CN109299543B - Design method of double-vector sensor acoustic probe super-directional beam pattern - Google Patents

Abstract

The invention relates to a design method of a superdirective beam pattern of an acoustic probe of a double-vector sensor, which is based on the double-vector sensor, wherein each single vector sensor comprises a sound pressure channel and a vibration velocity channel. An acoustic probe is formed by two vector sensors; the expected directivity diagram is represented in a general form by utilizing a Legendre function, the weight coefficient of the acoustic probe of the dual-vector sensor can be represented in an analytic function form of the weight coefficient of the generalized expected directivity diagram, and different acoustic probe beam patterns with super directivity can be obtained by changing the weight coefficient of the generalized expected directivity diagram. The directivity of the beam pattern of the acoustic probe designed by the method disclosed by the invention is larger than the directivity of the beam pattern of the acoustic probe designed by the methods disclosed by the documents 1, 2 and 3. Different acoustic probe beam patterns can be designed according to actual requirements, and the method is more flexible than the methods disclosed in the documents 1 and 2.

Description

Design method of double-vector sensor acoustic probe super-directional beam pattern

Technical Field

The invention belongs to a beam pattern design method of an acoustic probe, relates to a beam pattern design method of a double-vector sensor acoustic probe with super directivity, is suitable for the fields of orientation estimation, target positioning, voice recognition, hearing aids, music recording and the like, and belongs to the fields of acoustic array signal processing, voice signal processing and the like.

Background

Unidirectional acoustic probes have wide applications in the fields of orientation estimation, target localization, speech recognition, hearing aids and music recording, etc., due to their small size but good directivity. In the method disclosed in "a uni-directional microphone, j.acoust.soc.am.3,315-316 (1932)", two sound pressure sensors form an acoustic probe, and a cardioid beam pattern is obtained by combining sound pressure and first-order sound pressure gradient, but the directivity of the acoustic probe obtained by the method is only 6.02dB at most, and thus the method is difficult to meet the increasingly higher application requirements. The acoustic probe using the dual vibration velocity sensor disclosed in the document 2, "Unidirectional acoustic probe based on the specific velocity gradient, j.initial.soc.am.139, EL179-EL183 (2016)", can also obtain high directivity, and the directivity index can reach 8.75dB, however, the directivity pattern of the acoustic probe designed by the method is fixed, and is difficult to be flexibly adjusted according to actual requirements. Document 3 "a design method based on a flexible directivity pattern of a dual-vibration-velocity sensor acoustic probe, application No.: 201810519218.6 ", which is an extension of the method disclosed in document 3, can obtain a flexible beam pattern for the acoustic probe of the dual-vibration-velocity sensor, and the maximum directivity index can reach 9.03 dB. However, the directivity obtainable by the methods disclosed in documents 2 and 3 is still limited, and further improvement is required.

Disclosure of Invention

Technical problem to be solved

In order to avoid the defects of the prior art, the invention provides a design method of a superdirective beam pattern of an acoustic probe of a dual-vector sensor, and the defect that the directivity of the acoustic probe designed by the prior art is still not high enough is avoided.

Technical scheme

A design method for a superdirective beam pattern of a dual-vector sensor acoustic probe is characterized by comprising the following steps: the acoustic probe is formed by two single vector sensors including a sound pressure channel and a vibration velocity channel, and the beam pattern design steps are as follows:

step 1: given generalized expected beam pattern weight coefficients

B_d(θ)＝α₀P₀(cosθ)+α₁P₁(cosθ)+α₂P₂(cosθ)+α₃P₃(cosθ)

Wherein: p_n(cos θ) is the nth order Legendre function, θ is the pitch angle of the incident plane wave; a is said_nFor a given desired directivity pattern weight coefficient, the value is real and satisfies

Step 2: calculating weight coefficient omega of acoustic probe of dual-vector sensor₀，ω₁，ω₂And ω₃

The following steps:

wherein

β＝π；

ρ_pp,0＝1，ρ_pp,1＝j₀(kd)，

ρ_pr,0＝0＝ρ_rp,0，ρ_pr,1＝-ij₁(kd)＝-ρ_rp,1，

Wherein: k 2 pi/lambda is wave number, lambda is signal wavelength, a is half of distance d between two vector sensors, j_n(. cndot.) is a first class of n-th order spherical Bessel function, where (. cndot.)' represents derivation, and superscript ". cndot." represents conjugation,

and step 3: calculating directivity pattern of dual vector sensor acoustic probe

Substituting the weight coefficient in the step 2 into the following formula to obtain a directivity diagram B (theta) of the acoustic probe of the double-vector sensor:

wherein: p is a radical of₀And p₁Respectively normalized sound pressure signals received by two sound pressure channels in the vector sensor, and the expressions are p respectively₀(theta) ═ exp (ikacos theta) and p₁(θ)＝exp(-ikacosθ)；v₀And v₁Respectively are normalized vibration velocity signals received by two vibration velocity channels in the vector sensor, and the expressions are v respectively₀(θ) ═ cos θ exp (ikacos θ) and v₁(θ)＝-cosθexp(-ikacosθ)。

