# US 10,375,505 B2 · Apparatus and method for generating a sound field

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- Number: US 10,375,505 B2
- Document ID: US10375505B2
- Status: Granted
- Kind: B2
- Application number: 16/001,638
- Filed: 2018-06-06
- Published: 2018-10-04
- Granted: 2019-08-06
- Earliest claimed: 2016-06-30
- Assignees: Huawei Technologies Co., Ltd.; University of Southampton
- Applicants: Huawei Technologies Co., Ltd.; University of Southampton
- Inventors: Simone Fontana; Ferdinando Olivieri; Filippo Fazi; Philip Nelson
- Web page: https://patentgrep.com/patent/US10375505B2

## CPC

- H04S 7/303: {Tracking of listener position or orientation}
- H04R 1/403: {loud-speakers}
- H04R 3/04: for correcting frequency response
- H04R 3/12: for distributing signals to two or more loudspeakers {(specially adapted for hearing aids H04R25/407)}
- H04R 5/02: Spatial or constructional arrangements of loudspeakers
- H04S 7/30: {Control circuits for electronic adaptation of the sound field}
- H04S: STEREOPHONIC SYSTEMS
- H04R: LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS (producing sounds with frequency not determined by supply frequency G10K)

## Abstract

The disclosure relates to an apparatus for generating a sound field on the basis of an input audio signal. The apparatus comprises a plurality of transducers, wherein each transducer is configured to be driven by a transducer driving signal ql of the respective transducer; a plurality of filters configured to generate for each transducer the transducer driving signal ql of the respective transducer; and a control unit configured to provide or receive a first transducer driving signal vector q0 of dimension L such that the gradient of J(q;ψ) with respect to q is zero in (q0;ψ0), the control unit is further configured to provide a second transducer driving signal vector {tilde over (q)} of dimension L such that the gradient of the cost function J(q;ψ) with respect to q is [approximately] zero in ({tilde over (q)}; {tilde over (ψ)}), the control unit is configured to provide the second transducer driving signal vector {tilde over (q)}.

## Claims

### Claim 1

An apparatus for generating a sound field on the basis of an input audio signal, wherein the apparatus comprises:
a plurality of transducers, wherein each transducer of the plurality of transducers is configured to be driven by a transducer driving signal ql of the respective transducer, wherein l∈{1, . . . , L} and wherein l denotes the l-th transducer;
a plurality of filters configured to generate for each transducer of the plurality of transducers the transducer driving signal ql of the respective transducer, wherein each of the filters of the plurality of filters is defined by a filter transfer function and wherein the transducer driving signal ql of the respective transducer is based on the filter transfer function of the respective transducer and the input audio signal; and
a control unit configured to provide or receive a first transducer driving signal vector q0 of dimension L such that a gradient of J(q;ψ) with respect to q is zero in (q0;ψ0), wherein J(q;ψ) is a cost function having as variables a transducer driving signal vector q of dimension L and a weight matrix ψ of dimension M×M, and wherein ψ0 is a first weight matrix of dimension M×M,
wherein the control unit is further configured to provide a second transducer driving signal vector q of dimension L such that a gradient of the cost function J(q;ψ) with respect to q is zero or approximately zero in ({tilde over (q)}; {tilde over (ψ)}), wherein {tilde over (ψ)} is a second weight matrix of dimension M×M, and wherein the control unit is configured to provide the second transducer driving signal vector {tilde over (q)} on the basis of:
the first transducer driving signal vector q0,
the first weight matrix ψ0, and
the second weight matrix {tilde over (ψ)},
wherein the cost function is J(q;ψ)=∥{circumflex over (ψ)}({circumflex over (p)}−p)∥2+β∥q∥2, wherein {circumflex over (p)} is a target pressure vector of dimension M comprising M target pressure values {circumflex over (p)}m for a set of M control points, m∈{1, . . . , M}, p is a pressure vector of dimension M comprising M pressure values pm for the set of M control points, m∈{1, . . . , M}, and is a regularization parameter in the range of [0,∞).

