations to construct a beamformer for DMA with M microphones flexibly distributed over a plane, such as FDMA302 of fig. 3. As described above with respect to FIG. 1, the center of the DMA may be, but is not limited to, coincident with the origin of a two-dimensional coordinate system, where the azimuth angle is measured counterclockwise from the x-axis.

At 204, the processing device may specify a target WNG value for the DMA. As described above, WNG evaluates the beamformer's sensitivity to DMA's own imperfections (e.g., noise from its own hardware elements). The WNG associated with the DMA, as described above with respect to fig. 1, may be written as:

wherein H (ω) ═ H₁(ω) H₂(ω) ... H_m(ω)]^TIs a global filter of the beamformer associated with the DMA, the superscript H denotes the conjugate transpose operator, and H₁(ω) H₁(ω) ... H_M(ω)]^TIs a spatial filter for the M microphones.

At 206, the processing device may generate an order-N beam pattern and a corresponding order-N beamformer for the DMA, where N is an integer and a first WNG value corresponding to the order-N beamformer is less than a target WNG value. In this case, the nth order beam pattern does not reach the target WNG value, and therefore negatively affects the DF value more than necessary, e.g., there is more spatial noise than needed to achieve the target WNG value.

At 208, the processing device may generate an order N-1 beam pattern and corresponding beamformer for the DMA, where a second WNG value corresponding to an order N-1 directional beamformer is greater than the target WNG value. In this case, the order N-1 exceeds the target WNG value, so there is more spatial white noise (e.g., noise from a DMA microphone) than is needed based on the target WNG value.

At 210, the processing device may generate a fractional order beam pattern and a corresponding beamformer for the DMA, where a third WNG value corresponding to the fractional order beamformer matches the target WNG value and the fractional order beam pattern includes a first fractional contribution from the nth order beam pattern and a second fractional contribution from the N-1 order beam pattern.

As described above with respect to fig. 1, a continuous performance tradeoff between the nth order and the 0 th order beam patterns can be achieved by properly selecting the value of the fractional order a. Also as described above, the fractional order may be determined in a multi-stage manner, i.e., first establishing a tradeoff between order N +1 and order N beam patterns, then establishing a tradeoff between order N and order (N-1) beam patterns, and so on, up to omni-bearing. First, a fractional (N + α) order beam pattern (α ∈ [0,1]) that achieves a tradeoff between the N +1 order and the N order beam patterns may be determined.

At 212, the processing device may end execution of the operations to build a fractional beamformer for the DMA. As noted above with respect to fig. 1, as a final step in constructing the fractional order beamformer, the processing apparatus may generate a beamforming filter based on the generated fractional order beam pattern. As described above, the beamforming filter h (ω) may be derived by using a minimum norm method as described more fully below with respect to fig. 4:

compliance

The solution can be defined as:

the wave beam pattern B [ h (omega), theta ] constructed after the wave beam forming filter h (omega) is applied]Should correspond to the target beam pattern B (B)_N,θ-θ_s) And (6) matching.

Determining fractional order using DMA target WNG values

White noise amplification problems (e.g., WNG) can greatly affect the performance of DMA. Therefore, achieving reasonable WNG levels while also achieving relatively high DF values with DMA beamformers is an important issue. As described above, the WNG of a DMA may be defined as:

for fraction (N)_α) The order beam pattern can be written as:

wherein

And

whereinIs the real part of a complex number, andis a vector that determines the real coefficients of the beam pattern. Thus, by neglecting the approximation error without distortion constraint in the viewing direction, WNG of the nth order beam pattern can be defined as:

thus, at a given frequency,WNG of a beam pattern satisfies Thus for a given WNG valueDesired stepThe integer part of (1), i.e.Is obtained as:

then, can be set byTo calculate the fraction alpha, which is equivalent to solving the following equation:

wherein:

and

thus, the solution for the fractional part α can be determined as:

the fractional parameter α may be determined as [0,1]]Solutions within the range. Thus, the DMA beamformer can WNG with a given minimum fault toleranceIs constructed of whereinIs a constant determined by the robustness level of the DMA system.