Advantageous effects

The invention provides a design method of a superdirective beam pattern of an acoustic probe of a double-vector sensor, which is based on the double-vector sensor, wherein each single vector sensor comprises a sound pressure channel and a vibration velocity channel. An acoustic probe is formed by two vector sensors; the expected directivity diagram is represented in a general form by utilizing a Legendre function, the weight coefficient of the acoustic probe of the dual-vector sensor can be represented in an analytic function form of the weight coefficient of the generalized expected directivity diagram, and different acoustic probe beam patterns with super directivity can be obtained by changing the weight coefficient of the generalized expected directivity diagram.

The beneficial effects are as follows:

1. the directivity of the beam pattern of the acoustic probe designed by the method disclosed by the invention is larger than the directivity of the beam pattern of the acoustic probe designed by the methods disclosed by the documents 1, 2 and 3.

2. The method disclosed by the invention can design different acoustic probe beam patterns according to actual requirements, and is more flexible than the methods disclosed by the documents 1 and 2.

Drawings

FIG. 1 is a coordinate representation of a dual vector transducer acoustic probe.

Fig. 2(a) is a beam pattern corresponding to the three design examples. Fig. 2(b) shows the directivity index corresponding to the three design examples. FIG. 2(c) is an error sensitivity function index for three design examples.

Fig. 3(a) shows a broadband beam pattern designed for the corresponding example 1. Fig. 3(b) shows a broadband beam pattern designed for example 2. Fig. 3(c) shows a broadband beam pattern designed for example 3.

Detailed Description

The invention will now be further described with reference to the following examples and drawings:

the invention relates to a design method of a superdirective beam pattern of an acoustic probe of a double-vector sensor, wherein a single vector sensor comprises a sound pressure channel and a vibration velocity channel, and the acoustic probe is formed by utilizing two vector sensors; the expected directivity diagram is represented in a general form by utilizing a Legendre function, the weight coefficient of the acoustic probe of the dual-vector sensor can be represented in an analytic function form of the weight coefficient of the generalized expected directivity diagram, and different acoustic probe beam patterns with super directivity can be obtained by changing the weight coefficient of the generalized expected directivity diagram. The process is as follows:

a design method for a superdirective beam pattern of a dual-vector sensor acoustic probe is characterized by comprising the following steps:

1. given the generalized desired beam pattern weight coefficients.

Generalized desired beam pattern B_d(θ) is represented by the following formula:

B_d(θ)＝α₀P₀(cosθ)+α₁P₁(cosθ)+α₂P₂(cosθ)+α₃P₃(cosθ) (1)

wherein P is_n(cos θ) is the nth order Legendre function, θ is the pitch angle of the incident plane wave; a is said_nFor a given desired directivity pattern weight coefficient, the value is real and satisfies

Refer to fig. 1 and 2. For the dual-vector sensor acoustic probe shown in fig. 1, three design examples are given, and the weight coefficients of the corresponding generalized expected directivity pattern are respectively: example 1:

the corresponding desired beam pattern has a theoretical maximum directivity index (12.04dB), containing 6 nulls; example 2: alpha is alpha₀＝0.0172,α₁＝0.1873,α₂＝0.4828,α₃0.3127, the corresponding desired beam pattern has 5 nulls and a theoretical directivity index of 11.39 dB; example 3:

the corresponding desired beam pattern has only 1 null and the theoretical directivity index is 9.80 dB. The corresponding desired beam pattern is shown in fig. 2(a), and all three desired beam patterns are symmetrical up and down, wherein the desired beam patterns of example 1 and example 2 have similar main lobes, but the side lobes are different, and the main lobe of example 3 is wider. The directivity indices of the three desired beam patterns shown in fig. 1 are the theoretical upper limits of the directivity indices achievable by the dual-vector transducer acoustic probe in the three examples, respectively.

2. And calculating the weight coefficient of the acoustic probe of the dual-vector sensor.

The weight coefficients corresponding to the double-vector acoustic probe are respectively omega₀，ω₁，ω₂And ω₃Respectively calculated by the following formulas:

the above-mentioned

Wherein m is 0, 1.

