Method and device for rendering an audio soundfield representation

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)}.

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)}.