Fig. 3 illustrates a detailed arrangement of an FDMA and beamformer system 300 according to some embodiments of the present disclosure. As shown in fig. 3, system 300 may include FDMA302, analog-to-digital converter (ADC)304, and processing device 306. As described above, FDMA302 can include flexibly distributed microphones (m) arranged on a common corporate platform₀,m₁,...,m_k,...,m_M). The position of these microphones can be specified relative to a coordinate system (x, y). The coordinate system may include an origin (O) that may specify the location of the microphone. The coordinates of the microphone may be specified as:

r_k＝r_k[cos(ψ_k)sin(ψ_k)]^T,

k 1, 2.. M, where superscript T is the transpose operator, r_kRepresents the distance of the kth microphone from the origin, and_krepresenting the angular position of the kth microphone. The distance between microphone i and microphone j is

δ_ij＝||r_i-r_j||,

Where i, j ═ 1, 2.·, M, and | · | | |, are euclidean norms, assuming that the maximum distance between the two microphones is less than the wavelength (λ) of the sound wave.

Assume that the source signal is a plane wave from the far field, propagates at the speed of sound (c 340m/s) in a muffled environment, and impinges on FDMA 302. The incident direction of the source signal to FDMA302 is azimuth angle theta_s. The time delay between the kth microphone and the reference point (O) can be written as:

where k is 1, 2.

FDMA302 may be associated with a steering vector that may represent the relative phase shift of the incident far-field waveform across the microphone of FDMA 302. Thus, the steering vector is the response of FDMA302 to the impulse input. As described above, with the features of FDMA302, the steering vectors of FDMA302 can be defined as:

where superscript T is the transpose operator, j is the imaginary unit, j²-1, ω -2 pi f is the angular frequency, and f>0 is the time frequency.

As described above, the microphone sensor of FDMA302 can be from the incident direction θ_sAn acoustic signal originating from an acoustic source is received. In one embodiment, the acoustic signal may comprise a first component s (t) from the acoustic source and a second component v (t) of noise (e.g. additive noise), where t is time. Each microphone of FDMA302 can receive acoustic signal a_k(t), which may comprise a delayed copy of the first component s (t) from the sound source, denoted as s (t + d)_k) And is represented by v_k(t), where t is time, k is 1,2,_kis a microphone m_kTime delay of received acoustic signal to reference point, and v_k(t) denotes a microphone m_kThe noise component of (b). Microphone m of FDMA302_kThe electronic circuit of (a) may be_k(t) conversion to an electronic signal e which can be fed to the ADC 304_k(t), wherein k is 1, 2. In one embodiment, the ADC 304 may further convert the electronic signal e_k(t) conversion to a digital signal y_k(t) of (d). The analog-to-digital conversion may include converting the input e_k(t) is quantized to a discrete value y_k(t)。

In one embodimentThe processing means 306 may comprise an input interface (not shown) to receive the digital signal y_k(t) and identifying the sound source using the fractional beamformer 310, the fractional beamformer 310 being obtained using the above-described embodiment. To perform the fractional beamformer 310, in one embodiment, the processing device 306 may implement a pre-processor 308 that may further process the digital signal y for the fractional beamformer 310_k(t) of (d). Preprocessor 308 may include hardware circuitry and software routines to transform digital signal y using, for example, a short-time Fourier transform (e.g., STFT 404 shown in FIG. 4) or any suitable type of frequency transform_k(t) conversion to a frequency domain representation. The STFT may compute the fourier transform of its input signal over a series of time frames. Thus, the digital signal y may be processed over a series of time frames_k(t)。

In one embodiment, the preprocessing module 308 may be paired with the microphone m of FDMA302_kAssociated input y_k(t) performing STFT and computing a corresponding frequency domain representation (e.g., Y)_k(ω)406, as shown in FIG. 4). In one embodiment, the fractional beamformer 310 may receive the digital signal y_kFrequency of (t) represents Y_k(ω)406 and computes an estimate in the frequency domain (e.g., Z (ω)418, as shown in fig. 4) of the first component (s (t)) from the sound source. The frequency domain may be divided into a plurality (L) of subbands and the fractional beamformer 310 may compute an estimate (e.g., Z (ω))418 for each subband.

