Method and apparatus for higher order ambisonics encoding and decoding using singular value decomposition
The encoding and decoding of HOA signals using Singular Value Decomposition includes forming ( 11 ) based on sound source direction values and an Ambisonics order corresponding ket vectors (|Y(Ω5))) of spherical harmonics and an encoder mode matrix (Ξ 0χs ). From the audio input signal (|χ(Ω s ))) a singular threshold value (σ ε ) determined. On the encoder mode matrix a Singular Value Decomposition ( 13 ) is carried out in order to get related singular values which are compared with the threshold value, leading to a final encoder mode matrix rank ( r fin e ). Based on direction values (Ω l ) of loudspeakers and a decoder Ambisonics order (N l ), corresponding ket vectors (IY(Ω l ) ) and a decoder mode matrix (Ψ 0χL ) are formed ( 18 ). On the decoder mode matrix a Singular Value Decomposition ( 19 ) is carried out, providing a final decoder mode matrix rank ( r fin d ). From the final encoder and decoder mode matrix ranks a final mode matrix rank is determined, and from this final mode matrix rank and the encoder side Singular Value Decomposition an adjoint pseudo inverse (Ξ + ) † of the encoder mode matrix (Ξ 0χs ) and an Ambisonics ket vector (Ia′ s ) are calculated. The number of components of the Ambisonics ket vector is reduced ( 16 ) according to the final mode matrix rank so as to provide an adapted Ambisonics ket vector (|a′ l ). From the adapted Ambisonics ket vector, the output values of the decoder side Singular Value Decomposition and the final mode matrix rank an adjoint decoder mode matrix (Ψ) † is calculated ( 15 ), resulting in a ket vector (|y(Ω l ) ) of output signals for all loudspeakers.
1. A method for Higher Order Ambisonics (HOA) encoding comprising:
receiving an audio input signal (|χ(Ω s ) );
determining at least a ket vector (|Y(Ω s ) ) of spherical harmonics and an encoder mode matrix (Ξ o×s ) based on direction values (Ω s ) of sound sources and an Ambisonics order (N s ) of the audio input signal (|χ(Ω s ) );
determining two encoder unitary matrices (U s , V s † ) and an encoder diagonal matrix (Σ s ) containing singular values and a related encoder mode matrix rank (r s ) based on a Singular Value Decomposition of the encoder mode matrix (Ξ o×s );
determining a threshold value (σ ε ) based on the audio input signal (|χ(Ω s ) ), the singular values of the encoder diagonal matrix (Σ s ) and the encoder mode matrix rank (r s );
determining a final encoder mode matrix rank (r fin e ) based on a comparison of at least one (σ r ) of the singular values with the threshold value (σ ε ).
2. The method of claim 1 , wherein the ket vectors (|Y(Ω s ) )of spherical harmonics and the encoder mode matrix (Ξ o×s ) are based on a panning function (f s ) that includes a linear operation and a mapping of source positions in the audio input signal (|χ(Ω s ) ) to positions of the loudspeakers in the ket vector (|y(Ω l ) )of loudspeaker output signals.
3. An apparatus for Higher Order Ambisonics (HOA) encoding comprising:
a receiver for receiving an audio input signal (|χ(Ω s ) );
a processor configured to determine at least a ket vector (|Y(Ω s ) )of spherical harmonics and an encoder mode matrix (Ξ o×s ) based on direction values (Ω s ) of sound sources and an Ambisonics order (N s ) of the audio input signal (|χ(Ω s ) ), the processor further configured to determine two encoder unitary matrices (U s , V s † ) and an encoder diagonal matrix (Σ s ) containing singular values and a related encoder mode matrix rank (r s ) based on a Singular Value Decomposition of the encoder mode matrix (Ξ o×s );
wherein the processor is further configured to determine a threshold value (σ ε ) based on the audio input signal (|χ(Ω s ) ), the singular values of the encoder diagonal matrix (Σ s ) and the encoder mode matrix rank (r s );
wherein the processor is further configured to determine a final encoder mode matrix rank (r fin e ) based on a comparison of at least one (σ r ) of the singular values with the threshold value (σ ε ).
4. The apparatus of claim 3 , wherein the ket vectors (|Y(Ω s ) ) of spherical harmonics and the encoder mode matrix (Ξ o×s ) are based on a panning function (f s ) that includes a linear operation and a mapping of source positions in the audio input signal (|χ(Ω s ) ) to positions of the loudspeakers in the ket vector (|y(Ω l ) ) of loudspeaker output signals.
5. A method for Higher Order Ambisonics (HOA) decoding comprising:
receiving information regarding direction values (Ω l ) of loudspeakers and a decoder Ambisonics order (N 1 );
determining ket vectors (|Y(Ω l ) ) of spherical harmonics for loudspeakers located at directions corresponding to the direction values (σ l ) and a decoder mode matrix (Ψ o×L ) based on the direction values (σ l ) of loudspeakers and the decoder Ambisonics order (N l );
determining two corresponding decoder unitary matrices (U l † , V l ) and a decoder diagonal matrix (Σ l ) containing singular values and a final rank (r fin d ) of the decoder mode matrix (Ψ o×L ) based on a Singular Value Decomposition of the decoder mode matrix (Ψ o×L );
determining a final mode matrix rank (r fin ) based on the final encoder mode matrix rank (r fin e ) and the final decoder mode matrix rank (r fin d );
determining an adjoint pseudo inverse (Ξ + ) † of the encoder mode matrix (Ξ o×s ), resulting in an Ambisonics ket vector (|a′ s ), based on the encoder unitary matrices (U s , V s † ), the encoder diagonal matrix (Σ s ) and the final mode matrix rank (r fin );
determining an adapted Ambisonics ket vector (|a′ l ) based on a reduction of a number of components of the Ambisonics ket vector (|a′ s ) according to the final mode matrix rank (r fin );
determining an adjoint decoder mode matrix (Ψ) † , resulting in a ket vector (|y(Ω l ) ) of output signals for all loudspeakers, based on the adapted Ambisonics ket vector (|a′ l ), the decoder unitary matrices (U l † , V l ), the decoder diagonal matrix (Σ l ) and the final mode matrix rank.