The above-mentioned

Wherein

β＝π。

The rho_pp,0＝1，ρ_pp,1＝j₀(kd)，

ρ_pr,0＝0＝ρ_rp,0，ρ_pr,1＝-ij₁(kd)＝-ρ_rp,1Where k 2 pi/λ is the wavenumber, λ is the signal wavelength, a is half the distance d between two vector sensors, j is_n(. cndot.) is a first class of n-th order spherical Bessel function, where (. cndot.)' represents derivation, and superscript ". cndot." represents conjugation,

3. and calculating a directivity pattern of the acoustic probe of the dual-vector sensor.

Substituting the weight coefficients obtained by calculation in the formulas (2) to (5) into the following formula to obtain a directivity pattern B (theta) of the acoustic probe of the dual-vector sensor:

said p is₀And p₁Respectively normalized sound pressure signals received by two sound pressure channels in the vector sensor, and the expressions are p respectively₀(theta) ═ exp (ikacos theta) and p₁(θ)＝exp(-ikacosθ)；v₀And v₁Normalized vibration velocity information respectively received by two vibration velocity channels in vector sensorNumber, expression v respectively₀(θ) ═ cos θ exp (ikacos θ) and v₁(θ)＝-cosθexp(-ikacosθ)。

Refer to fig. 1. Corresponding to the dual vector transducer acoustic probe shown in fig. 1, the received signals corresponding to the two acoustic pressure channels are p₀And p₁The received signals corresponding to the vibration velocity channels are v₀And v₁。

Refer to fig. 2. The speed of sound used in the simulation was 344.63m/s, and the distance between the dual vector sensors was 27 mm. Fig. 2(b) is a graph showing the change of the directivity index with frequency of the beam patterns of the three acoustic probes of examples 1, 2 and 3. The directivity index in the three examples gradually reaches the theoretical value as the frequency gradually decreases. FIG. 2(c) is a graph of the error sensitivity index versus frequency for the beam patterns of the three acoustic probes of examples 1, 2 and 3. As the frequency decreases, the robustness decreases, resulting in greater sensitivity to errors.

Refer to fig. 3. Fig. 3(a) - (c) are designed broadband beam patterns corresponding to three examples of examples 1, 2 and 3 in sequence. The graphical results show that the broadband beam patterns corresponding to the three examples are well matched with the expected beam pattern in a wider frequency range, the directivity indexes of the broadband beam patterns are higher than those of the dual-sound-pressure sensor probe and the dual-vibration-velocity sensor probe, the broadband beam patterns have obvious frequency invariant response characteristics, and the application prospect is good.

Claims (1)

1. A design method for a superdirective beam pattern of a dual-vector sensor acoustic probe is characterized by comprising the following steps: the acoustic probe is formed by two single vector sensors including a sound pressure channel and a vibration velocity channel, and the beam pattern design steps are as follows:

step 1: given generalized expected beam pattern weight coefficients

B_d(θ)＝α₀P₀(cosθ)+α₁P₁(cosθ)+α₂P₂(cosθ)+α₃P₃(cosθ)

Wherein: p_n(cos θ) is the nth order Legendre function, θ is the pitch angle of the incident plane wave; a is said_nWeighting system for a given desired directivity patternNumber whose value is real and satisfies

Step 2: calculating weight coefficient omega of acoustic probe of dual-vector sensor₀，ω₁，ω₂And ω₃

The following steps:

wherein

β＝π；

ρ_pp,0＝1，ρ_pp,1＝j₀(kd)，

ρ_pr,0＝0＝ρ_rp,0，ρ_pr,1＝-ij₁(kd)＝-ρ_rp,1，

Wherein: k 2 pi/lambda is wave number, lambda is signal wavelength, a is half of distance d between two vector sensors, j_n(. cndot.) is a first class of n-th order spherical Bessel function, where (. cndot.)' represents derivation, and superscript ". cndot." represents conjugation,

and step 3: calculating directivity pattern of dual vector sensor acoustic probe

Substituting the weight coefficient in the step 2 into the following formula to obtain a directivity diagram B (theta) of the acoustic probe of the double-vector sensor:

wherein: p is a radical of₀And p₁Respectively normalized sound pressure signals received by two sound pressure channels in the vector sensor, and the expressions are p respectively₀(theta) ═ exp (ikacos theta) and p₁(θ)＝exp(-ikacosθ)；v₀And v₁Respectively are normalized vibration velocity signals received by two vibration velocity channels in the vector sensor, and the expressions are v respectively₀(θ) ═ cos θ exp (ikacos θ) and v₁(θ)＝-cosθexp(-ikacosθ)。

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