The processing device 306 may also include a post-processor 312, and the post-processor 312 may convert the estimate Z (ω)418 for each sub-band back to the time domain to provide an estimated sound source denoted x (t). The estimated sound source x (t) may be determined relative to the source signal received at a reference point (e.g., microphone sensor position) in FDMA 302.

Fig. 4 is a data flow diagram illustrating data flow for a Flexible Differential Microphone Array (FDMA) and beamformer system 400 according to an embodiment of the present disclosure. As shown in fig. 4, system 400 may include FDMA302 (as described above with respect to fig. 3) and beamforming filter h (ω) 416. FDMA302 can include M flexibly distributed microphones arranged on a common corporate platformWind (m)₁,m₂,...,m_k,...,m_M). These microphones may be located anywhere on the ensemble of platforms, for example, the location is flexible. The location of these microphones may be specified relative to a coordinate system (x, y), as explained more fully above with respect to fig. 3.

In one embodiment, data received from the M microphones of FDMA302 may be transmitted to each microphone M of FDMA302_kAssociated time domain input y_k(t) (shown in FIG. 3) is preprocessed using a Short Time Fourier Transform (STFT)404 to compute a corresponding frequency domain representation Y_k(ω)406, where (t) is the time of the input, ω (ω ═ 2 π f) denotes the angular frequency domain and k ═ 1, 2. In one embodiment, the beamforming filter h (ω)416 may receive the frequency representation Y_k(ω) (as y (ω)408) and calculates an estimate Z (ω)418 in the frequency domain of the first component s (t) from the sound source.

The beamforming filter h (ω)416 may be determined such that its beam pattern is as close as possible to the desired frequency-invariant beam pattern (as described above with respect to step 106 of the method 100 of fig. 1). To achieve this, the exponential function B [ h (ω), θ ] appearing in the beam pattern of the beamformer can be approximated using an nth order Jacobi-Anger expansion:

wherein J_n(x) Is a first class of nth order bessel functions. By using the Jacobi-Anger expansion described above and limiting the Jacobi-Anger series to the order ± N (since the maximum designable order can be determined as N based on the number M of microphones of FDMA 302), it is shown that the beam pattern of the beamformer can be written as:

whereinWhere N is 0, ± 1, ± 2, ·, ± N, is a vector of length M. Based on the representation developed by Jacobi-Anger, there are

Ψ(ω)h(ω)＝γ^*(θ_s)b_N,

Wherein

Is a (2N +1) XM matrix, with superscript denotes the complex conjugate. Thus, the beamforming filter h (ω) may be derived, for example, by using a minimum norm method:

complianceThe solution can be determined as:

as shown in fig. 4, the beamforming filter h (ω)416 may include three parts (the details of which have been discussed above): a (ω) depends on the positions of the M microphones of FDMA302 (where a (ω) ═ Ψ)^-1(ω), for M ═ 2N +1, a (ω) ═ Ψ^H(ω)[Ψ(ω)Ψ^H(ω)]^-1For M>2N +1, N being the order of FDMA302, Ψ being the angular position of the microphone, and superscript H representing the conjugate transpose operator), γ^*(thetas) steering of the beam pattern (where theta is the angle of incidence of the sound source), anddetermining a trade-off between shape of a beam pattern and performance (e.g., DF and WNG) of consecutive integer order beam patterns, whereAnd alpha is [0,1]]Real numbers within the range).

As seen in the data flow of system 400, the three portions of beamforming filter h (ω)416 operate independently of each other, so that adjustment of the microphone position, steering of the beam pattern, or control of the order of the beam pattern (and fractional order tradeoffs thereof) can be implemented separately without regard to the other portions. Thus, the methods described herein for generating fractional order beampatterns (and constructing corresponding fractional order beamformers) can be readily applied to existing differential microphone array systems to increase robustness without unnecessarily sacrificing DF by reducing the order of the system to the next lower integer value.

