# US 2017/0289725 A1 · Method and device for rendering an audio soundfield representation

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- Number: US 2017/0289725 A1
- Document ID: US20170289725A1
- Status: Published application
- Kind: A1
- Application number: 15/619,935
- Filed: 2017-06-12
- Published: 2017-10-05
- Earliest claimed: 2012-07-16
- Assignees: Dolby Laboratories Licensing Corporation
- Applicants: Dolby Laboratories Licensing Corporation
- Inventors: Johannes BOEHM; Florian KEILER
- Web page: https://patentgrep.com/patent/US20170289725A1

## CPC

- H04S 7/30: {Control circuits for electronic adaptation of the sound field}
- H04S 3/008: {in which the audio signals are in digital form, i.e. employing more than two discrete digital channels (data reduction aspects thereof based on psychoacoustics G10L19/02)}
- H04S 2420/11: Application of ambisonics in stereophonic audio systems
- H04S: STEREOPHONIC SYSTEMS

## Abstract

The invention discloses rendering sound field signals, such as Higher-Order Ambisonics (HOA), for arbitrary loudspeaker setups, where the rendering results in highly improved localization properties and is energy preserving. This is obtained by a new type of decode matrix for sound field data, and a new way to obtain the decode matrix. In a method for rendering an audio sound field representation for arbitrary spatial loudspeaker setups, the decode matrix (D) for the rendering to a given arrangement of target loudspeakers is obtained by steps of obtaining a number (L) of target speakers, their positions (L), positions (S) of a spherical modeling grid and a HOA order (N), generating (141) a mix matrix (G) from the positions (S) of the modeling grid and the positions (L) of the speakers, generating (142) a mode matrix ({tilde over (Ψ)})from the positions (S) of the spherical modeling grid and the HOA order, calculating (143) a first decode matrix ({circumflex over (D)}) from the mix matrix (G) and the mode matrix ({tilde over (Ψ)}), and smoothing and scaling (144, 145) the first decode matrix ({circumflex over (D)}) with smoothing and scaling coefficients.

## Claims

### Claim 1

A method for rendering a Higher-Order Ambisonics (HOA) representation of a sound or sound field, comprising:
rendering coefficients of the HOA sound field representation from a frequency domain to a spatial domain based on a smoothed decode matrix {tilde over (D)},
determining a mix matrix G based on L speakers and positions of a spherical modelling grid related to a HOA order N;
determining a mode matrix {tilde over (Ψ)} based on the spherical modelling grid and the HOA order N;
wherein a compact singular value decomposition of a product of the mode matrix {tilde over (Ψ)} with a Hermitian transposed mix matrix GH is determined based on U S VH={tilde over (Ψ)} GH, wherein U,V are based on Unitary matrices and S is based on a diagonal matrix with singular value elements, and a first decode matrix {circumflex over (D)} is determined based on the matrices U,V based on {circumflex over (D)}=V Ŝ UH, wherein Ŝ is a truncated compact singular value decomposition matrix that is either an identity matrix or a modified diagonal matrix, the modified diagonal matrix being determined based on the diagonal matrix with singular value elements by replacing a singular value element that is larger or equal than a threshold by ones, and replacing a singular value element that is smaller than the threshold by zeros, and
wherein the smoothed decode matrix {tilde over (D)} is determined based on smoothing and scaling of the first decode matrix {circumflex over (D)} with smoothing coefficients,
wherein a rendering matrix D is determined based on a Frobenius norm of the smoothed decode matrix {tilde over (D)}.

### Claim 2 (depends on 1)

The method of claim 1, wherein the smoothing is based on a first smoothing method that is based on a determination of L≧O3D, and the smoothing is further based on a second smoothing method that is based on a determination of L<O3D,
wherein O3D=(N+1)2, and wherein the smoothed decode matrix {tilde over (D)} is obtained based on the smoothing.

### Claim 3 (depends on 2)

The method of claim 2, wherein the second smoothing method is based on weighting coefficients that are based on elements of a Kaiser window.

### Claim 4 (depends on 3)

The method of claim 3, wherein the Kaiser window is determined based on =KaiserWindow(len, width), wherein len=2N+1, width=2N, wherein is a vector with 2N+1 real valued elements based on
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wherein lo denotes a zero-order Modified Bessel function of a first kind.

### Claim 5 (depends on 2)

The method of claim 2, wherein in the first smoothing method is based on weighting coefficients that are based on zeros of Legendre polynomials of order N+1.

### Claim 6 (depends on 1)

The method of claim 1, wherein the first decode matrix {circumflex over (D)} is smoothed to obtain the smoothed decode matrix {tilde over (D)}, and the smoothed decode matrix {tilde over (D)} is scaled based on a constant scaling factor cf.

### Claim 7 (depends on 1)

The method of claim 1, further comprising
buffering and serializing a spatial signal W which is obtained based on the rendering the coefficients of the HOA sound field representation, wherein time samples w(t) for L channels are obtained; and
delaying time samples w(t) individually for each of the L channels in delay lines, wherein L digital signals are obtained; and
wherein the delay lines compensate different loudspeaker distances.