6. The method of claim 5 , wherein the ket vectors (|Y(Ω l ) ) of the spherical harmonics for the loudspeakers and the decoder mode matrix (Ψ o×L ) are based on a corresponding panning function (f l ) that includes a linear operation and a mapping of the source positions in the audio input signal (|χ(Ω s ) ) to positions of the loudspeakers in the ket vector (|y(Ω l ) ) of loudspeaker output signals.
7. The method of claim 5 , wherein a preliminary adapted ket vector of time-dependent output signals of all loudspeakers is determined after determining the adjoint decoder mode matrix (Ψ) † , and wherein the preliminary adapted ket vector of time-dependent output signals of all loudspeakers is determined based on a panning matrix (G), resulting in the ket vector (|y(Ω l ) ) of output signals for all loudspeakers.
8. The method of one of claim 7 , wherein, the threshold value (σ ε ) is based on, within the singular values (σ i ), an amount value gap that is detected starting from a first singular value (σ 1 ), and if an amount value of a following singular value (σ i+1 ) is smaller than an amount value of a current singular value (σ i ), the amount value of that current singular value is taken as the threshold value (σ ε ).
9. The method of claim 5 , wherein the threshold value (σ ε ) is based on a signal-to-noise ratio SNR for a block of samples for all source signals and the threshold value (σ ε ) is set to
σ
ɛ
=
1
S
N
R
.
10. An apparatus for Higher Order Ambisonics (HOA) decoding comprising:
a receiver for receiving information regarding direction values (Ω l ) of loudspeakers and a decoder Ambisonics order (N l );
a processor configured to determine ket vectors (|Y(Ω l ) ) of spherical harmonics for loudspeakers located at directions corresponding to the direction values (Ω l ) and a decoder mode matrix (Ψ o×L ) based on the direction values (Ω l )of loudspeakers and the decoder Ambisonics order (N 1 ) and to determine two corresponding decoder unitary matrices (U l † , V l ) and a decoder diagonal matrix (Σ l ) containing singular values and a final rank (r fin d ) of the decoder mode matrix (Ψ o×L ) based on a Singular Value Decomposition of the decoder mode matrix (Ψ o×L );
wherein the processor is further configured to determine a final mode matrix rank (r fin ) based on the final encoder mode matrix rank (r fin e ) and the final decoder mode matrix rank (r fin d );
wherein the processor is further configured to determine an adjoint pseudo inverse (Ξ + ) † of the encoder mode matrix (Ξ o×s ), resulting in an Ambisonics ket vector (|a′ s ), based on the encoder unitary matrices (U s , V s † ), the encoder diagonal matrix (Σ s ) and the final mode matrix rank (r fin );
wherein the processor is further configured to determine an adapted Ambisonics ket vector (|a′ l ) based on a reduction of a number of components of the Ambisonics ket vector (|a′ s ) according to the final mode matrix rank (r fin );
wherein the processor is further configured to determine an adjoint decoder mode matrix (Ψ) † , resulting in a ket vector (|y(Ω l ) ) of output signals for all loudspeakers, based on the adapted Ambisonics ket vector (|a′ l ), the decoder unitary matrices (U l † , V l ), the decoder diagonal matrix (Σ l ) and the final mode matrix rank.
11. The apparatus of claim 10 , wherein the ket vectors (|Y(Ω l ) )of the spherical harmonics for the loudspeakers and the decoder mode matrix (Ψ o×L ) are based on a corresponding panning function (f l ) that includes a linear operation and a mapping of the source positions in the audio input signal (|χ(Ω s ) ) to positions of the loudspeakers in the ket vector (|y(Ω l ) ) of loudspeaker output signals.
12. The apparatus of claim 10 , wherein a preliminary adapted ket vector of time-dependent output signals of all loudspeakers is determined after determining the adjoint decoder mode matrix (Ψ) † , and
wherein the preliminary adapted ket vector of time-dependent output signals of all loudspeakers is determined based on a panning matrix (G), resulting in the ket vector (|y(Ω l ) ) of output signals for all loudspeakers.
13. The apparatus of claim 10 , wherein, the threshold value (σ ε ) is based on, within the singular values (σ i ), an amount value gap that is detected starting from a first singular value (σ 1 ), and if an amount value of a following singular value (σ i+1 ) is smaller than an amount value of a current singular value (σ i ), the amount value of that current singular value is taken as the threshold value (σ ε ).
14. The apparatus of claim 10 , wherein the threshold value (σ ε ) is based on a signal-to-noise ratio SNR for a block of samples for all source signals and the threshold value (σ ε ) is set to
σ
ɛ
=
1
S
N
R
.