Figures 5A-5C illustrate integer order beam patterns (502, 504, 506, and 508) and their corresponding DF and WNG values as a function of frequency (500B and 500C) according to some embodiments of the present disclosure. For DMA, the desired frequency independent beam pattern can be selected using the unique null of maximum multiplicity in the direction opposite to the viewing direction:

the advantage of such a beam pattern is that it is free of side lobes and is therefore desirable in many practical applications where the interference is mainly located behind the desired direction (e.g. the viewing direction). For the desired frequency-independent beam pattern, the respective coefficients b determining the shape of the beam patterns of different orders are_NGiven in table 1 below.

TABLE 1

Plots (500B and 500C) of the beam patterns (502, 504, 506, and 508) and their corresponding DF and WNG values as a function of frequency with a 1.0cm radius target consisting of seven microphonesQuasi-integer order (e.g., 0,1, 2, 3) uniform circular array correlation. In this case (e.g., M-7), the maximum designable order of the DMA is N-3, and thus M-2N + 1. Without loss of generality, assume that the desired viewing direction is 0 °, θ_s0 deg.. Fig. 5A shows beam patterns (502, 504, 506, and 508) of the 3 rd, 2 nd, 1 st, and 0 th order beam patterns of the circular DMA when f is 500 Hz. It is clear that the beam patterns (502, 504, 506 and 508) have unique nulls (except for 0 th order 508) at 180 ° and are 0 ° symmetric about the viewing direction.

As shown in fig. 5B and 5C, graphs 500B and 500C map the corresponding DF and WNG values for the 3 rd, 2 nd, 1 st, and 0 th order beam patterns (502, 504, 506, and 508), respectively, as a function of frequency f (khz). As can be seen in graphs 500B and 500C, the higher order beamformer (e.g., 3 rd order) has a very small WNG value at low frequencies, indicating that the beamformer significantly amplifies white noise. Thus, it is clear that WNG can only be improved by reducing the integer order of the circular DMA for a fixed number of microphones (e.g., M ═ 7). However, for circular DMA, this order reduction results in a flatter beam pattern and a much lower DF. For example, if a circular DMA system has a minimum tolerated WNG requirement of-20 dB (e.g., a robustness requirement), only first order circular DMAs below 800Hz and second order circular DMAs between 800Hz and 2300Hz can be implemented as shown in FIGS. 5A-5C.

Figures 6A-6C illustrate graphs (600B and 600C) of integer and fractional order beam patterns (602, 604, 606, and 608) and their corresponding DF and WNG values as a function of frequency, according to some embodiments of the present disclosure.

Graphs (600B and 600C) of beam patterns (602, 604, 606, and 608) and their corresponding DF and WNG values as a function of frequency versus fractional order N, which may include seven microphones, with a radius of 1.0cm_αE {3.0,2.6,2.4,2.0} uniform circular array. As with fig. 5A-5C (e.g., M-7), the maximum designable order of the DMA is N-3, so M-2N +1, and the desired viewing direction is assumed to be 0 °, θ_s0 deg.. Fig. 6A shows beam patterns (602, 604, 606, and 608) of the 3 rd, 2.6 th, 2.4 th, and 2 nd order beam patterns of the circular DMA when f is 500 Hz. It is clear that it is possible to use,the beam patterns (602, 604, 606, and 608) have a unique null at 180 ° and are symmetrical with respect to the viewing direction of 0 °.

As shown in fig. 6B and 6C, graphs 600B and 600C map the respective DF and WNG values of the 3 rd, 2.6 th, 2.4 th and 2 nd order beam patterns (502, 504, 506 and 508), respectively, as a function of frequency f (khz). As can be seen in graphs 600B and 600C, the fractional order beamformer can achieve a good compromise between the performance of the third and second order beamformers for circular DMA. Thus, with a target WNG of-20 dB, the fractional order N that meets the requirements for each frequency can be determined separately, as shown in FIGS. 5A-5C_αIs a suitable value of. Thus, it is clear that for a fixed number of microphones (e.g., M ═ 7), WNG can now be improved by reducing the fractional order of the circular DMAs so that DF is not unnecessarily lost after the WNG target has been met. However, this fractional order reduction does not result in excessive flattening of the beam pattern and only reduces the DF of the circular DMA within the range needed to achieve the target WNG value.