### Claim 8

An apparatus for rendering a Higher-Order Ambisonics (HOA) representation of a sound or sound field, comprising:
a decoder configured to decode coefficients of the HOA sound field representation, the decoder including:
a renderer configured to render coefficients of the HOA sound field representation from a frequency domain to a spatial domain based on a smoothed decode matrix {tilde over (D)},
a processing unit configured to determine a mix matrix G based on L speakers and positions of a spherical modelling grid related to a HOA order N and
determining a mode matrix {tilde over (Ψ)} based on the spherical modelling grid and the HOA order N and determining a mode matrix {tilde over (Ψ)} based on the spherical modelling grid and the HOA order N;
wherein the processing unit is further configured to determine a compact singular value decomposition of a product of the mode matrix {tilde over (Ψ)} with a Hermitian transposed mix matrix GH is determined based on U S VH={tilde over (Ψ)} GH, and
wherein U,V are based on Unitary matrices and S is based on a diagonal matrix with singular value elements, and a first decode matrix {circumflex over (D)} is determined based on the matrices U,V based on {circumflex over (D)}=V Ŝ UH,
wherein Ŝ is a truncated compact singular value decomposition matrix that is either an identity matrix or a modified diagonal matrix, the modified diagonal matrix being determined based on the diagonal matrix with singular value elements by replacing a singular value element that is larger or equal than a threshold by ones, and replacing a singular value element that is smaller than the threshold by zeros, and
wherein Ŝ the smoothed decode matrix {tilde over (D)} is determined based on smoothing and scaling of the first decode matrix {circumflex over (D)} with smoothing coefficients,
wherein a rendering matrix D is determined based on a Frobenius norm of the smoothed decode matrix {tilde over (D)}.

### Claim 9 (depends on 8)

The apparatus of claim 8, wherein the decoder is configured to apply the smoothed decode matrix {tilde over (D)} to the HOA sound field representation to determine a decoded audio signal.

### Claim 10 (depends on 8)

The apparatus of claim 8, further comprising a storage for storing the smoothed decode matrix {tilde over (D)}.

### Claim 11 (depends on 8)

The apparatus of claim 8, wherein the smoothing is based on a first smoothing method that is based on a determination of L≧O3D, and the smoothing is further based on a second smoothing method that is based on a determination of L<O3D, wherein O3D=(N+1)2, and wherein the smoothed decode matrix {tilde over (D)} is obtained based on the smoothing.

### Claim 12 (depends on 11)

The apparatus of claim 11, wherein in the second smoothing method is based on weighting coefficients that are based on elements of a Kaiser window.

### Claim 13 (depends on 12)

The apparatus of claim 12, wherein the Kaiser window is determined based on =KaiserWindow(len,width), wherein len=2N+1, width=2N, wherein is a vector with 2N+1 real valued elements based on
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wherein lo denotes a zero-order Modified Bessel function of a first kind.

### Claim 14 (depends on 11)

The apparatus of claim 11, wherein in the first smoothing method is based on weighting coefficients that are based on zeros of Legendre polynomials of order N+1.

### Claim 15 (depends on 8)

The apparatus of claim 8, wherein the first decode matrix {circumflex over (D)} is smoothed to obtain the smoothed decode matrix {tilde over (D)}, and the smoothed decode matrix {tilde over (D)} is scaled based on a constant scaling factor cf.

### Claim 16

A non-transitory computer readable medium having stored thereon executable instructions to cause a computer to perform a method for rendering a Higher-Order Ambisonics (HOA) representation of a sound or sound field, the method comprising:
rendering coefficients of the HOA sound field representation from a frequency domain to a spatial domain based on a smoothed decode matrix {tilde over (D)},
determining a mix matrix G based on L speakers and positions of a spherical modelling grid related to a HOA order N;
determining a mode matrix {tilde over (Ψ)} based on the spherical modelling grid and the HOA order N;
wherein a compact singular value decomposition of a product of the mode matrix {tilde over (Ψ)} with a Hermitian transposed mix matrix GH is determined based on U S VH={tilde over (Ψ)} GH, wherein U,V are based on Unitary matrices and S is based on a diagonal matrix with singular value elements, and a first decode matrix {circumflex over (D)} is determined based on the matrices U,V based on {circumflex over (D)}=V Ŝ UH, wherein Ŝ is a truncated compact singular value decomposition matrix that is either an identity matrix or a modified diagonal matrix, the modified diagonal matrix being determined based on the diagonal matrix with singular value elements by replacing a singular value element that is larger or equal than a threshold by ones, and replacing a singular value element that is smaller than the threshold by zeros, and
wherein the smoothed decode matrix b is determined based on smoothing and scaling of the first decode matrix {circumflex over (D)} with smoothing coefficients,
wherein a rendering matrix D is determined based on a Frobenius norm of the smoothed decode matrix {tilde over (D)}.