Method and device rendering an audio soundfield representation for audio playback
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 for the rendering to a given arrangement of target loudspeakers is obtained by steps of obtaining a number of target speakers, their positions, positions of a spherical modeling grid and a HOA order, generating a mix matrix from the positions of the modeling grid and the positions of the speakers, generating a mode matrix from the positions of the spherical modeling grid and the HOA order, calculating a first decode matrix from the mix matrix and the mode matrix, and smoothing and scaling the first decode matrix with smoothing and scaling coefficients.
1. A method for rendering a Higher-Order Ambisonics (HOA) representation of a sound or sound field, comprising:
decoding coefficients of the HOA sound field representation;
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;
rendering the coefficients of the HOA sound field representation from a frequency domain to a spatial domain based on a smoothed decode matrix {tilde over (D)};
wherein a compact singular value decomposition of a product of the mode matrix {tilde over (Ψ)} with a Hermitian transpose of the mix matrix G is determined based on U S V H ={tilde over (Ψ)}G H ,
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 U H , 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 determined based on the diagonal matrix with first and second singular value elements, wherein at least a first singular value element that is larger or equal than a threshold is equal to ones, and at least a second singular value element that is smaller than the threshold is equal to zero, 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.
2. The method of claim 1 , wherein the smoothing is based on a first smoothing method that is based on a determination of L≧O 3D , and the smoothing is further based on a second smoothing method that is based on a determination of L<O 3D ,
wherein O 3D =(N+1) 2 , and wherein the smoothed decode matrix {tilde over (D)} is obtained based on the smoothing.
3. The method of claim 2 , wherein the second smoothing method is based on weighting coefficients that are based on elements of a Kaiser window.
4. 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 I o denotes a zero-order Modified Bessel function of a first kind.
5. 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.
6. 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 a constant scaling factor c f is determined based on a Frobenius norm of the smoothed decode matrix {tilde over (D)}.
7. 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 c f .
8. 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.
9. The method according to claim 1 , wherein the threshold depends on values of the diagonal matrix with singular value elements.
10. The method according to claim 9 , wherein the threshold depends on a maximum element S 1 of the diagonal matrix with singular value elements.
11. 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 to determine 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 the product of the mode matrix {tilde over (Ψ)} with a Hermitian transpose of the mix matrix G, based on U S V H ={tilde over (Ψ)}G H , and
wherein U,V are based on Unitary matrices and S is a diagonal matrix with singular value elements, and
wherein the processing unit is further configured to determine a first decode matrix {circumflex over (D)} from the matrices U,V according to {circumflex over (D)}=V Ŝ U H , wherein Ŝ is a truncated compact singular value decomposition matrix that is either an identity matrix or a modified diagonal matrix that is determined based on the diagonal matrix with first and second singular value elements,
wherein at least a first singular value element that is larger or equal than a threshold is equal to one, and at least a second singular value element that is smaller than the threshold is equal to zero, 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.
12. The apparatus of claim 11 , 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.
13. The apparatus of claim 11 , further comprising a storage for storing the smoothed decode matrix {tilde over (D)}.
14. The apparatus of claim 11 , wherein the smoothing is based on a first smoothing method that is based on a determination of L≧O 3D , and the smoothing is further based on a second smoothing method that is based on a determination of L<O 3D , wherein O 3D =(N+1) 2 , and wherein the smoothed decode matrix {tilde over (D)} is obtained based on the smoothing.
15. The apparatus of claim 14 , wherein in the second smoothing method is based on weighting coefficients that are based on elements of a Kaiser window.
16. The apparatus of claim 11 , wherein the processing unit is further configured to smooth the first decode matrix {circumflex over (D)} to obtain the smoothed decode matrix {tilde over (D)}, and the processing unit is further configured to determine a constant scaling factor c f based on a Frobenius norm of the smoothed decode matrix {tilde over (D)}.
17. The apparatus of claim 11 , wherein the threshold depends on the values of the diagonal matrix with singular value elements.
18. The apparatus of claim 17 , wherein the threshold depends on a maximum element S 1 of the diagonal matrix with singular value elements.
19. 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:
decoding coefficients of the HOA sound field representation;
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;
rendering the coefficients of the HOA sound field representation from a frequency domain to a spatial domain based on a smoothed decode matrix {tilde over (D)};
wherein a compact singular value decomposition of a product of the mode matrix {tilde over (Ψ)} with a Hermitian transpose of the mix matrix G is determined based on U S V H ={tilde over (Ψ)}G H ,
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 U H , 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 determined based on the diagonal matrix with first and second singular value elements, wherein at least a first singular value element that is larger or equal than a threshold is equal to ones, and at least a second singular value element that is smaller than the threshold is equal to zero, 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.