Thus, a WNG value W with a known minimum tolerance can be designed₀Is provided, wherein W is assumed₀Is a constant determined by the robustness level of the system. As discussed, the maximum designable order of DMA is three-order for seven microphones, i.e., N-3. Thus, for each frequency, a third order DMA can be designed directly if it already satisfies the minimum tolerant WNG. Otherwise, embodiments may include that the fractional order N may be determined first_αThen designing a corresponding fractional order DMA processing device. A robust DMA beamformer can meet the desired level of robustness over the frequency band of interest by sacrificing some of the directivity, i.e., achieving a performance tradeoff between a high DF value and good robustness.

Figures 7A-7B illustrate graphs (700A and 700B) of DF and WNG values as a function of fractional order according to some embodiments of the present disclosure. In order to more clearly see the fractional order N_αThe effect on beamforming performance, graphs 700A and 700B plot fractional order N as the order from 3 to 0_αDF and WNG of the circular DMA of fig. 6A-6C. The experimental conditions were the same as in fig. 6A-6C, so that M ═ 7,the maximum designable order of the DMA is N-3, such that M-2N +1, assuming the desired viewing direction is 0 °, i.e. θ_s0 ° and a frequency f of 500 Hz.

As seen in graphs 700A and 700B, DF is scaled by the fractional order N_αAnd decreases with fractional order N of WNG_αBut increases to achieve a continuous tradeoff in performance of the circular DMA between order N and 0. Thus, N_αThe value of (chosen for designing a circular DMA) controls the performance tradeoff between large DF values and white noise amplification.

Circular dma (cdma) and linear dma (ldma) with fractional order:

CDMA can be designed with M microphones distributed as a uniform circular array, which is equivalent tor_mR, M1, 2, M, wherein r_mRepresents the distance (e.g., radius) of the mth microphone from the origin, and ψ_mRepresenting the angular position of the mth microphone. Thus, based on the analysis described above with respect to fig. 4, the beamforming filter for CDMA can be defined as:

LDMA can be designed with M microphones distributed as a uniform linear array, which is equivalent to psi_mPi, M1, 2, …, M and r_m＝(m-1)r₀Wherein r is_mRepresents the distance from the m-th microphone to the origin, and_mrepresenting the angular position of the mth microphone. Thus, based on the analysis described above with respect to fig. 4, the beamforming filter of the LDMA can be defined as:

because electronic steering is not possible with LDMA, the determination of the beamforming filter does not require the steering matrix γ^*(θ_s)。

Fig. 8 is a block diagram illustrating a machine in the example form of a computer system 800 in which a set or sequence of instructions may be executed to cause the machine to perform any one of the methodologies discussed herein, according to an example embodiment. In alternative embodiments, the machine operates as a standalone device or may be connected (e.g., networked) to other machines. In a networked deployment, the machine may operate in the capacity of a server or a client machine in server-client network environment, or it may act as a peer machine in a peer-to-peer (or distributed) network environment. The machine may be an in-vehicle system, a wearable device, a Personal Computer (PC), a tablet PC, a hybrid tablet, a Personal Digital Assistant (PDA), a mobile telephone, or any machine capable of executing instructions (sequential or otherwise) that specify actions to be taken by that machine. Further, while only a single machine is illustrated, the term "machine" shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. Similarly, the term "processor-based system" shall be taken to include any collection of one or more machines controlled or operated by a processor (e.g., a computer) to individually or jointly execute instructions to perform any one or more of the methodologies discussed herein.