### Claim 2 (depends on 1)

The apparatus of claim 1, wherein the control unit is configured to compute the second transducer driving signal vector {tilde over (q)} on the basis of a truncated Neumann series of order N as
{tilde over (q)}=Σn=0N(−(ZHψ0Z+βI)−1ZHΔψZ)n(q0+(ZHψ0Z+βI)−1ZHΔψ{circumflex over (p)}),
wherein Z is a transfer matrix of dimension M×L, I is the identity matrix of dimension L×L, Δψ denotes the difference between ψ0 and {tilde over (ψ)} and the superscript H denotes Hermitian transposition.

### Claim 3 (depends on 2)

The apparatus of claim 2, wherein the sound field comprises an acoustically bright zone, an acoustically dark zone and an acoustically grey zone and wherein the cost function J(q;ψ) is given by the following equation:
∥pB−pB∥2+ψD∥pD∥2+ψG∥pG∥2+β∥q∥2,
and wherein the gradient of J(q;ψ) with respect to q is zero in (q0;ψ0) under the constraint that |Σl=1LZmlql|2=|pm|2|pm,min|2 for each m E B where B is the set of indices of control points in the bright zone and |pm,min|2 is a positive real number associated with the respective desired minimum level of sound energy at a respective control point in the bright zone,
wherein PB denotes a sound pressure at a control point in the bright zone, pB denotes a desired sound pressure at the control point in the bright zone, pD denotes a respective sound pressure at a plurality of control points in the dark zone, pG denotes a respective sound pressure at a plurality of control points in the grey zone, Zml denotes the element in the m-th row and the l-th column of the transfer matrix Z ψD denotes a dark zone weighting parameter, ψG denotes a grey zone weighting parameter and PB,min denotes a desired minimum level of sound energy at the control point in the bright zone.

### Claim 4 (depends on 3)

The apparatus of claim 3, wherein the control unit is configured to provide the second transducer driving signal vector {tilde over (q)} in response to an adjustment of the desired minimum level of sound energy at the control point in the bright zone.

### Claim 5 (depends on 3)

The apparatus of claim 3, wherein the truncated Neumann series of order N is defined by the following equation:
Σn=0NΔψDnEn,
wherein ΔψD denotes an adjustment of the dark zone weighting parameter ψD and wherein the matrix E is defined by the following equation:
E=−A−1ZDHZD,
wherein the matrix A is defined by the following equation:
A=ZBHZB+ψDZDHZD+ψGZGHZG+βI,
wherein ZB denotes the transfer matrix for the bright zone, ZD denotes the transfer matrix for the dark zone, and ZG denotes the transfer matrix for the grey zone.

### Claim 6 (depends on 5)

The apparatus of claim 5, wherein the control unit is configured to determine the adjustment ΔψD of the dark zone weighting parameter ψD by determining the root of the following equation within the interval −0.5≤ΔψD≤0.5:
Σn=0N|ΔψD|n|zBTEnq|−|pB,min|=0,
wherein zBT denotes portion of the transfer matrix defining a vector and pB,min denotes a desired minimum level of sound energy at the control point in the bright zone.

### Claim 7 (depends on 2)

The apparatus of claim 2, wherein the order N of the truncated Neumann series depends on frequency.

### Claim 8 (depends on 7)

The apparatus of claim 7, wherein the order N of the truncated Neumann series decreases with increasing frequency.

### Claim 9 (depends on 7)

The apparatus of claim 7, wherein the control unit is configured to determine the order N of the truncated Neumann series on the basis of the following equation:
N
=
min
N
⁢
{
ɛ
≤
ɛ
MAX
}
,
wherein εMAX denotes an error threshold and ε denotes an error measure defined by the following equation:
ɛ
=
10
⁢
⁢
log
10
(

q
~
N
-
q
~

2

q
~

2
)
,
wherein {tilde over (q)}N denotes the transducer driving signal vector determined on the basis of the truncated Neumann series.