The example computer system 800 includes at least one processor 802 (e.g., a Central Processing Unit (CPU), a Graphics Processing Unit (GPU) or both, processor cores, compute nodes, etc.), a main memory 804 and a static memory 806, which communicate with each other via a link 808 (e.g., a bus). The computer system 800 may also include a video display unit 810, an alphanumeric input device 812 (e.g., a keyboard), and a User Interface (UI) navigation device 814 (e.g., a mouse). In one embodiment, the video display unit 810, the input device 812, and the UI navigation device 814 are incorporated into a touch screen display. The computer system 800 may additionally include a storage device 816 (e.g., a drive unit), a signal generation device 818 (e.g., a speaker), a network interface device 820, and one or more sensors (not shown), such as a Global Positioning System (GPS) sensor, compass, accelerometer, gyroscope, magnetometer, or other sensor.

The storage 816 includes a machine-readable medium 822 on which is stored one or more sets of data structures and instructions 824 (e.g., software) embodied or used by any one or more of the methods or functions described herein. The instructions 824 may also reside, completely or at least partially, within the main memory 804, static memory 806, and/or within the processor 802 during execution thereof by the computer system 800, the main memory 804, static memory 806, and/or the processor 802 also constituting machine-readable media.

While the machine-readable medium 822 is shown in an example embodiment to be a single medium, the term "machine-readable medium" can include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more instructions 824. The term "machine-readable medium" shall also be taken to include any tangible medium that is capable of storing, encoding or carrying instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure, or that is capable of storing, encoding or carrying data structures used by or associated with such instructions. The term "machine-readable medium" shall accordingly be taken to include, but not be limited to, solid-state memories and optical and magnetic media. Specific examples of a machine-readable medium include volatile and non-volatile memory, including by way of example but not limitation semiconductor memory devices (e.g., electrically programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices), magnetic disks such as internal hard disks and removable magnetic disks, magneto-optical disks, and CD-ROM and DVD-ROM disks.

The instructions 824 may further be transmitted or received over a communication network 826 using a transmission medium via the network interface device 820 using any of a number of well-known transmission protocols (e.g., HTTP). Examples of communication networks include a Local Area Network (LAN), a Wide Area Network (WAN), the Internet, mobile telephone networks, Plain Old Telephone (POTS) networks, and wireless data networks (e.g., Wi-Fi, 3G, and 4GLTE/LTE-A or WiMAX networks). The term "transmission medium" shall be taken to include any intangible medium that is capable of storing, encoding or carrying instructions for execution by the machine, and includes digital or analog communications signals or other intangible medium to facilitate communication of such software.

Language(s): in the preceding description, numerous details have been set forth. However, it will be apparent to one having ordinary skill in the art having had the benefit of the present disclosure that the present disclosure may be practiced without these specific details. In some instances, well-known structures and devices are shown in block diagram form, rather than in detail, in order to avoid obscuring the present disclosure.

Some portions of the detailed description have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, considered to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like.

It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the following discussions, it is appreciated that throughout the description, discussions utilizing terms such as "dividing," "analyzing," "determining," "enabling," "identifying," "modifying," or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (e.g., electronic) quantities within the computer system's registers and memories into other data represented as physical quantities within the computer system memories or other such information storage, transmission or display devices.

The word "example" or "exemplary" is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "exemplary" or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the word "example" or "exemplary" is intended to present concepts in a concrete fashion. The term "or" as used in this application is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise indicated, or clear from context, "X comprises a or B" is intended to mean any of the natural inclusive permutations. That is, if X comprises A; x comprises B; or X includes A and B, then "X includes A or B" is satisfied under any of the above circumstances. In addition, the articles "a" and "an" as used in this application and the appended claims should generally be construed to mean "one or more" unless specified otherwise or clear from context to be directed to a singular form. Furthermore, the use of the terms "an embodiment" or "one embodiment" or "an implementation" or "one implementation" throughout is not intended to refer to the same embodiment or implementation unless so described.

Reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or".

It is to be understood that the above description is intended to be illustrative, and not restrictive. Many other embodiments will be apparent to those of skill in the art upon reading and understanding the above description. The scope of the disclosure should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.