### Claim 10 (depends on 1)

The apparatus of claim 1, wherein the first transducer driving signal vector q0 is
q0=(ZHψ0Z+βI)−1ZHψ0p,
wherein Z is a transfer matrix of dimension M×L.

### Claim 11 (depends on 1)

The apparatus of claim 1, wherein the control unit is configured to determine the regularization factor β on the basis of a normalized Tikhonov regularization.

### Claim 12 (depends on 1)

The apparatus of claim 1, wherein the apparatus further comprises a memory configured to store the first transducer driving signal vector q0.

### Claim 13

A method for generating a sound field on the basis of an input audio signal, wherein the method comprises the steps of:
providing or receiving a first transducer driving signal vector q0 of dimension L such that a gradient of J(q;ψ) with respect to q is zero in (q0;ψ0), wherein J(q;ψ) is a cost function having as variables a transducer driving signal vector q of dimension L and a weight matrix ψ of dimension M×M, and wherein ψ0 is a first weight matrix of dimension M×M;
providing a second transducer driving signal vector {tilde over (q)} of dimension L such that a gradient of the cost function J(q;ψ) with respect to q is zero in ({tilde over (q)}; {tilde over (ψ)}), wherein {tilde over (ψ)} is a second weight matrix of dimension M×M, and wherein the second transducer driving signal vector {tilde over (q)} is provided on the basis of:
the first transducer driving signal vector q0,
the first weight matrix ψ0, and
the second weight matrix {tilde over (ψ)}; and
driving each transducer of a plurality of L transducers by a respective component {tilde over (q)}l, l∈{1, . . . , L}, of the second transducer driving signal vector {tilde over (q)};
wherein the cost function is J(q;ψ)=∥{tilde over (ψ)}(p−p)∥2+β∥q∥2, wherein p is a target pressure vector of dimension M comprising M target pressure values pm for a set of M control points, m∈{1, . . . , M}, p is a pressure vector of dimension M comprising M pressure values pm for the set of M control points, m∈{1, . . . , M}, and β is a regularization parameter in the range of [0,∞).

### Claim 14

A non-transitory storage medium carrying a program code which when executed by one or more processors of a computer causes the computer to perform a method of generating a sound field on the basis of an input audio signal, wherein the method comprises the steps of:
providing or receiving a first transducer driving signal vector q0 of dimension L such that a gradient of J(q;ψ) with respect to q is zero in (q0;ψ0), wherein J(q;ψ) is a cost function having as variables a transducer driving signal vector q of dimension L and a weight matrix ψ of dimension M×M, and wherein ψ0 is a first weight matrix of dimension M×M;
providing a second transducer driving signal vector {tilde over (q)} of dimension L such that a gradient of the cost function J(q;ψ) with respect to q is zero in ({tilde over (q)}; {tilde over (ψ)}), wherein {tilde over (ψ)} is a second weight matrix of dimension M×M, and wherein the second transducer driving signal vector {tilde over (q)} is provided on the basis of:
the first transducer driving signal vector q0,
the first weight matrix ψ0, and
the second weight matrix {tilde over (ψ)}; and
driving each transducer of a plurality of L transducers by a respective component {tilde over (q)}l, l∈{1, . . . , L}, of the second transducer driving signal vector {tilde over (q)};
wherein the cost function is J(q;ψ)=∥{tilde over (ψ)}(p−p)∥2+β∥q∥2, wherein p is a target pressure vector of dimension M comprising M target pressure values pm for a set of M control points, m∈{1, . . . , M}, p is a pressure vector of dimension M comprising M pressure values Pm for the set of M control points, m∈{1, . . . , M}, and β is a regularization parameter in the range of [0,∞).